# Electrostatic Potential And Capacitance Questions

We provide electrostatic potential and capacitance practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on electrostatic potential and capacitance skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of electrostatic potential and capacitance Questions

Question NoQuestionsClass
1If charge density of an infinite charged plate is doubled and the distance of
point charge is tripled from the infinite charged plate, then electric field is increased ( _{text {thes }} )
12
2A capacitors has square plates each of
side ( l ) making an angle a with each
other as shown in the figure. Then, for
small value of a the capacitance ( C ) is
given by :
( ^{mathbf{A}} cdot frac{epsilon_{0} I^{2}}{d}left(1-frac{a l}{2 d}right) )
В ( cdot frac{epsilon_{0} I^{2}}{2 d}left(1-frac{a l}{d}right) )
c. ( frac{epsilon_{0} I^{2}}{d}left(1-frac{a l}{d}right) )
D ( cdot frac{epsilon_{0} I^{2}}{2 d}left(1+frac{a l}{d}right) )
12
3Consider a system of three charges ( frac{mathbf{q}}{mathbf{3}} )
( frac{mathbf{q}}{mathbf{3}} ) and ( -frac{mathbf{2 q}}{mathbf{3}} ) placed at points ( mathbf{A}, mathbf{B} ) and
C, respectively, as shown in the figure.
Take 0 to be the centre of the circle of
radius ( mathbf{R} ) and angle ( mathbf{C A B}=mathbf{6 0}^{mathbf{0}} )
A ( cdot ) The electric field at point ( mathrm{O} ) is ( frac{mathrm{q}}{8 pi epsilon_{0} mathrm{R}^{2}} ) directed along the negative x-axis
B. The potential energy of the system is zero
C. The magnitude of the force between the charges at ( C ) and ( mathrm{B} ) is ( frac{mathrm{q}^{2}}{54 pi epsilon_{0} mathrm{R}^{2}} )
D. The potential at point ( mathrm{O} ) is ( frac{mathrm{q}}{12 pi epsilon_{0} mathrm{R}} )
12
4An uncharged capacitor of capacitance ( 4 mu F, ) a battery of emf 12 volt and a resistor of ( 2.5 ~ M Omega ) are connected
in series. The time after which ( v_{c} ) ?
( 3 v_{R}=0.693 )
A. 6.93 sec
B. ( 13.86 mathrm{sec} )
c. ( 20.52 mathrm{sec} )
D. none of these
12
5Assertion
The force between two electric charges
in a dielectric medium is less than it
would be in a vacuum.
Reason
Quantity of energy stored in an electric field per unit volume of a dielectric medium is greater than that of vaccum
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
12
6When a charge of amount ( Q ) is given to an isolated metal plate ( X ) of surface area ( A, ) its surface charge density
becomes ( sigma_{1} . ) When an isolated identical
plate ( Y ) is brought close to ( X, ) the surface charge density on X becomes
( sigma_{2} . ) When ( y ) is earthed, the surface
charge density becomes ( sigma_{3} )
This question has multiple correct options
A ( cdot sigma_{1}=frac{Q}{A} )
В. ( sigma_{1}=frac{Q}{2 A} )
( mathbf{C} cdot sigma_{1}=sigma_{2} )
D. ( _{sigma_{3}}=frac{Q}{A} )
12
7Complete the following statements with an appropriate word /term be filled in the blank space(s).

The equivalent capacitance ( C ) for the parallel combination of three
capacitance ( C_{1}, C_{2} ) and ( C_{3} ) is given by
( C=dots )
A ( cdot C_{1}+C_{2}+C_{3} )
B. ( frac{1}{C_{1}+C_{2}+C_{3}} )
( ^{c}left(frac{1}{frac{1}{C_{1}}+frac{1}{C_{2}}+frac{1}{C_{3}}}right) )
( ^{mathrm{D}} cdotleft(frac{1}{C_{1}}+frac{1}{C_{2}}+frac{1}{C_{3}}right) )

12
8Calculate the change in potential
energy of a particle of charge ( +boldsymbol{q} ) that is
brought from a distance of ( 3 r ) to a
distance of ( 2 r ) in the electric field
of charge ( -q ? )
( mathbf{A} cdot k q^{2} / r )
B ( .-k q^{2} / 6 r )
c. ( k q^{2} / 4 r^{2} )
D. ( -k q^{2} / 4 r^{2} )
E . ( k q^{2} / r^{2} )
12
9Why is the potential inside a hollow spherical charged conductor, constant
and has the same value as on its
surface ?
12
10Two charges ( q_{1}=12 times 10^{-9} mathrm{C} ) and ( q_{2}= )
( -12 times 10^{-9} C ) are placed ( 10 c m ) apart. The
potential at a point ( 6 mathrm{cm} ) from ( q_{1} ) on the
line joining the two charges is :
A. 3500 Volt
B. 900 Volt
c. ( 1800 V ) olt
D. -900 Volt
12
11A charged particle having a charge of
( -2 times 10^{-6} C ) is placed close to a non
conducting plate having a surface charge density as ( 4 times 10^{-6} mathrm{Cm}^{-2} . ) What
will be the force of attraction between
them:
A . ( 0.5 N )
B. ( 0.45 N )
c. ( 0.25 N )
( D ldots .0 .75 N )
12
12A positive charge and a negative charge are held in place and initially form a
dipole. Then a uncharged conducting bar is placed in between them.

How is the force between the charges
affected?
A. The force increases.
B. The force is unaffected.
c. The force decreases.
D. The answer cannot be determined.

12
13A cloud is at a potential of ( 8 times 10^{9} V )
relative to the ground. A charge of ( 40 C ) is transferred in a lightning stroke
between the cloud and the earth. The
energy released is:
A ( cdot 3.2 times 10^{11} J )
B . ( 5 times 10^{9} J )
c. ( 2 times 10^{9} J )
D. ( 32 times 10^{12} J )
12
14A cloud carries a charge of 1000 C at a potential of ( 5 mathrm{kV} ). If the cloud discharge,
the amount of energy released:
A ( .5 times 10^{6} J )
В. ( 2.5 times 10^{6} J )
( c cdot 10^{7} J )
D ( .5 times 10^{3} J )
12
15mass ( m ) carrying charge ( q . ) The bead
can freely move on the smooth fixed ring placed on a smooth horizontal plan.
In the same plane a charge ( +Q ) has also
been fixed as shown. The potential at
the point ( boldsymbol{P} ) due to ( +boldsymbol{Q} ) is ( boldsymbol{V} ). The velocity
with which the bead should projected
from the point ( P ) so that it can complete
a circle should be greater than
A ( cdot sqrt{frac{6 q V}{m}} )
B. ( sqrt{frac{q V}{m}} )
c. ( sqrt{frac{3 q V}{m}} )
D. nont
12
16Fill in the blank.
The electric potential ( V ) at any point ( x, y, z ) (all in meters) in space is given
by ( V=4 x^{2} ) volts. The electric field at
the point ( (1 m, 0,2 m) ) is ( _{—–} V / m )
12
17What is not true of equipotential
surface?
A. The PD between any two points on the surface is zero
B. The electric field is always perpendicular to the surface
C. Equipotential surfaces are always spherical
D. No work is done in moving a charge along the surface
12
18What is the area of the plates of a 2 F parallel plate capacitor, given that the separation between the plates is 0.5 ( mathrm{cm} ?[ ) You will realise from your answer
why ordinary capacitors are in the range of F or less. However, electrolytic capacitors do have a much larger capacitance (0.1 ( F ) ) because of very minute separation between the conductors.
12
19Among identical spheres ( A ) and ( B )
having charges ( -15 C ) and ( -16 C: )
A. ( -15 C ) is at higher potential
B. ( -16 C ) is at higher potential
c. both are at equal potential
D. no such comparison can be made
12
20In an uniform electric field ( boldsymbol{E}=mathbf{1 0} boldsymbol{N} / boldsymbol{C} )
as shown in figure, find ( V_{B}-V_{C}: )
( mathbf{A} cdot 10 V )
B. ( -10 V )
( mathbf{c} cdot 20 V )
D ( .-20 V )
12
21A conductor with a cavity is charged positively and its surface charge density is ( sigma . ) If ( E ) and ( V ) represent the electric field and potential, then inside the cavity:
( mathbf{A} cdot ) and ( V=0 )
B. ( E=0 ) and ( V=0 )
c. ( E=0 ) and ( sigma= ) constant
D. ( V=0 ) and ( sigma= ) constant
E . ( E=0 ) and ( V= ) constant
12
22An ellipsoidal cavity is carved within a perfect conductor. A positive charge q is
placed at the centre of the cavity. The points ( A ) and ( B ) are on the cavity surfaces as shown in the figure. Then
This question has multiple correct options
A. Electric field near A in the cavity = Electric field near B in the cavity
B. Charge density at A = charge density at B
c. Potential at ( A= ) potential at ( B )
D. Total electric flux through the surface of the cavity is ( q / epsilon_{0} )
12
23If metal section of shape H is inserted in
between two parallel plates as shown in figure and ( A ) is the area of each plate then the equivalent capacitance is :
A ( cdot frac{A epsilon_{0}}{a}-frac{A epsilon_{0}}{b} )
В. ( frac{A epsilon_{0}}{a+b} )
c. ( frac{A epsilon_{0}}{a}+frac{A epsilon_{0}}{b} )
D. ( frac{A epsilon_{0}}{a-b} )
12
24A conducting sphere of radius ( mathrm{R} ) is given a charge ( Q . ) The electric potential and the electric field at the centre of the
sphere respectively are :
A ( cdot ) zero and ( frac{Q}{4 pi epsilon_{0} R^{2}} )
в. ( frac{Q}{4 pi epsilon_{0} R} ) and zerc
c. ( frac{Q}{4 pi epsilon_{6} R} ) and ( frac{Q}{4 pi epsilon_{0} R^{2}} )
D. Both are zero
12
25In above shown figure, the two plates of
the capacitor of charge ( +mathrm{Q} ) and ( -mathrm{Q}, ) which points lie on the same equipotential?
( A cdot 1 ) and 2 only
B. 1 and 3 only
C. 2 and 4 only
D. 3 and 4 only
E. ( 1,2,3, ) and 4 all lie on the same equipotential, since the electric field is uniform
12
26If a slab of insulating material ( 4 times ) ( 10^{-5} m ) thick is introduced between the
plates of a parallel plate capacitor, the distance between the plates has to be increased by ( 3.5 times 10^{-5} m ) to restore the
capacity to original value. Then the dielectric constant of the material of
slab is :
( A cdot 8 )
B. 6
c. 12
D. 10
12
27A capacitor of capacitance ( 2 mu F ) is
charged to a voltage of ( 6 mathrm{V} ). The charge
on its plates is:
A . ( 1.2 times 10^{-5} C )
B . ( 3 times 10^{-6} C )
c. ( frac{1}{3} times 10^{-6} C )
D. ( frac{1}{12} times 10^{-6} mathrm{C} )
12
Nưe:
points at infinite distance from the
spheres)? The diagram shows two spheres, charged uniformly as indicated. All
regions are along a line connecting the centers of the objects.

Region ( A ) is anywhere to the left of the 5.0 Coulomb charge. Region B is to the right of the 5.0 Coulomb charge and closer to the 5.0 Coulomb charge than to the 3.0 Coulomb charge. Region ( C ) is to
the right of the 5.0 Coulomb charge but closer to the 3.0 Coulomb charge than to the 5.0 Coulomb charge. Region D is anywhere to the right of the 3.0 Coulomb charge.
( A cdot A )
B. B
( c cdot c )
D.
E. There is no region where the electric potential could possibly be zero

12
29In a region, uniform electric field exists as ( overrightarrow{boldsymbol{E}}=[mathbf{1 0 hat { boldsymbol { i } }}+mathbf{1 0 hat { boldsymbol { j } }}] boldsymbol{N} / boldsymbol{C} . ) If the
potential of origin is 0 volts, the potential of point ( (10 m, 10 m, 10 m) )
12
30Two capacitors of capacity ( C_{1} ) and ( C_{2} )
are connected in parallel, then the
equivalent capacity is:
A ( cdot C_{1}+C_{2} )
в. ( C_{1} C_{2} /left(C_{1}+C_{2}right) )
c. ( C_{1} / C_{2} )
D. ( C_{2} / C_{1} )
12
31A parallel plate capacitor has plates
with area ( A & ) separation ( d . A ) battery charges the plates to a potential
difference of ( V_{0} . ) The battery is then
disconnected & a di-electric slab of
constant ( K & ) thickness ( d ) is
introduced. Calculate the positive work done by the system (capacitor ( + ) slab) on the man who introduces the slab.
12
32A parallel plate capacitor has two square plates with equal and opposite charges. The surface charge densities
on the plate are ( +sigma ) and ( -sigma )
respectively. In the region between the plates the magnitude of electric field is:
A ( cdot frac{sigma}{2 varepsilon_{0}} )
в. ( frac{sigma}{varepsilon_{0}} )
( c cdot 0 )
D. none of these
12
33A hollow conducting spherical shell of radius ( R ) is charged with ( Q ) coulomb.
The amount of work done for moving any
charge ( q ) from the centre to the surface of the shell will be
A ( cdot frac{q Q}{4 pi epsilon_{0} R} )
B. Zero
c. ( frac{Q q}{pi epsilon_{0} R} )
D ( frac{2 Q q}{pi epsilon_{0} R} )
12
34The work done in placing a charge of ( 8 times 10^{-18} ) coulomb on a condenser of
A ( cdot 16 times 10^{-32} ) joule
B. ( 3.2 times 10^{-26} ) joule
C ( cdot 4 times 10^{-10} ) joule
D. ( 32 times 10^{-32} ) joule
12
35Two capacitors of ( 0.5 mu F ) and ( 1 mu F ) are connected in parallel across a battery. If the charge on ( 0.5 mu F ) is ( 50 mu C ), the charge
on the other capacitor is :
A. ( 100 mu C )
B. ( 50 mu C )
c. ( 25 mu C )
D. zero
12
36There are two concentric spherical shells of radii ( r ) and ( 2 r . ) Initially a
charge ( Q ) is given to the inner shell and
both the switches are open. Now ( S_{2} ) is closed and opened, The charge flowing
through the switch ( S_{2} ) in the process is
A. ( Q )
в. ( frac{Q}{4} )
( c cdot frac{Q}{2} )
D. ( frac{2 Q}{3} )
12
37A dipole of dipole moment ( overrightarrow{boldsymbol{p}} ) is kept along an electric field ( overrightarrow{boldsymbol{E}} ) such that ( overrightarrow{boldsymbol{E}} ) and ( vec{p} ) are in the same direction. Find the work done in rotating the dipole by an angle ( pi )
A. ( W=3 E p )
в. ( W=2 E p )
c. ( W=4 ) Ер.
D. ( W=5 E p )
12
38In a parallel plate capacitor, the
capacitance:
A. increases with increase in the distance between the
plates
B. decreases if a dielectric material is put between the plates
C. increases with decrease in the distance between the plates
D. increases with decrease in the area of the plates
12
39Two identical thin rings, each of radius
10cm carrying charges ( 10 C ) and ( 5 C ) are
coaxially placed at a distance ( 10 mathrm{cm} ) a part. The work done in moving a charge
( q ) from the centre of the first ring to that
of the second is
A ( cdot frac{q}{8 pi varepsilon_{0}}left(frac{sqrt{2}+1}{sqrt{2}}right) )
В. ( frac{q}{8 pi varepsilon_{0}}left(frac{sqrt{2}-1}{sqrt{2}}right) )
c. ( frac{q}{4 pi varepsilon_{0}}left(frac{sqrt{2}+1}{sqrt{2}}right) )
D. ( frac{q}{4 pi varepsilon_{0}}left(frac{sqrt{2}-1}{sqrt{2}}right) )
E ( cdot frac{q}{4 pi varepsilon_{0}}left(frac{sqrt{3}+1}{sqrt{2}}right) )
12
40When a metal plate is introduced
between the two plates of a charged capacitor and insulated from them,
then
This question has multiple correct options
A. the metal plate divides the capacitor into two capacitors connected in parallel to each other
B. the metal plate divides the capacitor into two capacitors connected in series with each other
C. the metal plate is equivalent to a dielectric of zero dielectric constant
D. the metal plate is equivalent to a dielectric of infinite dielectric constant
12
41Figure shows three points ( A, B ) and ( C ) in a region of uniform electric field ( vec{E} ). The
line ( A B ) is perpendicular and ( B C ) is parallel to the field lines. Then which of
the following holds good. Here ( boldsymbol{V}_{boldsymbol{A}}, boldsymbol{V}_{boldsymbol{B}} )
and ( V_{C} ) represents the electric potential
at point ( A, B ) and ( C ) respectively.
( mathbf{A} cdot V_{A}=V_{B}=V_{C} )
B ( cdot V_{A}=V_{B}>V_{C} )
( mathbf{c} cdot V_{A}=V_{B}V_{B}=V_{C} )
12
42A ( 10 mu F ) capacitor is connected across
a ( 200 V, 50 H z ) A.C. supply. The peak
current through the circuit is :
A. ( 0.6 A )
в. ( 0.6 sqrt{2} A )
D. ( 0.6 pi A )
12
43A large insulated sphere of radius ( r )
charged with ( Q ) units of electricity is placed in contact with a small insulated uncharged sphere of radius ( r^{prime} ) and is
then separated. The charge on the smaller sphere will now be:
A ( cdot frac{Qleft(r^{prime}+rright)}{r^{prime}} )
в. ( frac{Qleft(r^{prime}+rright)}{r} )
c. ( frac{Q r}{left(r^{prime}+rright)} )
D. ( frac{Q_{r}^{prime}}{left(r^{prime}+rright)} )
12
44n the given circuit, find the potential
difference across the 6 ( mu ) F capacitor in
4.4
3.22
( c cdot 6 v )
D
12
45Consider the figure given. Each
capacitor has capacitance ( C . ) The
capacitance between 1 and 3 is :
( A cdot frac{3 C}{4} )
B. ( frac{3 C}{2} )
( c cdot frac{5 C}{2} )
D. ( frac{50}{1} )
12
46Two tiny spheres carrying charges 1.8 ( mu C ) and ( 2.8 mu C ) are located at ( 40 mathrm{cm} )
apart. The potential at the mid-point of the line joining the two charges is
A ( cdot 3.8 times 10^{4} v )
B . ( 2.1 times 10^{5} mathrm{v} )
c. ( 4.3 times 10^{4} v )
D. 3.6 ( times 10^{5} mathrm{v} )
12
47A parallel plate capacitor is charged
and then isolated. The effect of
increasing the plate separation on charge, potential and capacitance respectively are:
A. constant, decreases, decreases
B. increases, decreases, decreases
c. constant, decreases, increases
D. constant, increases, decreases
12
48Three charges ( Q,+q ) and ( +q ) are placed
at the vertices of a right angle isosceles triangle as shown. The net electrostatic
energy of the configuration is zero, if ( boldsymbol{Q} )
is equal to:
( mathbf{A} )
B.
( mathbf{c} .-2 q )
D. ( +q )
12
491 V equals:
A . 1 J
B. ( 1 mathrm{JC}^{-1} )
( c cdot 1 C J^{-1} )
D. 1 JC
12
50Which one of the following gives the resultant capacitor when capacitors are joined in series?
A. The sum of the individual capacitors
B. The reciprocal of the sum of the reciprocals of the individual capacitors
c. The reciprocal of the sum of the capacitors
D. The sum of the reciprocals of the individual capacitors
12
51Which of the following statement are
true?
A. Charge ( q_{3} ) applies a large force on charge ( q_{2} ) than on
charge ( q_{1} )
B. Charge ( q_{3} ) applies a smaller force on charge ( q_{2} ) than on
charge ( q_{1} )
C. Charge ( q_{3} ) applies equal force on bothy the charges.
D. Charge ( q_{3} ) applies no force on any of the charges.
12
52If the charge of ( 10 mu C ) and ( -2 mu C ) are
given to two plates of a capacitor which
are connected across a battery of ( 12 V )
find the capacitance of the capacitor.
в. ( 0.5 mu F )
c. ( 0.41 mu F )
D. ( 0.66 mu F )
12
53The value of equivalent capacitance of
the combination shown in figure,
between the points ( boldsymbol{P} ) and ( boldsymbol{Q} ) is
A. ( 3 C )
B. ( 2 C )
( c . C )
D. ( C / 3 )
12
54The work done in carrying in point
charge from one point to the another in an electrostatic field depends on the path along which the point charge is carried
A. True
B. False
12
55Two points charges placed at a distance
( r, ) in the air experience a certain force then the distance at which they will experience the same force in the
medium off dielectric constant K is
A. ( K r )
в. ( frac{r}{K} )
c. ( frac{r}{sqrt{K}} )
D. ( r sqrt{K} )
12
56Two identical capacitors are joined in
parallel and charged to a potential ( V )
Capacitors are separated and then connected in series, i.e., the positive plate of one is connected to the negative plate of other. Identify the correct
option:
A. The charges on the free plates are enhanced.
B. The charges on the free plates decrease.
c. The energy stored in the system increase
D. The potential difference between the free plates is ( 2 V )
12
57How much work would be required to move a proton from the negative to the positive plate?
A. ( -3.6 times 10^{-18} J )
в. ( 3.6 times 10^{-19} mathrm{J} )
c. ( 3.6 times 10^{-18} mathrm{J} )
D. ( -3.6 times 10^{-19} mathrm{J} )
12
58Two equal point charges are fixed at ( x=-a ) and ( x=+a ) on the ( X- ) axis
Another point charge ( Q ) is placed at the
origin. The change in electrical potential energy ( Q ) when it is displaced by a smal
distance ( x ) along the ( X ) -axis, is approximately proportional to
( A cdot x )
в. ( x^{2} )
c. ( x^{3} )
D. ( 1 / x )
12
59If dielectric is inserted in charged capacitor (battery removed), then quantity that remains constant is.
A. Capacitance
B. Potential
c. Intensity
D. charge
12
60Find the equivalent capacitance
between the point ( A ) and ( B ) in given
figure where ( boldsymbol{C}=mathbf{5} boldsymbol{mu} boldsymbol{F} )
12
61A spherical capacitor has an inner sphere of radius ( 12 mathrm{cm} ) and an outer
sphere of radius ( 13 mathrm{cm} . ) The outer sphere is earthed and the inner sphere is given
a charge of ( 2.5 mu C . ) The space between
the concentric spheres is filled with a liquid of dielectric constant 32
(a) Determine the capacitance of the capacitor.
(b) What is the potential of the inner sphere?
(c) Compare the capacitance of this capacitor with that of an isolated
sphere of radius 12 cm. Explain why the latter is much smaller.
12
62A metal sphere of radius a is having
charge ( +Q ) on it Now it is connected with
a metal wire to a concentric spherica
shell of radius 2 a Then the net potential
at the surface of outer shell is
( ^{A} cdot frac{K Q}{a} )
в. ( frac{K Q}{2 a} )
c. ( frac{3}{2} frac{K Q}{a} )
D. ( frac{2 K Q}{a} )
12
63A ( 500 mu F ) capacitor is charged at a
steady rate of ( 100 mu C / ) sec. The potential difference across the capacitor will be
( 10 V ) after an interval of
( mathbf{A} cdot 5 ) sec
B. 20 sec
c. 25 sec
D. 50 sec
12
64The potential difference between point B
and ( mathrm{C} ) of the circuit is
A ( cdot frac{left(C_{2}-C_{1}right)}{V} )
B. ( frac{left(C_{4}-C_{3}right)}{V} )
c. ( frac{left(C_{2} C_{3}-C_{1} C_{4}right)}{left(C_{1}+C_{2}+C_{3}+C_{4}right)} cdot V )
D. ( frac{C_{1} C_{4}-C_{2} C_{3}}{left(C_{1}+C_{2}right) timesleft(C_{3}+C_{4}right)} cdot V )
12
65The dielectric strength of air is ( 3 times 10^{6} v )
( / mathrm{m} . ) A parallel plate air capacitor has
( operatorname{area} 20 c m^{2} ) and plate separation ( 1 mathrm{mm} )
Then maximum r.m.s. voltage of an A.C. source which can be safely connected to this capacitor is
A . 212.2
B. 21.22
c. ( 2.122 mathrm{v} )
D. 2122 V
12
66The gap between the plates of a parallel
plate capacitor of area ( A ) and distance
between plates ( d ), is filled with a
dielectric whose permittivity varies
linearly from ( epsilon_{1} ) at one plate to ( epsilon_{2} ) at the
other. The capacitance of capacitor is :
( mathbf{A} cdot epsilon_{0}left(epsilon_{1}+epsilon_{2}right) A / d )
В ( cdot epsilon_{0}left(epsilon_{2}+epsilon_{1}right) A / 2 d )
( mathbf{c} cdot epsilon_{A} / dleft[d ln left(epsilon_{2} / epsilon_{1}right)right] )
D. ( epsilon_{0}left(epsilon_{2}-epsilon_{1}right) A /left[d l nleft(epsilon_{2} / epsilon_{1}right)right] )
12
67f the electric potential of the inner shell
is ( 10 V ) and that of the outer shell is ( 5 V )
then the potential at the centre will be
( 4.10 V )
( 3.5 V )
( c .15 V )
D
12
68Write a relation for polarisation ( vec{P} ) of ( a ) dielectric material in the presence of an external electric field ( vec{E} ).12
69A parallel plate capacitor is to be designed with a voltage rating ( 1 k V ) using a material of dielectric constant
10 and dielectric strength ( 10^{6} V m^{-1} ) What minimum area of the plates is required to have a capacitoance of ( 88.5 p F ? )
12
70A parallel plate capacitor is connected to a battery. The quantities charge, voltage, electric field and energy associated with this capacitor are given
by ( Q_{0}, V_{0}, E_{0}, ) and ( U_{0} ) respectively. ( A ) dielectric slab is now introduced to fill
the space between the plates with the battery still in connection. The corresponding quantities now given by ( Q, V, E ) and ( U ) are related to the
previous ones are :
A ( cdot Q>Q_{0} )
в. ( V>V_{0} )
c. ( E>E_{0} )
D. ( U<U_{0} )
12
71Two charges ( 5 times 10^{-8} C ) and ( -3 x )
( 10^{-8} C ) are located ( 16 mathrm{cm} ) apart. At what
point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
A. ( 20 mathrm{cm} ) away from the positive charge on the side of negative charge
B. ( 40 mathrm{cm} ) away from the negative charge on the side of positive charge
c. ( 40 mathrm{cm} ) away from the positive charge on the side of negative charge
D. ( 20 mathrm{cm} ) away from the negative charge on the side of positive charge
12
72Find the potential energy to a system of four particles placed at the vertices of a square of side ( l ). Also obtain the
potential at the centre of the square
12
73A parallel-plate capacitor is connected to a battery. A metal sheet of negligible thickness is placed between the plates. The sheet remains parallel to the plates of the capacitor. It’s capacitance will:
A. Increase
B. Decrease
c. Remains the same
D. Becomes infinite
12
74Two capacitors of capacity ( C_{1} ) and ( C_{2} )
are connected in parallel, then the
equivalent capacity is:
A ( cdot C_{1}+C_{2} )
в. ( C_{1} C_{2} /left(C_{1}+C_{2}right) )
c. ( C_{1} / C_{2} )
D. ( C_{2} / C_{1} )
12
75( n ) capacitors each of capacitance ( 2 mu F ) are connected in parallel and a potential difference of ( 200 mathrm{V} ) is applied to the
combination. The total charge on all the positive plates is 1 Coulomb then ( n ) is
equal to :
A . 3333
в. 3000
( c .2500 )
D. 25
12
76The potential across a 25.0 microfarad capacitor is ( 5.0 mathrm{V} ). What is the charge on the capacitor?
A. 0.20 microcoulombs
B. 5.0 microcoulombs
c. 125 microcoulombs
D. 30.0 microcoulombs
E. we cannot determine the charge on the capacitor with the given information.
12
77( 2 mu F ) capacitance has P.D across its two terminals of ( 200 mathrm{V} . ) It is disconnected
from the battery and when another uncharged capacitance is connected in parallel to it, P.D becomes 20 V. The capacity of another capacitance will be:
A ( .2 mu F )
в. ( 4 mu F )
c. ( 10 mu F )
( mathbf{D} cdot 16 mu F )
12
78The capacity of a parallel plate condenser is ( 10 mu F, ) when the distance
between its plates is ( 8 mathrm{cm} ). If the
distance between the plates is reduced
to ( 4 mathrm{cm}, ) then the capacity of this parallel plate condenser will be :
A ( .5 mu F )
B. ( 10 mu F )
c. ( 20 mu F )
D. ( 40 mu F )
12
79An air-gap parallel plate capacitor is
fully charged by a battery.
What combination of two
measurements will allow someone to
calculate the magnitude of the electric
field in between the capacitor plates?
A. The potential difference of the battery and the area of the plates.
B. The charge on the plates and the distance between the plates.
C. The charge on the plates and the area of the plates.
D. The area of the plates and the distance between the plates
E. More than two measurements are needed to calculate the electric field in between the capacitor plates.
12
80The potential at a point due to a charge
of ( 5 times 10^{-7} C ) located ( 10 c m ) away is:
A ( cdot 3.5 times 10^{5} V )
B . ( 3.5 times 10^{4} V )
c. ( 4.5 times 10^{4} V )
D. ( 4.5 times 10^{5} V )
12
81A square loop ABCD, carrying a current
( I_{2}, ) is placed near and coplanar with a
long straight conductor XY carrying a
current ( I_{1}, ) as shown in the figure. The
net force on the loop will be :
A ( cdot frac{mu_{0} I_{1} I_{2}}{2 pi} )
В. ( frac{mu_{0} I_{1} I_{2} L}{2 pi} )
c. ( frac{2 mu_{0} I_{1} I_{2} L}{3 pi} )
D. ( frac{2 mu_{0} I_{1} I_{2}}{3 pi} )
12
82A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral
A. A potential difference appears between the two cylinders when a charge density is given to the inner cylinder
B. A potential difference appears between the two cylinders when a charge density is given to the outer cylinder
c. No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders.
D. No potential difference appears between the two cylinders when same charge density is given to both the cylinders.
12
83toppr
smaller sphere with a large amount of
negative charge.

The differences in color for the larger
sphere demonstrate that the smaller,
negatively charged sphere has influenced the larger sphere so that some electrons have moved left,
causing the left side to become
negative and the right side to become
positive, although the large sphere
remains neutral, as a whole.

Which of the following tables best
describes the electric field and electric
potential inside the large sphere, while the small, negative sphere is near it?
Large Negative Charge
A. Electric Field Inside Large Sphere – Electric Potential Inside Large Sphere, zero – same everywhere
B. Electric Field Inside Large Sphere – Electric Potential Inside Large Sphere, non-zero pointing left – higher on right
C. Electric Field Inside Large Sphere – Electric Potential Inside Large Sphere, non-zero pointing right – higher on left
D. Electric Field Inside Large Sphere – Electric Potential Inside Large Sphere, non-zero pointing left – same everywhere
E. Electric Field Inside Large Sphere – Electric Potential Inside Large Sphere, non-zero pointing right – same everywhere

12
84A capacitor of ( 10 mu F ) is connected to a
( mathbf{1 0} boldsymbol{V} ) cell. The maximum charge on the
capacitor will be:
A. ( 1 mu C )
B. ( 10 mu C )
c. ( 100 mu C )
D. ( 1000 mu C )
12
85In the definition of electric potential, the electric potential at infinity is assumed to be
A . infinity
B. zero
c. 1
D. None of these
12
86Below, three different arrangement of identical capacitors are shown. What is the correct order of total capacitance
values for the arrangements, greatest first?
( mathbf{A} cdot 1,2,3 )
в. 3,2,1
( c cdot 3,1,2 )
D. 2,3,1
E .2,1,3
12
87Consider the situation of figure. The
work done in taking a point charge from
( P ) to ( A ) is ( W_{A}, ) from ( P ) to ( B ) is ( W_{B} ) and from
( P ) to ( C ) is ( W_{C} . ) Then :
( mathbf{A} cdot W_{A}<W_{B}W_{B}>W_{C} )
( mathbf{c} cdot W_{A}=W_{B}=W_{C} )
D. None of these
12
88What is the electric potential at a distance of ( 9 mathrm{cm} ) from 3 nC?
( mathbf{A} cdot 270 V )
в. ( 3 V )
( mathbf{c} .300 V )
D. 30V
12
89Find the equivalent capacitance of the
arrangement of three capacitors shown
in figure between points ( X ) and ( Y )
12
90Consider a spherical shell of radius ( mathrm{R} ) with a total charge + q uniformly spread on its surface(center of the chell lies at
the origin ( x=0 ) ). Two point charges, ( +q ) and ( -q ) are brought, one after the other, from far away and placed at ( x=-a / 2 )
and ( boldsymbol{x}=+boldsymbol{a} / 2(boldsymbol{a}<boldsymbol{R}), ) respectively
Magnitude of the work done in this
process is?
A ( cdot(Q+q)^{2} cdot 4 pi varepsilon_{0} )
( a )
B. Zero
( mathbf{c} cdot q^{2} / 4 pi varepsilon_{0} )
D ( cdot Q q / 4 pi varepsilon_{0} a )
12
91Two charged spheres of radii ( boldsymbol{R}_{1} ) and ( boldsymbol{R}_{2} )
have equal surface charge density. The ratio of their potential at an equidistant external point is
A ( cdot frac{R_{2}}{R_{1}} )
в. ( left(frac{R_{2}}{R_{1}}right)^{2} )
( ^{mathbf{c}} cdotleft(frac{R_{1}}{R_{2}}right)^{2} )
D. ( frac{R_{1}}{R_{2}} )
12
92The length of a conductor is halved. Its conductance will be?
A. Halvedd
B. Unchanged
c. Doubled
12
93Four chargers ( q_{1}=-0.02 mu C, q_{2}= )
( +0.04 mu C, q_{3}=+0.02 mu C, ) and ( q_{4}= )
( -0.04 mu C ) are at the four corners of a
square of side ( 9 mathrm{cm} ). Then the potential at
the centre of the square is :
A . ( 9 V )
в. ( 3 V )
( mathrm{c} .1 .2 mathrm{V} )
D. Zero
12
94An electrical technician requires a
capacitance of ( 2 mu F ) in a circuit across
a potential difference of ( 1 mathrm{kV} . ) A large number of ( 1 mu F ) capacitors are available to him each of which can withstand a potential difference of not more than ( 400 mathrm{V} . ) Suggest a possible arrangement that requires the minimum number of capacitors.
12
95S.I. unit of electrical capacity.
c. Coulomb
D. stat Coulomb
12
96Find ( V_{b a} ) if ( 12 J ) of work has to be done
against an electric field to take a
charge of ( 10^{-2} C ) from ( a ) to ( b )
A . ( 1000 V )
B. 1200V
c. ( 1100 V )
D. 2400V
12
97which of the following is/are not
proportional to the inverse square of the
distance ( times ? )
This question has multiple correct options
A. The potential at a distance ( x ) from an isolated point charge
B. the electric field at a distance ( x ) from an isolated point charge
C. The force per unit length between two thin, straight, infinitely long current carrying conductors, parallel to each other, separated by a distance ( x )
D. The gravitational attraction between two small bodies kept at a distance x apart
12
9864 small drops of mercury each of radius ( r ) and change ( q ) coalesce to from a big drop. The ratio of the surface charge density of each small drop with that of big drop is:
A . 4: 1
B. 1: 4
( mathbf{c} cdot 1: 64 )
D. 64: 1
12
99Calculate the electrostatic potential
energy of an electron-proton system of hydrogen atom. In the first Bohr orbit of hydrogen atom, the radius of the orbit is ( 5.3 times 10^{-11} m )
A. ( -4.35 times 10^{-18} mathrm{J} )
В. ( -2.175 times 10^{-18} mathrm{J} )
c. ( -4.35 times 10^{-19} J )
D. ( -2.175 times 10^{-19} mathrm{J} )
12
100A hollow spherical conductor of radius
( R ) is given a charge ( Q . ) Work done in
moving a charge ( q ) from its centre to surface is :
A ( cdot frac{Q q}{4 pi varepsilon_{0} R} )
в. ( frac{Q q}{2 pi varepsilon_{0} R} )
c. ( frac{Q q}{pi varepsilon_{0} R} )
D. zero
12
101The two plate ( X ) and ( Y ) of a parallel-
plates capacitor of capacitance ( mathbf{C} ) are
given a charge of amount Q each. ( X ) is
now joined to the positive terminal and
y to the negative terminal of a cell of
emf ( varepsilon=Q / C )
This question has multiple correct options
A. Charge of amount Q will flow from the positive terminal to the negative terminal of the cell through the capacitor.
B. The total charge on the plate ( X ) will be ( 2 Q )
C. The total charge on the plate Y will be zero.
D. The cell will supply ( C varepsilon^{2} ) amount of energy.
12
102A plane electromagnetic wave travelling in a non magnetic medium is given by
( boldsymbol{E}=left(boldsymbol{9} times mathbf{1 0}^{8} boldsymbol{N} boldsymbol{C}^{-1}right) boldsymbol{s i n}[(boldsymbol{9} times )
( left.10^{8} text { rads}^{-1}right) t-left(6 m^{-1}right) x )
Where ( x ) is in metre and ( t ) is in second.
The dielectric constant of the medium
is:
A. 5
B. 4
( c cdot 3 )
D.
12
103A capacitor of capacity ( 10 mu F ) is
charged to a potential of ( 10000 mathrm{V} ) and a
wire is stretched by ( 0.2 m ) by a force of
( mathbf{5 0 0 0} N . ) The ration of the potential energies stored in them will be
A . 1
в. 500
c. 0.002
D. 0.0001
12
104Four identical metal plates are located
in air at equal distance ( d ) from one
another as shown in figure. The area of
each plate is equal to ( A ). Find the
capacitance of the system between points ( A ) and ( B )
12
105In a circuit, ( 5 C ) of charge is passed
through a battery in 3 hours. The plates of the battery are maintained at the
potential difference of 12 V. Then, the amount of work done by a battery is:
A . 60 J
в. 180
c. 20
D. ( 6.48 times 10^{5} ) 」
12
106A ( 10.0 mu F ) parallel-plate capacitor with
circular plates is connected to a ( 12.0 mathrm{V} )
battery. How much charge ( (text { in } mu C) )
would be on the plates if their separation were doubled while the capacitor remained connected to the
battery?
12
107Two identical thin rings each of radius ( r ) are coaxillary placed at a distance have equal charge q each. Work done in moving a charge ( q^{prime} ) from the centre of one ring to that of the other is?
A . Infinity
В. ( frac{q^{2}}{4 pi varepsilon_{0} r} )
c. zero
D. ( frac{q q^{prime}}{4 pi varepsilon_{0} r} )
12
108A parallel plate capacitor is charged. If the plates are pulled apart
A. The capacitance increases
B. The potential difference increases
c. The total charge increases
D. The charge and potential difference remain the same
12
109A parallel plate condenser with oil between the plates (dielectric constant
of oil ( K=2 ) ) has a capacitance ( C . ) If the oil is removed, then capacitance of the capacitor becomes:
A ( cdot sqrt{2} C )
B. 2C
c. ( frac{c}{sqrt{2}} )
D. ( frac{c}{2} )
12
110Two electric charges of ( 9 mu C ) and ( -3 mu C ) are placed ( 0.16 m ) apart in air. There will be
a point ( mathrm{P} ) at which electric potential is
( z ) ero on the line joining the two charges
and in between them. The distance of ( mathrm{P} )
from ( 9 mu C ) charge is:
A ( .0 .14 m )
B. ( 0.12 m )
c. ( 0.08 m )
D. ( 0.06 m )
12
111If one of the two electrons of a ( boldsymbol{H}_{2} )
molecule is removed, we get a hydrogen
molecular ion ( boldsymbol{H}_{2}^{+} . ) In the ground state
of an ( H_{2}^{+}, ) the two protons are separated by roughly ( 1.5 A ), and the electron is roughly ( 1 A ) from each proton. Determine the potential energy of the system. Specify your choice of the zero of potential energy.
12
112The work done (in Joule) in carrying a charge of 100 coulomb between two points having a potential difference of 10 volt is:
A . ( 0 . )
B. 10
( c cdot 100 )
D. 1000
12
113An isolated parallel plate capacitor is charged upto a certain potential difference. When a ( 3 m m ) thick slab is
introduced between the plates then in order to maintain the same potential difference, the distance between the
plates is increased by ( 2.4 m m ). Find the dielectric constant of the slab. (Assume
charge remains constant)
A. 5
в. 10
( c cdot 2.5 )
D. 7.5
12
114At room temperature, if the relative
permittivity of water be 80 and the relative permeability be 0.0222 , then the velocity of light in water is
( boldsymbol{m} / boldsymbol{s}^{-1} )
A . ( 3 times 10^{8} )
В. ( 2.25 times 10^{8} )
c. ( 2.5 times 10^{8} )
D. ( 3.5 times 10^{8} )
12
115Two parallel plate capacitor of capacitances ( C ) and ( 2 C ) are connected in parallel and charged to a potential difference V. If the battery
is disconnected and the space between the plate of the capacitor of capacince ( C ) is completely filled with a material of dielectric constant ( K, ) then the potential difference across the capacitor will be
come
A. ( 3 V(K+2) )
B. ( frac{(K+2)}{3 V} )
c. ( frac{3 V}{(K+2)} )
D. ( frac{3(K+2)}{V} )
12
116A conductor A is given a charge of amount ( +Q ) and then placed inside a
deep metal can B, without touching it.
Then:
This question has multiple correct options
A. The potential of A does not change when it is place inside B.
B. If ( B ) is earthed, ( +Q ) amount charge flows from it into the earth.
C. If ( B ) is earthed, the potential of ( A ) is reduced
D. Either (B) or (C) is true or both the true only if the outer surface of B is connected to earth and not its inner surface
12
117Charges ( 2 mu C ) and ( 1 mu C ) are placed at
corners ( A ) and ( B ) of square of side ( 5 mathrm{cm} )
as shown in figure. The amount of work to be done against the electric field in moving a charge of ( 1.0 times 10^{-6} C ) from ( C )
to ( D ) is :
B. 0.053 J
c. ( 0.017 J )
begin{tabular}{l}
.0 .035 \
hline
end{tabular}
12
118A hollow metallic sphere of radius
( 10 mathrm{cm} ) is given a charge of ( 3.2 times 10^{-9} mathrm{C} )
The electric intensity at a point ( 4 mathrm{cm} )
from the centre is
A ( cdot 9 times 10^{-9} N C^{-1} )
В. ( 288 N C^{-1} )
c. ( 2.88 N C^{-1} )
D. zero
12
119A uniform charged solid sphere of radius ( R ) has potential ( V_{0} ) (measure with respect to ( infty ) ) on its surface. For this sphere the equipotential surfaces with potentials ( frac{3 V_{0}}{2}, frac{5 V_{0}}{4}, frac{3 V_{0}}{4}, frac{V_{0}}{4} ) have
radius ( R_{1}, R_{2}, R_{3} ) and ( R_{4} ) respectively.
Then
A. ( R_{1}=0 ) and ( R_{2}>left(R_{4} R_{3}right) )
B. ( R_{1} neq 0 ) and ( left(R_{2} R_{1}right)>left(R_{4} R_{3}right) )
c. ( R_{1}=0 ) and ( R_{2}<left(R_{4} R_{3}right) )
D . ( 2 R<R_{4} )
12
120Find equivalent capacitance between
points ( A ) and ( B: )
Essume each conducting plate is having same dimensions and neglect the thickness of the plate, ( frac{varepsilon_{0} A}{d}=7 mu F ) where A is area of plates
( mathbf{A} cdot 7 mu F )
B. ( 11 mu F )
( mathbf{c} cdot 12 mu F )
D. ( 15 mu F )
12
121Assertion
Charge on all the condensers connected in series is the same.
Reason
Charge present on a capacitor is directly proportional to its capacitance
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
12
122Potential at the point of a pointed
conductor is greater than the other points on surface:
A. True
B. False
12
123The work done in moving a single positive charge from infinity to a point is called ( ldots . . ) at that point
A. Electricity
B. Electric potential
D. None of these
12
124topp
difference across the plates with
respect to the charge on the condenser?
( A )
B.
( c )
( D )
12
125Consider a huge charge reservoir at potential ( V=200 ) volts. A spherical
capacitor ( C_{1}=40 n F ) is brought in
contact with the charge reservoir and
then removed.
Afterwards, another spherical capacitor
( C_{2}=30 n F ) is brought in contact with
( C_{1} ) and removed. This process is
repeated many times. Assume that potential of reservoir does not change during this exercise. Then the charge in
( (mu C) ) on ( C_{2} ) after a very long time is :
A . 6
B. 3
( c .9 )
D. 12
12
126The figure shows a circuit consisting of four capacitors. Find the effective
capacitance between ( boldsymbol{X} ) and ( boldsymbol{Y} )
12
127A solid conducting sphere having a
charge ( Q ) is surrounded by an
uncharged concentric conducting
hollow spherical shell. Let the potential difference between the surface of the
solid sphere and that of the outer surface of the hollow shell be ( V ). If the
shell is now given a charge ( -3 Q ), the
new potential difference between the
same two surfaces is:
( mathbf{A} cdot V )
B. ( 2 V )
c. ( 4 V )
( mathbf{D} cdot-2 V )
12
128In the following network, potential at 0
is
( 4.4 v )
( 3.3 v )
( c cdot 6 v )
( D cdot 4.8 v )
12
129A capacitor consists of two metal plates each ( 10 mathrm{cm} ) by ( 20 mathrm{cm} ; ) they are separated by a 2.0 mm thick insulator
with dielectric constant 4.1 and
dielectric strength ( 6.0107 mathrm{V} / mathrm{m} . ) What is
the capacitance in ( boldsymbol{p} boldsymbol{F}left(mathbf{1 0}^{-12} boldsymbol{F}right) ? )
A . 75
B. 100
( c cdot 240 )
D. 360
12
Nư.
between the plates. The battery is then
disconnected and a dielectric slab of
dielectric constant ( K ) is placed in between the plates of the capacitor as
shown.

Now, answer the following questions based on above information. The
electric field in the gaps between the
plates and the dielectric slab will is :
A ( cdot frac{varepsilon A V}{d} )
в. ( frac{V}{d} )
( c cdot frac{K V}{d} )
D. ( frac{V}{d-t} )

12
131If the dielectric constant and dielectric
strength be denoted by ( K ) and ( X ) respectively, then a material, suitable for use as a dielectric in a capacitors,
must have :
A. high ( K ) and high ( X )
B. high ( K ) and low ( X )
c. low ( K ) and high ( X )
D. low ( K ) and low ( X )
12
132Two charges ( q_{1} ) and ( q_{2} ) are placed ( 30 c m )
a part as shown. A third charge ( q_{3} ) is
moved along the circle of radius ( 40 mathrm{cm} )
from ( C ) to ( D ). The change in the potential energy of the system is ( frac{q_{3} K}{4 pi epsilon_{0}} )
Find K?
( mathbf{A} cdot 8 q_{2} )
B. ( 8 q )
( c cdot 6 q_{2} )
D. ( 6 q )
12
133Consider a point charge with ( boldsymbol{q}=mathbf{1 . 5} times )
( 10^{-8} C . ) Then, the radius of an
equipotential surface having a potential of ( 30 V ) is :
A ( .0 .45 m )
в. 4.5 т
c. infinite
D. none of the above
12
134is said to be done
when an electric charge flows through a conductor at some potential difference.
12
135The diagram shows equipotential lines
from an unknown charge configuration.
Determine where in the diagram the
field is closest to uniform:
( A cdot A )
B. B
( c cdot c )
( D )
12
136A ( 10.0 mu F ) parallel-plate capacitor with
circular plates is connected to a ( 12.0 mathrm{V} )
battery. What is the charge on each plate ( (operatorname{in} mu C) ? )
12
137Match the following two columns:
( begin{array}{llll} & text { Column I } & & text { Column II } \ text { A. } & begin{array}{l}text { Electrical } \ text { resistance }end{array} & 1 . & {left[M L^{3} T^{-3} A^{-2}right]} \ text {B. } & begin{array}{l}text { Electrical } \ text { potential }end{array} & 2 . & {left[M L^{2} T^{-3} A^{-2}right]} \ text {C. } & begin{array}{l}text { Specific } \ text { resistance }end{array} & 3 . & {left[M L^{2} T^{-3} A^{-1}right]} \ text {D. } & begin{array}{l}text { Specific } \ text { conductance }end{array} & 4 . & text { None of these }end{array} )
( mathbf{A} cdot A-2, B-3, C-1, D-4 )
( mathbf{B} cdot A-2, B-4, C-3, D-1 )
c. ( A-1, B-2, C-3, D-3 )
D. ( A-1, B-3, C-2, D-4 )
12
138State whether given statement is True or False

The dielectric constant is the ability of a material to establish an electric field.
A. True
B. False

12
139A charge of ( 20 mu C ) produces an electric
field. Two points are ( 10 mathrm{cm} ) and ( 5 mathrm{cm} )
away from this charge. Find the values of potentials at these points and also find the amount of work done to take an
electron from one point to the other
12
140Given four capacitors each of capacity ( 12 mu )
F. To get a capacity of ( 9 mu mathrm{F} ), what
combination can be used:
A. All in series
B. All in parallel
c. 3 in parallel and 1 series with them
D. 2 in parallel and 2 in series
12
141Some charge is being given to a
conductor. Then its potential:
A. is maximum somewhere between surface and centre.
B. is maximum at surface.
C. is maximum at centre.
D. remains same throughout the conductor
12
142Two particles ( X ) and ( Y ) having equal
charges after being accelerated thorough the same potential difference enter a region of uniform magnetic field and describe circular paths of radius
( boldsymbol{R}_{1} ) and ( boldsymbol{R}_{2} ) respectively. the ratio of
mass of ( X ) to that of ( Y ) is
( mathbf{A} cdot sqrt{R_{1} / R_{2}} )
в. ( R_{2} / R_{1} )
c. ( left(R_{1} / R_{2}right)^{2} )
D. ( R_{1} / R_{2} )
12
143Identify the correct statement from
below:
( mathbf{A} cdot ) A will be at higher potential
B. B will be at higher potential
C. Both will be at same potential
D. Can’t be said
12
144Two identical capacitors are connected in series with a source of potential V. If ( mathrm{Q} ) is the charge on one of the capacitors, the capacitance of each capacitor is:
A ( cdot ) Q/2
B. 2Q/V
c. ( mathrm{Q} / mathrm{v} )
D. None of these
12
145A parallel plate air has a capacity of ( 20 mu F ). what will be the new capacity if a
marble slab of dielectric constant 8 is
introduced between the two plates?
12
146Three capacitors ( 2 mu F, 3 mu F ) and ( 6 mu F ) are connected in series. The effective
capacitance of the combination is:
( mathbf{A} cdot 11 mu F )
в. ( 1 mu F )
c. ( 1.2 mu F )
D. ( 2 mu F )
12
147A parallel plate capacitor is charged and then disconnected from the
charging battery. If the plates are now moved farther apart by pulling at them by means of insulating handles, then:
A. the energy stored in the capacitor decreases
B. the capacitance of the capacitor increases
c. the charge on the capacitor decreases
D. the voltage across the capacitor increases
12
148The potential energy of the system of two identically charged spheres as shown in the figure is equal to (Assume the charge distribution to be uniform)
( ^{mathbf{A}} cdot frac{q^{2}}{4 pi varepsilon_{0}}left[frac{1}{R}+frac{1}{r}right] )
в. ( frac{1}{4 pi varepsilon_{0}} frac{q^{2}}{r} )
c. ( frac{1}{4 pi varepsilon_{0}} frac{q^{2}}{(R+r)} )
D. None of these
12
149What is dielectric substance?12
150Dielectric constant of a metal is
A. zero
B. Infinite
c. Finite
D. Unpredictable
12
151A parallel plate capacitors is formed by stacking n equally spaced plates connected alternately. If capacitance between two adjacent plates is ( C ) then the resultant capacitance is :
A. ( (n-1) C )
в. ( (n+1) C )
( c . c )
D. ( n C )
12
152Two ( C u^{64} ) nuclei touch each other. The
electrostatics repulsive energy of the system will be
A. 0.788 MeV
в. 7.88 Ме ( V )
c. 126.15 MeV
D. 788 MeV
12
153A charge of ( 1 mu C ) is given to one plate of
a capacitors and a charge of ( 2 mu mathrm{C} ) is
given to the other plate of a ( 0.1 mu mathrm{F} ) capacitor. Find the potential difference across the two plates of the capacitor:
( mathbf{A} cdot 5 V )
в. ( 10 V )
( mathrm{c} cdot 15 mathrm{V} )
D. 30 ( V )
12
154The radius of two metallic sphere ( A ) and
( B ) are ( r_{1} ) and ( r_{2} ) respectively ( left(r_{1}>r_{2}right) )
They are connected by a thin wire and the system is given a certain charge. The charge will be greater
A. Equal to both
B. Zero on both
c. on the surface of sphere ( A )
D. On the surface of sphere ( B )
12
155A parallel plate air capacitor has
capacity’ ( C^{prime}, ) distance of separation
between plate is ‘ ( d^{prime} ) and potential
difference ( ^{prime} V^{prime} ) is applied between the
plates. Force of attraction between the
plates of the parallel plate air capacitor is:
( ^{mathbf{A}} cdot frac{C^{2} V^{2}}{2 d^{2}} )
B. ( frac{C^{2} V^{2}}{2 d} )
( c cdot frac{C V^{2}}{2 d} )
D. ( frac{C^{2} V}{d} )
12
156In the electric field of an point charge ( q )
a certain charge is carried from point ( mathbf{A} )
to ( mathrm{B}, mathrm{C}, mathrm{D} ) and ( mathrm{E} ). Then the work done
during movement along each path is:
A. least along the path AB
B. least along the path AD
C. zero along any one of the path ( A B, A C, A D ) and ( A E )
D. least along AE
12
157The work done by electric field in
carrying a point charge of ( 5 mu C ) from a
point ( A ) to point ( B ) is 10 mJ. The potential
difference ( boldsymbol{V}_{boldsymbol{A}}-boldsymbol{V}_{boldsymbol{B}} ) is the:
( A cdot+2 k V )
B. -2 kV
( c cdot+2000 v )
D. -2000V
12
158Equipotential surfaces are
A. Surfaces that are perpendicular to gravitational fields
B. Surfaces that have same mass on top of it
c. surface that have same radius of curvature
D. Surfaces that have same gravitational field on it
12
159The plates of a parallel plate capacitor
are charged with surface densities ( sigma_{1} )
and ( sigma_{2}left(sigma_{1}=sigma text { and } sigma_{2}=-sigmaright) )
respectively and placed horizontally. The electric field at points :
This question has multiple correct options
A. inside the region between the plates will be zeroro
B. above the upper plate and below the lower plate will be zero
c. everywhere in space will be zero
D. inside the region between the plates will be uniform and non zero (neglecting other effects)
12
160Charges ( 1 mu C ) are placed at each of the four corners of a square of side ( 2 sqrt{2} m )
The potential at the point of intersection of the diagonals is ( _{-}-_{-}-_{-}(K=9 times )
( left.mathbf{1 0}^{mathbf{9}} boldsymbol{S} boldsymbol{I} text { unit }right) )
( mathbf{A} cdot 18 times 10^{3} V )
в. ( 1800 mathrm{V} )
( mathbf{c} cdot 18 sqrt{2} times 10^{3} V )
D. None of these
12
161If the charge on a capacitor is increased by 2 colomb, the energy stored in it increases by ( 21 % ). The original charge on the capacitor is
A . 10
B. 20
c. 30
D. 40
12
162A uniformly charged solid sphere or
radius ( boldsymbol{R} ) has potential ( boldsymbol{V}_{mathbf{0}} ) (measured
with respect to ( infty ) ) on its surface. For
this sphere the equipotential surfaces with potentials ( frac{3 V_{0}}{2}, frac{5 V_{0}}{4}, frac{3 V_{0}}{4}, frac{V_{0}}{4} )
have radius ( boldsymbol{R}_{1}, boldsymbol{R}_{2}, boldsymbol{R}_{3} ) and ( boldsymbol{R}_{4} )
respectively. Then
A ( cdot R_{1}=0 ) and ( R_{2}left(R_{4}-R_{3}right) )
B . ( R_{1} neq 0 ) and ( left(R_{1}-R_{1}right)>left(R_{4}-R_{3}right) )
c. ( R_{1}=0 ) and ( R_{2}>left(R_{4}-R_{3}right) )
D. none of these
12
163sheets having charges ( Q ) and ( 2 Q ) are
placed parallel to each other as shown in Fig. The charge distribution on the
four faces of the two plates is also
shown. The electric field intensities at
three points ( 1,2, ) and 3 are
( vec{E}_{1}, vec{E}_{2}, ) and ( vec{E}_{3}, ) respectively. Then the magnitudes of ( overrightarrow{boldsymbol{E}}_{1}, overrightarrow{boldsymbol{E}}_{3} ) and ( overrightarrow{boldsymbol{E}}_{2} ) are
respectively (surface area of plates):
( A )
( 0, frac{Q}{varepsilon_{0} S}, 0 )
B. ( frac{5 Q}{6 varepsilon_{0} S}, frac{Q}{2 varepsilon_{0} S}, 0 )
c. ( frac{5 Q}{6 varepsilon_{0} S}, frac{Q}{varepsilon_{0} S}, frac{Q}{3 varepsilon_{0} S} )
D.
( 0, frac{Q}{2 varepsilon_{0} S}, 0 )
12
164Calculate the area of the plates of a one
farad parallel plate capacitor if separation between plates is ( 1 mathrm{mm} ) and plates are in vacuum:
A ( cdot 18 times 10^{8} m^{2} )
B . ( 0.3 times 10^{8} m^{2} )
c. ( 1.3 times 10^{8} m^{2} )
D. ( 1.13 times 10^{8} m^{2} )
12
165A pendulum with a bob hanging is suspended such that the electric field is in upward direction. At equilibrium of the bob, the change in tension in the string will be (assuming rest condition)
A . ( m g )
в. ( q E )
( c cdot 2 q E )
D. ( q E / 2 )
12
166In an isolated parallel plate capacitor of
capacitance ( C, ) the four surfaces have
charges ( Q_{1}, Q_{2}, Q_{3} ) and ( Q_{4} ) as shown.
The potential difference between the
plates is:
( A )
в. ( frac{Q_{2}+Q_{3}}{2 C} )
c. ( frac{Q_{2}-Q_{3}}{2 C} )
D. ( frac{Q_{1}+Q_{4}}{2 C} )
12
167In the arrangement of capacitors shown
in Figure, if each capacitor is ( 9 mathrm{pF} ), the effective capacitance between ( A ) and ( B )
is
A . ( 10 p )
В. 15 p
( c .20 p F )
D. ( 5 p F )
12
168The effective capacitance between the
point ( P ) and ( Q ) of the arrangement shown in the figure is:
12
169A child stands inside a large charged metal sphere. Will her hair stand on
end?
A. Yes
B. No
c. Incomplete information
D. No guess about her hair style
12
170A condenser of capacity ( C ) is charged to
a potential difference of ( V_{1} . ) The plates of the condenser are then connected to
an ideal inductor of inductance ( L ). The
current through the inductor when the
potential difference across the
condenser reduces to ( V_{2} ) is
( left(frac{Cleft(V_{1}-V_{2}right)^{2}}{L}right)^{frac{1}{2}} )
в. ( frac{Cleft(V_{1}^{2}-V_{2}^{2}right)}{L} )
c. ( frac{Cleft(V_{1}^{2}+V_{2}^{2}right)}{L} )
( left(frac{Cleft(V_{1}^{2}-V_{2}^{2}right)}{L}right)^{frac{1}{2}} )
12
171The plates of a parallel plate capacitor are charged upto ( 100 V . ) now, after removing the battery, a ( 2 m m ) thick plate is inserted between the plates. Then, to maintain the same potential difference, the distance between the
capacitor plates is increased by ( 1.6 m m ) The dielectric constant of the plate is :
A . 5
B. 1.25
( c cdot 4 )
D. 2.5
12
172An uncharged metal object ( M ) is
insultated from its surroundings.A
positively charges metal sphere ( boldsymbol{S} ) is
then brought near to ( M . ) Which diagram
illustrate the resultant distribution of
charge on ( S ) and ( M )
( A )
в.
( c )
D.
12
173A parallel plate capacitor, at a capacity ( 100 mu F ), is charged by a battery at ( 50 mathrm{V} )
The battery remains connected and if the plates of the capacitor are separated so that the distance between them is
reduced to half of the original distance, the additional energy given by the battery to the capacitor in ( J ) is:
A ( cdot 125 times 10^{-3} )
В. ( 12.5 times 10^{-3} )
с. ( 1.25 times 10^{-3} )
.
D. ( 0.125 times 10^{-3} )
12
174Identify the true expression:
A ( cdot V=J C^{-1} )
B. ( V=J C )
( mathbf{c} cdot V=J C^{-2} )
D. ( V=J C^{-3} )
12
175A particle having mass 1 g and electric
charge ( 10^{-8} mathrm{C} ) travels from a point ( mathrm{A} )
having electric potential ( 600 mathrm{V} ) to the point B having zero potential. What would be the change in its kinetic
energy?
A . ( -6 times 10^{-6} ) erg
В. ( -6 times 10^{-6} ) j
c. ( 6 times 10^{-6} ) j
D. ( 6 times 10^{-6} ) erg
12
176Find equivalent capacitance between
points ( A ) and ( B ) :
( ^{A} cdot frac{5 C}{3} )
в. ( frac{4 C}{3} )
( c . C )
0.20
12
177( P, Q ) and ( R ) are three points in a uniform
electric field. The electric potential is
A. minimum at R
B. minimum at
( c . ) minimum at
D. Same at all three points
12
178Two point charges ( 10^{-5} mathrm{C} ) and ( -10^{-5} mathrm{C} ) are released from large separation. Their masses are 100 gm and 200 gm. If velocity of approach (in ( mathrm{m} / mathrm{s} ) ) of them when they are separated by distance ( 3 m ) is ( frac{x}{4} m / s . ) Then ( x ) is :
A . 12
B. 1
( c cdot 4 )
D. 8
12
179The electric potential at point ( X ) is 20 V and at point Y is – 40 V. Then, the work done by an external force in moving an electron from ( X ) to ( Y ) is:
( mathbf{A} cdot 13 times 10^{-8} J )
В. ( 9.6 times 10^{-18} mathrm{J} )
c. ( 3.2 times 10^{-8} J )
D. ( 30 times 10^{-15} mathrm{J} )
12
180Draw a neat labelled diagram of a parallel plate capacitor completely filled with dielectric.12
181Equipotentials at a great distance from a collection of charges whose total sum is not zero are approximately:
A. spheres
B. planes
c. paraboloids
D. ellipsoids.
12
182Five identical parallel conducting
plates each of area A have separation ‘d between successive surface. The plates
are connected to the terminal of a
battery as shown in the figure. The effective capacitance of the circuit is
A ( cdot frac{A varepsilon_{0}}{4 d} )
в. ( frac{4 A varepsilon_{0}}{d} )
c. ( frac{A varepsilon_{0}}{3 d} )
D. ( frac{3 A varepsilon_{0}}{4 d} )
12
183Three charges ( +1 mu C,+3 mu C ) and ( -5 mu C )
are kept at the vertices of an equilateral triangle of sides ( 60 mathrm{cm} ). Find the
electrostatic potential energy of the system of charges.
12
184Two similar parallel plate capacitors
each of capacity ( C_{o} ) are connected in
series, The combination is connected
with a voltage source of ( V_{o} . ) Now
separation between the plates of one
capacitor is increased by a distance ( boldsymbol{d} )
and the separation between the plates of another capacitor is decreased by the
distance ( d / 2 ) The distance between the
plates of each capacitor was ( boldsymbol{d} ) before the change in separation. Then, select the correct choice :
A. the new capacity of the system will increase
B. the new capacity of the system will decrease
c. the new capacity of the system will remain same
D. data insufficient
12
185Derive an expression for the capacitance of a parallel plate capacitor. Why does the capacitance
increase by using dielectric in
capacitor?
12
186The associated figure shows an electric
charge ( +q ) located at the centre of a hollow uncharged conducting metal sphere. Outside the sphere is a second
charge ( +Q . ) Both charges are positive.
Choose the description below that
describes the net electrical forces on
each charge in this situation.
A. Both charges experience the same net force directed
B. No net force experienced by either charge.
c. There is no net force on Q but a net force on q
D. There is no net force on q but a net force on ( Q )
E. Both charges experience a net force but they are diff
12
187There are n identical capacitors, which are connected in parallel to a potential
difference ( V . ) These capacitors are then reconnected, in series. The potential difference between the extreme ends is:
A . zero
в. ( n V )
c. ( (n-1) V )
D. none of the above
12
188State whether the given statement is True or False:
Six negative point charges are arranged symmetrically around a circle centered at point ( P ) as shown in the diagram below. All points charges are of the same magnitude Electric Field at ( mathrm{P} ) will be zero while
electric potential at point ( P ) will be non
zero.
A. True
B. False
12
189Column ( I ) has some statements about
the system shown in column ( I I, ) Match appropriate column.
12
190Two thick plates having same charges (same charge density ( sigma ) ) are placed side by side. Consider the case of infinite plate. Find the difference between the electric field present
between the plate and remaining space of the plate, ( (varepsilon=text { permittivity }) )
A ( cdot frac{sigma}{varepsilon} )
в. ( 2 frac{sigma}{varepsilon} )
c. ( frac{sigma}{2 varepsilon} )
D.
12
191Two thin wire rings each having a
radius ( R ) are placed at a distance
d apart with their axes coinciding. The
charges on the two rings are ( +q ) and ( -q ) The potential difference between the
centres of the two rings is
A ( cdot frac{Q cdot R}{4 pi varepsilon d^{2}} )
B ( cdot frac{Q}{2 pi varepsilon_{0}}left[frac{1}{R}-frac{1}{sqrt{R^{2}+d^{2}}}right] )
c. ( frac{Q}{4 pi varepsilon_{0}}left[frac{1}{R}-frac{1}{sqrt{R^{2}+bar{d}^{2}}}right] )
D.
12
192A unit charge moves on an equipotential surface from a point ( A ) to
point ( mathrm{B} ), then :
A. ( V_{A}-V_{B}=+v e )
в. ( V_{A}-V_{B}=0 )
( mathbf{c} cdot V_{A}-V_{B}=-v e )
D. it is stationary
12
193Two small identical metal balls ( A ) and ( B )
radius r are placed apart The distance
between centre of balls is ( a_{0} ) The net
potential of ball ( A ) is ( V_{1} ) and that of ( B ) is
( V_{2} ) Let ( q_{1} ) and ( q_{2} ) are the charges on balls
A and B respectively Then the charge on
( A ) and ( B ) are ( left(left(g i v e n r<<a_{0}right)right) )
This question has multiple correct options
A ( cdot q_{1}=4 pi varepsilon_{0} frac{a_{0} rleft(V_{1} a_{0}-V_{2} rright)}{a_{0}^{2}-r^{2}} )
В. ( quad q_{1}=4 pi varepsilon_{0} frac{a_{0} rleft(V_{1} a_{0}+V_{2} rright)}{a_{0}^{2}+r^{2}} )
( ^{mathbf{C}} cdot_{q_{2}}=4 pi varepsilon_{0} frac{a_{0} rleft(V_{2} a_{0}+V_{1} rright)}{a_{0}^{2}+r^{2}} )
D. ( _{q_{2}}=4 pi varepsilon_{0} frac{a_{0} rleft(V_{2} a_{0}-V_{1} rright)}{a_{0}^{2}-r^{2}} )
12
194A parallel plate air capacitor has a capacitance of ( 5 mu F . ) It becomes ( 50 mu F ) when a dielectric medium occupies the
entire space between its two plates.
What is the dielectric constant of the
medium?
12
195The breakdown field strength for dry air
is ( 3 times 10^{6} mathrm{V} / mathrm{m} ). Each of the plates of the
parallel plate capacitor has an area of
( 0.2 m^{2} . ) The maximum charge that can be
collected is : (Given permittivity of air ( left.epsilon_{circ}=8.85 times 10^{-12} C^{2} / N m^{2}right) )
A. ( 5.3 mu ) С
в. ( 0.6 mu mathrm{c} )
c. ( 1.5 mu ) С
D. ( 4.56 mu ) С
12
Who did
at the four corners of a square with
sides of length D.

What is the electric potential at the
center of the square? (k is Coulomb constant.)
( A cdot frac{4 k Q}{D} )
в.
c. ( frac{2 k Q}{left(D cos 45^{circ}right)} )
( D )
( E )

12
197If charge on left plate of the ( 5 mu F )
capacitor in the circuit segment shown
in the figure is ( -20 mu C ), the charge on
the right plate of ( 3 mu F ) capacitor is :
( mathbf{A} cdot+8.57 mu C )
B. ( -8.57 mu C )
c. ( +11.42 mu C )
D. ( -11.42 mu C )
12
198A parallel plate capacitor with air between the plates has a capacitance of ( 8 p Fleft(1 p F=10^{-12} Fright) . ) What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a
substance of dielectric constant ( 6 ? )
12
199For capacitors in the series combination, the total capacitance ( C ) is
given by
( ^{mathbf{A}} cdot_{C}=left(frac{1}{C_{1}}+frac{1}{C_{2}}+ldots ldotsright) )
в. ( C=C_{1}+C_{2}+ldots )
( ^{mathbf{c}} cdot frac{1}{bar{C}}=left(frac{1}{C_{1}}+frac{1}{C_{2}}+ldots . .right) )
( stackrel{mathrm{D}}{mathrm{C}}=C_{1}+C_{2}+ldots )
12
200a conducting sphere ( A ) of radius a, with
charge ( Q, ) is placed concentrically
inside a conducting shell ( B ) of radius ( b )
B is earthed. ( C ) is the common centre of
A and B:
This question has multiple correct options
A ( cdot ) The field at a distance r from ( mathrm{C} ), where ( a leq r leq b ), is ( k frac{Q}{r^{2}} )
B. The potential at a distance r from C, where ( a leq r leq b ), is
( k frac{Q}{r} )
C. The potential difference between A and B is, ( k Qleft(frac{1}{a}-frac{1}{b}right) )
D. The potential difference between r and C, where ( a leq ) ( r leq b, ) is ( k Qleft(frac{1}{a}-frac{1}{b}right) )
12
201The potential difference between two parallel plates ( 1 mathrm{cm} ) apart is ( 100 mathrm{V} ). The electric field strength between them is :
A. ( 100 V / m )
в. ( 1000 V / m )
c. ( 10^{4} V / m )
D. ( 50 V / m )
12
202A network of four capacitors of capacity
equal to ( C_{1}=C, C_{2}=2 C, C_{3}=3 C )
and ( C_{4}=4 C ) are connected to a battery
as shown in the figure. The ratio of the
charges on ( C_{2} ) and ( C_{4} ) is:
12
203topp
spherical shell with inner radius ( c ) and
outer radius ( d ) (as shown in Fig). The
inner shell has total charge ( +2 q ) and the
outer shell has charge ( +4 q ). Calculate
the electric field in terms of ( q ) and the
distance ( r ) from the common centre of
the two shells for:
( a<r<b )
A. zero
в. ( frac{1}{4 pi varepsilon_{8}} frac{2 q}{r^{2}} )
C. ( -frac{1}{4 pi varepsilon_{0}} frac{6 q}{r^{2}} )
D. ( frac{1}{4 pi varepsilon_{0}} frac{q}{r^{2}} )
12
204Assertion
Each of the plates of a parallel-plate capacitor is given equal positive charge
Q. The charges on the facing surfaces will be same.
Reason
A negative charge (-Q) will be induced on each of the facing surfaces.
A. If both Assertion and Reason are correct and Reason the correct explanation of Assertion
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct
12
205Why must electrostatic field be normal
to the surface at every point of a charged conductor?
12
206A fourth charge with charge ( +3 q ) is
slowly moved in from infinity to point ( boldsymbol{P} )
How much work must be done in this
process?
( A )
в. ( frac{3 q^{2}}{2 pi epsilon_{0} a} )
c. ( frac{3 q^{2}}{sqrt{3} pi epsilon_{0} a} )
D. ( frac{3 q^{2}}{4 pi epsilon_{n}} )
12
207Two metallic plates are kept parallel to
one another and charges are given to
them as shown in figure. Find the charge on all the four faces
12
208Derive an expression for the energy stored per unit volume (energy density) in an electric field. OR Obtain an
expression for energy density of a medium.
12
209The potential at a point due to a charge of ( 5 times 10^{-7} C ) located ( 10 c m ) away is
( 4.5 times 10^{4} V . ) The work done in bringing a
charge of ( 4 times 10^{-9} C ) from infinity to
that point is:
A ( .2 .4 times 10^{-4} J )
В. ( 1.8 times 10^{-4} mathrm{J} )
c. ( 3.2 times 10^{-5} J )
D. ( 4.1 times 10^{-5} J )
12
210The potential of a large liquid drop when eight liquid drops are combined is ( 20 V )
Then the potential of each single drop
was:
A . ( 10 V )
в. ( 7.5 V )
( c .5 V )
D. 2.5V
12
211The energy density in a parallel plate capacitor is given as ( 1.8 times 10^{-9} J / m^{3} )
The value of the electric field in the
region between the plates is :
( left(epsilon_{0}=9 times 10^{-12}right) )
( mathbf{A} cdot 6.6 N C^{-1} )
B. ( 20 N C^{-1} )
( mathbf{c} cdot 66 N C^{-1} )
D. ( 2 N C^{-1} )
12
212A1 ( mu F ) capacitor and a ( 2 mu F ) capacitor
are connected in series across a ( 1200 mathrm{V} )
supply line. The charged capacitors are
disconnected from the line and from
each other and reconnected with
terminals of like sign together. Find the final charge on each and the voltage
across them:
A ( cdot frac{1600}{13} V )
В. ( frac{1600}{32} V )
c. ( frac{1600}{3} V )
D. ( frac{160}{3} V )
12
213A condenser of capacity ( 2 mu F ) is charged
to a potential of ( 200 mathrm{V} ). It is now connected to an uncharged condenser of capacity ( 3 mu F ). The common potential is :
A . 200
B. ( 100 mathrm{V} )
c. ( 80 v )
D. 40
12
214Two conducting plates ( A ) and ( B ) are
parallel. A is given a charge ( Q_{1} ) and ( B ) is
given a charge ( Q_{2} ). The charge on inner
side of B is :
( A )
[
frac{Q_{2}-Q_{1}}{2}
]
в.
[
frac{left(Q_{1}-Q_{2}right)}{2}
]
( c )
[
frac{left(Q_{1}+Q_{2}right)}{2}
]
( D )
[
frac{-left(Q_{1}+Q_{2}right)}{2}
]
12
215The charge appearing on the outer surface of extreme left plate is :
A . ( -(Q / 2) )
B. ( (Q / 2) )
( c cdot Q )
D. –
12
216A hollow metal sphere of radius ( 5 mathrm{cm} ) is
charged such that the potential on its surface is 10 volts. The potential at the
centre of the sphere will be:
A . zero
B. 5 volts
c. 10 volts
D. 0.2 volts
12
217What is the S.I. unit of electric
potential?
A. ampere
B. volt
c. volt.m
D. coulomb
12
218Two electric charges of ( 9 mu C ) and ( -3 mu C ) are placed ( 0.16 mathrm{m} ) apart in air. There are two points ( A ) and ( B ) on the line joining the two charges at distances of (i) ( 0.04 m ) from ( -3 mu C ) and in between the charges
and
(ii) ( 0.08 m ) from ( -3 mu C ) and out side
the two charges. The potentials at ( A ) and
B are :
A. ( 0 V, 5 V )
в. ( 0 V, 0 V )
c. ( 5 V, 0 V )
D. ( 5 V, 10 V )
12
219plates ( A, B ) and ( C ) are placed as shown.
Switches ( S_{1} ) and ( S_{2} ) are open, and can
connect ( A ) and ( C ) to earth when closed.
( +Q ) charge is given to ( B: )
This question has multiple correct options
A. If ( S_{1} ) is closed with ( S_{2} ) open, a charge of amount ( Q ) will
pass through ( S_{1} )
B. If ( S_{2} ) is closed with ( S_{1} ) open, a charge of amount ( Q ) will pass through ( S_{2} )
c. If ( S_{1} ) and ( S_{2} ) are closed together, a charge of amount
Q/3 will pass through ( S_{1} ), and a charge of amount
( 2 Q / 3 ) will pass through ( S_{2} )
D. All the above statements are incorrect
12
220A parallel plate condenser has plates of
area ( 200 mathrm{cm}^{2} ) and separation ( 0.05 mathrm{cm} )
The space between plates have been
filled with a dielectric having ( mathbf{k}=mathbf{8} ) and
then charged to 300 volts. The stored energy:
A . ( 121.5 times 10^{-6} mathrm{J} )
В. ( 28 times 10^{-6} mathrm{J} )
D. ( 1.6 times 64 times 10^{-5} mathrm{J} )
12
221Show that the force on each plate of a parallel plate capacitor has
a magnitude equal to ( left(frac{1}{2}right) mathrm{QE} ), where ( mathrm{Q} ) is
the charge on the capacitor, and E is the magnitude of electric field between the
plates. Explain the origin of the factor.
12
222The relative permittivity of water is ( 81 . ) If
( varepsilon_{0} ) and ( varepsilon ) are permittivities of vaccum
and water respectively Then:
A ( cdot varepsilon_{0}=9 varepsilon_{w} )
В. ( varepsilon_{0}=81 varepsilon_{w} )
( mathbf{c} cdot varepsilon_{w}=9 varepsilon_{0} )
D. ( varepsilon_{w}=81 varepsilon_{0} )
12
223Two parallel wires are suspended in vacuum. When the potential difference between the wires is 30 V then the
charge on the wires is ( 140 mu C ). The capacitance of the system of wires will be:
A ( .4 .66 mu F )
в. ( 5 mu F )
c. ( 10.21 mu F )
( mathbf{D} cdot 50 mu F )
12
224A non conducting rod ( A B ) of length ( sqrt{3} R ) uniformly distributed charge of linear charge density ( lambda ) and.a non-conducting ring of uniformly distributed charge ( Q ) are placed as shown in the figure. Point
A is the centre of ring and line ( A B ) is the
axis of the ring, perpendicular to plane of ring. The electrostatic
interaction energy between ring and rod
is
A ( cdot frac{Q lambda}{4 pi epsilon_{l}} ln (2+sqrt{3}) )
c. ( frac{Q lambda}{4 pi epsilon} ln (2-sqrt{3}) )
D・frac{Qlambda } ( {2 pi epsilon} ln (2-sqrt{3}) )
12
225Two charges are at a distance ( d ) apart. If
( boldsymbol{d} )
a copper plate of thickness ( frac{u}{2} ) is kept
between them, the effective force will be
A. ( F / 2 )
B. zero
( c cdot 2 F )
D. ( sqrt{2} F )
12
226Complete the following statements with an appropriate word /term be filled in
the blank space(s).

The equivalent capacitance ( C ) for the series combination of three
capacitance ( C_{1}, C_{2} ) and ( C_{3} ) is given by
( frac{1}{C}= )
A. ( C_{1}+C_{2}+C_{3} )
( ^{text {В }} cdotleft(frac{1}{C_{1}+C_{2}+C_{3}}right) )
( left(frac{1}{frac{1}{C_{1}}+frac{1}{C_{2}}+frac{1}{C_{3}}}right) )
D ( cdotleft(frac{1}{C_{1}}+frac{1}{C_{2}}+frac{1}{C_{3}}right) )

12
227toppr
an electric field that decreases with
altitude. Near the surface of the earth,
the field is about ( 100 V m^{-1} . ) Why then
do we not get an electric shock as we
step out of our house into the open?
(Assume the house to be a steel cage so
there is no field inside!)
(b) A man fixes outside his house one evening a two metre high insulating slab
carrying on its top a large aluminium sheet
of area ( 1 m^{2} ). Will he get an electric shock if
he touches the metal sheet next morning?
(c) The discharging current in the atmosphere due to the small conductivity of
air is known to be 1800 A on an average
Over the globe. Why then does the atmosphere not discharge itself completely
in due course and become electrically
neutral? In other words, what keeps the atmosphere charged?
(d) What are the forms of energy into which the electrical energy of the atmosphere is dissipated during a lightning?
(Hint: The earth has an electric field of
about ( 100 mathrm{Vm}^{-1} ) at its surface in the
downward direction, corresponding to a Surface charge density ( =-10^{-9} mathrm{Cm}^{-2} ). Due
to the slight conductivity of the atmosphere
up to about ( 50 mathrm{km} ) (beyond which it is
good conductor), about ( +1800 mathrm{C} ) is pumped every second into the earth as a whole. The earth, however, does not get discharged since thunderstorms and lightning occurring continually allover the globe pump an equal amount of negative charge on the earth.)
12
228A capacitor of capacitance ( 9 n F ) having
dielectric slab of ( varepsilon_{r}=2.4 ) dielectric
strength ( 20 mathrm{MV} / mathrm{m} ) and ( boldsymbol{P . D .}=20 mathrm{V} )
Calculate area of plates.
В . ( 4.2 times 10^{-4} mathrm{m}^{2} )
c. ( 1.4 times 10^{-4} m^{2} )
D. 2.4 ( times 10^{-4} m^{2} )
12
229A parallel-plate capacitor is connected
to a cell. Its positive plate ( A ) and its
negative plate ( boldsymbol{B} ) have charges ( +boldsymbol{Q} ) and
( -Q ) respectively. A third plate ( C )
identical to ( A ) and ( B, ) with charge ( +Q )
is now introduced midway between ( boldsymbol{A} )
and ( B, ) parallel to them. Which of the
following are correct?
This question has multiple correct options
A ( cdot ) The charge on the inner face of ( B ) is now ( -frac{3 Q}{2} )
B. There is no change in the potential difference between
( A ) and ( B )
C. The potential difference between ( A ) and ( C ) is one-third of the potential difference between ( B ) and ( C )
D. The charge on the inner face of ( A ) is now ( Q / 2 )
12
230An electric circuit requires a total
capacitance of ( 2 mu F ) across potential of
( mathbf{1 0 0 0} V ). Large number 1 ( mu boldsymbol{F} )
capacitances are available each of which would breakdown if the potential is more than ( 350 V ) How many
capacitances are required to make the
circuit.
A .24
B . 20
c. 18
D. 12
12
231A series combination of two
capacitances of value 0.1 mu ( F ) and
( 1 mu F ) is connected with a source of voltage 500 volts. The potential difference in volts across the capacitor of value 0.1 mu ( F ) will be :
( mathbf{A} cdot 50 )
в. 500
c. 45.5
D. 454.5
12
232Five identical plates are connected
across a battery as shown. If the charge
on plate 1 be ( +q, ) then the charges on the plates 2,3,4 and 5 are:
( mathbf{A} cdot-q,+q,-q,+q )
в. ( -2 q,+2 q,-2 q,+q )
c. ( -q,+2 q,-2 q,+q )
D. none of the above
12
233If ( 4 times 10^{20} e V ) is required to move a
charge of ( 0.25 C ) between two points, the potential difference between these
two points is:
( mathbf{A} cdot 256 V )
в. ( frac{1}{256} V )
( mathbf{c} cdot 256 times 10^{+19} V )
D. ( 250 V )
12
234A parallel plate capacitor is charged and the charging battery is then disconnected. If the plates of the capacitor are now moved apart by means of insulting handles:
A. the charge on capacitors increases
B. the voltage across the capacitors decreases
c. the capacitance increases
D. the electrostatic energy stored in the capacitor increases
12
235The negative gradient of potential is
A. Electric force
B. Torque
C. Electric current
D. Electric field intensity
12
236In the figure a potential of ( +1200 mathrm{V} ) is
given to point ( A ) and point ( B ) is
earthed,what is the potential at the
point
A . ( 100 mathrm{V} )
B. 200
c. ( 400 mathrm{v} )
D. 600 v
12
237In the figure, identical capacitors are
connected in the given three
configurations.The ratio of the total capacitancies in (i), (ii) and (iii)
respectively, is :
( mathbf{A} cdot 3: 5: 5 )
B. 3: 3: 5
( mathbf{c} cdot 5: 4: 4 )
( mathbf{D} cdot 5: 5: 3 )
12
238The work done in moving a charge of 5 coulombs from a point at 230 volts to another point at 240 volts is.
A. 50
B . 15
c. 100
D. 500
12
239A capacitor contains two square plates
with side lengths ( 5.0 mathrm{cm} . ) The plates are separated by ( 2.0 mathrm{mm} . ) Dry air fills the space between the plates. Dry air has a dielectric constant of 1.00 and
experiences dielectric breakdown when the electric field exceeds ( 3.010^{4} V / c m ) What is the magnitude of charge that
can be stored on each plate before the capacitor exceeds its breakdown limit and sends a spark between the plates?
( mathbf{A} cdot 6.6 times 10^{-8} C )
В. ( 6.6 times 10^{-5} C )
c. ( 3.3 times 10^{-7} C )
D . 3.3 ( times 10^{-8} mathrm{C} )
E . ( 8.1 times 10^{-2} C )
12
240Electricity at rest is called
A. Dynamic Electricity
B. Static Electricity
C. Both (a) and (b)
D. None of these
12
241012
242In figure, a particle has mass ( boldsymbol{m}=mathbf{5} boldsymbol{g} )
and charge ( boldsymbol{q}^{prime}=mathbf{2} times mathbf{1 0}^{-mathbf{9}} boldsymbol{C} ) starts from
rest at point ( a ) and moves in a straight line to point ( b ). What is its speed ( v ) at point ( b ? )
A ( .2 .65 mathrm{cms}^{-1} )
B. ( 3.65 mathrm{cms}^{-1} )
c. ( 4.65 mathrm{cms}^{-1} )
D. ( 5.65 mathrm{cms}^{-1} )
12
243Two long conductors, separated by a
distance ( boldsymbol{d} ) carry currents ( boldsymbol{I}_{1} ) and ( boldsymbol{I}_{2} ) in
the same direction. They exert a force ( boldsymbol{F} )
on each other. Now the current in one of
them is increased to two times and its
direction is reversed. The distance is
also increases to ( 3 d ). The new value of
the force between them is:
A . ( -2 F )
в. ( F / 3 )
( mathrm{c} cdot-2 F / 3 )
D. ( -F / 3 )
12
244Statement(A): Negative charges always
move from a higher potential to lower potential point Statement (B): Electric potential is
vector.
A. A is true but B is false
B. B is true but A is false
c. Both A and B false
D. Both A and R are true
12
245The arc ( A B ) with the centre ( C ) and the
infinitely long wire having linear charge density ( lambda ) are lying in the same plane.
The minimum amount of work to be
done to move a point charge ( q_{0} ) from
point ( A ) to ( B ) through a circular path ( A B )
of radius ( a ) is equal to:
A ( cdot frac{q_{0}^{2}}{2 pi varepsilon_{0}} log left(frac{2}{3}right) )
в. ( frac{q_{0} lambda}{2 pi varepsilon_{0}} log left(frac{3}{2}right) )
c. ( frac{q_{0} lambda}{2 pi varepsilon_{0}} log left(frac{2}{3}right) )
D. ( frac{q_{0} lambda}{sqrt{2} pi varepsilon_{0}} )
12
246Four identical plates ( 1,2,3, ) and 4 are
placed parallel to each other at equal
distance as shown in the figure. Plates
1 and 4 are joined together and the
space between 2 and 3 is filled with a
dielectric of dielectric constant ( k=2 )
The capacitance of the system between
1 and ( 3 & 2 ) and 4 are ( C_{1} ) and ( C_{2} )
respectively. The ratio ( C_{1} / C_{2} ) is :
( mathbf{A} cdot 5 )
( overline{3} )
B.
( c cdot frac{3}{5} )
D. 5 7
12
247Two capacitors of plate area ( A ) are joined as shown in the figure. Their central rigid part is movable. The capacity of the combination will be:
A ( cdot frac{epsilon_{0} A}{a-b} )
в. ( frac{epsilon_{0} A}{a+b} )
c. ( frac{2 in_{0} A}{a+b} )
D. ( frac{a-b}{epsilon_{0} a} )
12
248Two concentric shells have radii R and
2R, charges ( boldsymbol{q}_{A} ) and ( boldsymbol{q}_{B} ) and potentials ( 2 mathbf{V} )
and (3/2)V respectively. Now shell B is earthed and let charges on them
become ( boldsymbol{q}_{A}^{prime} ) and ( boldsymbol{q}_{B}^{prime} . ) Then
This question has multiple correct options
B ( cdotleft|q_{A}^{prime}right| / q_{B}^{prime} mid=1 )
c. Potential of A after earthing becomes (3/2)V
D. Potential difference between A and B after earthing becomes V/2
12
249A conducting body 1 has some initial charge ( Q, ) and its capacitance is ( C . ) There are two other conducting bodies, 2 and ( 3, ) having capacitances: ( C_{2}=2 C )
and ( C_{3} rightarrow infty . ) Bodies 2 and 3 are
initially uncharged. “Body 2 is touched with body ( 1 . ) Then, body 2 is removed from body 1 and touched with body 3 and then removed”. This process is
repeated ( N ) times. Then, the charge on
body 1 at the end must be :
A ( cdot Q / 3^{N} )
B . ( Q / 3^{N-1} )
c. ( Q / N^{3} )
D. None
12
250A parallel-plate capacitor is charged from a cell and then disconnected from
the cell. The separation between the plates is now doubled. This question has multiple correct options
A. The potential difference between the plates will become double
B. The field between the plates will not change.
c. The energy of the capacitor doubles
D. Some work will have to be done by an external agent on the plates.
12
uniform field between the parallel
plates as shown in figure. Assume that
the field between the plates is uniform
and directed vertically downward, and
that the field outside the plates is zero. The electron enters the field at a point
midway between the plates. Mass of electron is ( 9.1 times 10^{-31} k g . ) If the electron
just misses the upper plate, the time of flight of the electron up to this instant is :
A ( cdot 1.25 times 10^{-9} s )
в. ( 32.5 times 10^{-6} s )
C ( cdot 1.25 times 10^{-10} s )
D. ( 32.5 times 10^{-8} s )
12
252A parallel plate capacitor of capacitance ( C ) is connected to a battery and is charge to a potential difference
( V . ) Another capacitor of capacitor ( 2 C ) is similarly charged to a potential
difference ( 2 V . ) The charging battery is now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is:
A . zero
B ( cdot(3 / 2) C V^{2} )
( mathbf{c} cdot 25 / 6 C V^{2} )
( mathbf{D} cdot(9 / 2) C V^{2} )
12
253When two capacitors are joined in series the resultant capacity is ( 2.4 mu F ) and when the same two are joined in parallel the resultant capacity is ( 10 mu F ). Their individual capacities are :
( mathbf{A} cdot 7 mu F, 3 mu F )
в. ( 1 mu F, 9 mu F )
( mathbf{c} cdot 6 mu F, 4 mu F )
D. ( 8 mu F, 2 mu F )
12
254A charged spherical drop of mercury is in equilibrium in a plane horizontal air capacitor and the intensity of the
electric field is ( 6 times 10^{4} V m^{-1} . ) If the
charge on the drop is ( 8 times 10^{-18} C, ) the
radius of the drop is :
( left[rho_{a i r}=1.29 k g / m^{3} ; rho_{H g}=13.6 times 10^{3}right. )
A ( cdot 0.95 times 10^{-8} m )
n
в. ( 2.7 times 10^{-10} mathrm{m} )
c. ( 2.7 times 10^{-8} mathrm{m} )
D. ( 0.95 times 10^{-6} mathrm{m} )
12
255Identical metal plates are located in air at equal distance ( d ) from one another
The area of each plate is equal to ( A ). If
the capacitance of the system between ( P ) and ( Q ) if the plates are interconnected
as shown in the figure is given as ( frac{x}{2} varepsilon_{0} frac{A}{d} ) Find ( x: )
12
256A dielectric is introduced in a charged
and isolated parallel plate capacitor, which of the following remains unchanged?
A. Energy
B. Charge
c. Electric field
D. Potential difference
12
257The force experienced by a charged particle of charge ( q ) at (1,1,1) is
A. ( -5 q )
в. ( 5 q hat{imath} )
c. ( 5 q(hat{i}+hat{j}) )
D. ( -5 q(hat{i}+hat{j}) )
12
258Four equal charges ( +Q ) are placed at the four corners of a body of side ( a ) each. Work done in removing a charge ( -boldsymbol{Q} ) from its centre to infinity is
A. zero
В. ( frac{sqrt{2} Q^{2}}{4 pi varepsilon_{0} a} )
c. ( frac{sqrt{2} Q^{2}}{pi varepsilon_{0} a} )
( ^{mathrm{D}} cdot frac{Q^{2}}{2 pi varepsilon_{0} a} )
12
259The amount of charge stored in a capacitor is directly proportional to the voltage applied across the capacitor.
A. True
B. False
12
260Along the ( X ) -axis, three charges ( frac{q}{2},-q ) and ( frac{q}{2} ) are placed at ( x=0, x=a ) and ( x=2 a ) respectively. The resultant electric potential at ( x=a+r(text { if }, a<r) ) is :
( left(epsilon_{0} ) is the permittivity of free space) right.
A ( cdot frac{q a}{4 pi epsilon_{0} r^{2}} )
в. ( frac{q a^{2}}{4 pi epsilon_{0} r^{3}} )
( ^{mathbf{C}} cdot frac{qleft(a^{2} / 4right)}{4 pi epsilon_{0} r^{3}} )
D. ( frac{q}{4 pi epsilon_{0} r} )
12
261Three charges all of ( +q ) are brought
together so that they form an equilateral triangle, with a distance ( r )
between them.

Determine the electrostatic potential
energy needed to bring the system together from infinity:
( A )
B. ( frac{3 q^{2}}{4 pi epsilon_{0} r} )
c. ( frac{5 q^{2}}{4 pi epsilon_{0} r} )
D. ( frac{7 q^{2}}{4 pi epsilon_{0} r} )

12
262Four capacitor are connected, as shown
Calculate the equivalent capacitance between the points ( boldsymbol{P} ) and ( boldsymbol{Q} )
begin{tabular}{c|cc|c|c}
hline ( mathbf{P} ) & & & & \
hline & & & & \
( 2 mu mathbf{F} ) & ( 3 mu mathbf{F} ) & ( mathbf{5} mu mathbf{F} ) & ( mathbf{1 0 mu F} ) & \
hline
end{tabular}
12
263The space between the plates of a parallel plate capacitor is filled with a dielectric’ whose ‘dielectric constant’
varies with distance as per the relation,
( boldsymbol{K}(boldsymbol{x})=boldsymbol{K}_{o}+boldsymbol{lambda} boldsymbol{x}(boldsymbol{lambda}=boldsymbol{a} text { constant }) ) The
capacitance ( C, ) of this capacitor, would be related to its ‘vacuum’ capacitance
( C_{o} ) as per the relation:
( ^{mathbf{A}} cdot c=frac{lambda d}{ln left(1+k_{o} lambda dright)} C_{o} )
B. ( c=frac{lambda}{d cdot ln left(1+k_{o} lambda dright)} C_{o} )
( ^{mathrm{c}} cdot_{C}=frac{lambda d}{ln left(1+lambda d / K_{o}right)} C_{o} )
D. ( c=frac{lambda}{d cdot ln left(1+k_{o} / lambda dright)} C_{o} )
12
264An infinite number of charges ‘q’ each are placed along the ( x ) – axis at ( x=1, x=4 )
( x=8 ) and ( s o ) on. If the distance are in meters calculate the electric potential
at ( x=0 )
( A cdot frac{3 q}{8 F C_{0}} )
B. ( frac{q}{2 pi_{0}} )
( c cdot frac{2 q}{pi_{0} q} )
D. ( frac{49}{pi_{0} q} )
12
265Two small spheres each carrying a charge ( q ) are placed ( r ) metre apart. If one of the spheres is taken around the other
one in a circular path, the work done will
be equal to :
A. force between them ( x ) r
B. force between them ( times 2 pi r )
c. force between them / r ( pi ) r
D. zero
12
266Six capacitors each of capacitance of
( 2 mu F ) are connected as shown in the
figure. The effective capacitance
between ( A ) and ( B ) is:
( mathbf{A} cdot 12 mu F )
в. ( frac{8}{3} mu F )
( c .6 mu F )
D ( frac{2}{3} mu F )
12
267High frequency capacitor offers
A. more resistance
B. less resistance
C. zero resistance
D. None of these
12
268An infinite nonconducting sheet has a
surface charge density ( boldsymbol{sigma}= )
( 0.10 mu C / m^{2} ) on one side. How far apart
are equipotential surfaces whose potentials differ by ( 50 V ? )
A. ( 8.8 mathrm{mm} )
B. ( 8.8 mathrm{cm} )
( c .8 .8 m )
D. ( 8.8 mu m )
12
269Figure shows three concentric thin
spherical shells ( A, B, ) and ( C ) of radii ( R )
( 2 R, ) and ( 3 R ) respectively. The shell B is
earthed and ( A ) and ( C ) are given charges
and ( 2 q ) respectively. If the charge on
surfaces ( 1,2,3, ) and 4 are ( q_{1}, q_{2}, q_{3}, ) and
( q_{4} ) respectively, then match the
following columns :
12
270What is the equivalent capacitance of
the combination?
12
271toppr ócin
conductor as shown. Now as the point
charge ( Q ) is pushed away from
conductor, the potential difference
( left(V_{A}-V_{B}right) ) between two points ( A ) and
( B ) within the cavity of sphere remains
constant
Reason
The electric field due to charge on outer
surface of conductor and outside the
conductor is zero at all points inside the
conductor
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
12
272( underbrace{frac{i}{i}}{k} )12
273Electric potential is :
A. a scalar quantity
B. a vector quantity
C. neither scalar nor vector
D. sometimes scalar and sometimes vector
12
274If an electron is released from rest at
point ( p ) in the diagram, what will it do?
A. Move to the right
B. Move to the left
C. Move toward the top of the screen
D. Move toward the bottom of the screen
12
275Derive the formula for the electric
potential energy of an electric dipole in a uniform electric field.
12
276Two fixed charges ( -2 Q ) and ( Q ) are located at the points with coordinates ( (-3 a, 0) ) and ( (+3 a, 0), ) respectively, in the xy plane.
a. Show that all points in the xy plane
where the electric potential due to the
two charges is zero lie on a circle.Find its
radius and the location of its center.
b. Give the expression ( V(x) ) at a general point on the ( x ) -axis and sketch the
function ( V(x) ) on the whole ( x ) -axis.
c. If a particle of charge +q starts from rest at the center of the circle, show by a
short quantitative argument that the
particle eventually crosses the circle. Find its speed when it does so.
12
277The capacity and the energy stored in a charged parallel plate condenser with air between its plates are respectively ( C 0 ) and ( W 0 . ) If the air is replaced by glass (dielectric constant = 5) between
the plates, the capacity of the plates
and the energy stored in it will
respectively be:
12
278Two identical spheres, one positively charged and the other negatively charged are held d cm apart. If the magnitude of the charges on the two spheres is equal, find the electric potential at a point midway on the line joining the centres of the two spheres.
A. zero
B. ( 10 mathrm{v} )
( c .5 v )
D. ( 1.6 times 10^{-19} mathrm{V} )
12
279Four identical charges are placed at the points (1,0,0),(0,1,0),(-1,0,0) and ( (0, )
-1,0)
This question has multiple correct options
A. The potential at the origin is zero.
B. The field at the origin is zero
c. The potential at all points on the z-axis, other than the origin, is zero.
D. The field at all points on the z-axis, other than the origin, acts along the z-axis
12
280A electric charge ( 10^{-8} C ) is placed at the
point ( (4 m, 7 m, 2 m) . ) At the point ( (1 m, 3 m, 2 m) ) the electric
A. potential will be ( 18 V )
B. field has no ( Y ) -component
c. field will be along ( Z ) -axis
D. potential will be ( 1.8 V )
12
281The effective capacity of the network
between terminals A and B is-
( A cdot 6 mu F )
B. ( 20 mu F )
( mathbf{c} cdot 3 mu F )
D. ( 10 mu F )
12
282The radius of a nucleus of an atom
( (Z=50) ) is ( 9 times 10^{-10} m ) then potential
on its surface, will be:
A . ( 80 V )
B. ( 8 k V )
( mathrm{c} .9 mathrm{V} )
D. ( 9 k V )
12
283Two infinitely long parallel plates of equal areas ( 6 mathrm{cm}^{2} ) are separated by a distance of ( 1 mathrm{cm} . ) While one of the plates has a charge of ( +10 n C ) and the other
has ( -10 n C . ) The magnitude of the
electric field between the plates, if ( varepsilon_{0}= ) ( frac{10^{-9}}{36 pi} F / m ) is?
A. ( 0.6 pi V / m )
в. ( 6 pi k V / m )
c. ( 600 pi k V / m )
D. ( 60 pi V / m )
E . ( 6 pi )
12
284The 90 pF capacitor is connected to a 12 V battery. How many electrons are transferred from one plate to another?
( mathbf{A} cdot 1.1 times 10^{9} )
B . ( 6.7 times 10^{9} )
( mathrm{c} cdot 4 times 10^{19} )
D . ( 5 times 10^{19} )
12
285There are two uncharged identical metallic spheres 1 and 2 of radius ( r )
separated by a distance ( d(d>>r) . A ) charged metallic sphere of same radius having charge ( q ) is touched with one of the sphere. After sometime it is moved
away from the system. Now the uncharged sphere is earthed. Charge on earthed sphere is :
( A cdot+frac{q}{2} frac{q}{2} )
B. ( -frac{q}{2} )
c. ( -frac{q r}{2 d} )
D. ( -frac{q d}{2 r} )
12
286The dimensional formula of electric
potential is given by
( mathbf{A} cdotleft[M L^{2} T^{-3} A^{-1}right] )
B. ( left[M L^{2} T^{-2} A^{-1}right] )
( mathbf{c} cdotleft[M L^{2} T^{-1} A^{-1}right] )
D. ( left[M L^{2} T^{-2}right] )
12
287In a parallel plate capacitor, the capacity increases if :
A. area of the plate is decreased
B. distance between the plates increases
C . area of the plate increases
D. dielectric constant decrease
12
288What is the electric potential at the
centre of square of side 1 m? The
charges ( 1 times 10^{-8} C,-2 times 10^{-8} C, 3 times )
( 10^{-8} C ) and ( 2 times 10^{-8} C ) are placed at the
corners of the square.
( mathbf{A} cdot 205 V )
B. ( 308 V )
( c .509 V )
D. ( 110 V )
12
289When a ( 15 V ) dc source was applied across a choke coild then a current of 5
Amp flows in it. If the same coil is
connected to a ( 15 V, 50 ) rad/s ac source
a current of ( 3 A m p ) flows in the circuit
and its resonance frequency if a ( 2500 mu f ) capacitor is connected in series with the coil.
12
290In the following circuit potential at
point ‘A’ is zero.Which resistance
consumes maximum power?
12
291The following arrangement consists of five identical metal plates. Area of each plate is ( A ) and separation between the successive plates is d. The capacitance between ( P ) and
A. ( frac{5 varepsilon_{0} A}{d} )
В. ( frac{7}{3} varepsilon_{0} frac{A}{d} )
c. ( frac{4}{3} frac{varepsilon_{0} A}{d} )
D. ( frac{5}{3} frac{varepsilon_{0} A}{d} )
12
292Assertion
From the relation ( C=frac{q}{V} . ) We can say
that, if more charge q is given q is given to a conductor, its capacity should
increase.
Reason
Ratio ( frac{q}{V} ) will remain constant for a given
conductor.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
12
293Which of the following is not dielectric materials?
A. Silicon dioxide
B. Silicon nitride
c. Titanium oxide
D. None of the above
12
294An electron of mass ( M_{e}, ) initially at rest moves through a certain distance in a uniform electric field in time ( t_{1} . A )
proton of mass ( M_{p} ) also intially at rest,
takes time ( t_{2} ) to move through an equal distance in this uniform electric field.
Neglecting the effect of gravity, the ratio ( t_{2} / t_{1} ) is nearly equal to:
A . 1
в. ( sqrt{frac{M_{p}}{M_{e}}} )
c. ( sqrt{frac{M_{e}}{M_{p}}} )
D. 1836
12
295In bringing an electron towards another electron, the electrostatic potential
energy of the system:
A . decreases
B. increases
c. remains same
D. becomes zero
12
296When a dielectric is introduced
between the plates of a condenser, the capacity of condenser:
A . increases
B. decreases
c. remains same
D. none of these
12
297Select the correct statements:
A. The electric lines of force are always closed curves.
B. Electric line of forced is parallel to equipotential surface
C. Electric line of force is perpendicular to equipotential surface.
D. Electric line of force is always the path of a positively charged particle.
12
298Two positive point charges are of ( 12 C ) and ( 8 C ) are ( 10 mathrm{cm} ) apart from each other
The work done in bringing them ( 4 c m ) closer is
A . ( 5.8 J )
в. ( 13 e V )
c. ( 5.8 e V )
D. ( 13 J )
12
299Three identical dipoles with charges ( q )
and -q and separation between the
charges are placed at the corners of an equilateral triangle of side d as shown in
Fig. ( 3.123 . ) Find the interaction energy of
the system ( (a< )
12
300The capacitance of a parallel plate
capacitor with air as medium is ( 3 mu mathrm{F} ) As a dielectric is introduced between
the plates, the capacitance becomes 15
( mu mathrm{F} . ) The permittivity of the medium in
( C^{2} N^{-1} m^{-2} ) is
A . ( 8.15 times 10^{-11} )
В. ( 0.44 times 10^{-10} )
C . ( 15.2 times 10^{12} )
D. ( 1.6 times 10^{-14} )
12
301Electric Potential on the surface of a
charged spherical shell of radius ( 10 mathrm{cm} )
is 50 volt. Find the value of electric
potential at a distance of ( 20 mathrm{cm} ) from the center of spherical shell.
12
302A conductor ( A ) is given a charge of
amount ( +mathrm{Q} ) and then placed inside a deep metal cab ( mathrm{B} ), without touching it:
This question has multiple correct options
A. the potential of A does not change when it is placed inside
B. if B is earthed, ( +Q ) amount of charge will flow from it into the earth
( mathrm{C} ). if ( mathrm{B} ) is earthed, the potential of ( mathrm{A} ) will be reduced
D. either(b) or (c) are true, or both are true only if the outer surface of B is connected to the earth and not its
inner surface
12
303If we increase the distance between two
plates of the capacitor, the capacitance will
A. decrease
B. remain same
c. increase
D. first decrease then increase
12
304Define energy density of the median surrounding a charged conductor and state its formula.12
305Two parallel metal plates having charges ( +Q ) and ( -Q ) face each other at a certain distance between them. If the
plates are now dipped in kerosene oil tank, the electric field between the
plates will :
A. become zero
B. increase
c. decrease
D. remains same
12
306UUUOOO
70. The capacitor of an oscillatory circuit of frequency 10000
is enclosed in a container. When the containeris evacuated the
frequency changes by 50 Hz, the dielectric constant of the gas
(a) 1.1
(b) 1.01
(c) 1.001
(d) 1.0001
12
307A charge ( +q ) is placed at the origin 0 of
( X-Y ) axes as shown in the figure. The
work done in taking a charge ( Q ) from ( A )
to B along the straight line AB is:
A ( cdot frac{q Q}{4 pi epsilon_{0}}left(frac{a-b}{a b}right) )
В ( cdot frac{q Q}{4 pi epsilon_{0}}left(frac{b-a}{a b}right) )
c. ( frac{q Q}{4 pi epsilon_{0}}left(frac{b}{a^{2}}-frac{1}{b}right) )
D. ( frac{q Q}{4 pi epsilon_{0}}left(frac{a}{b^{2}}-frac{1}{b}right) )
12
308Illustrate a condition in which :
Electric field is zero but potential is not
zero.
12
What happens to the charge on the
plates, the voltage across the plates,
and the capacitance of the capacitor as
a result of moving the plates closer
together?
( A )
begin{tabular}{|l|l|}
hline multicolumn{1}{|c|} { Capacitor } & Values after Plates are Moved Closer Together \
hline Charges on Plates & same \
Voltage Across Plates Capacitance & larger larger \
hline
end{tabular}
B. begin{tabular}{|l|l|}
hline multicolumn{1}{|c|} { Capacitor } & Values after Plates are Moved Closer Together \
hline Charges on Plates & same \
Voltage Across Plates & smaller \
Capacitance & larger \
hline
end{tabular}
( c )
begin{tabular}{|l|l|}
hline multicolumn{1}{|c|} { Capacitor } & Values after Plates are Moved Closer Together \
hline Charges on Plates & larger \
Voltage Across Plates Capacitance & same same \
hline
end{tabular}
D. begin{tabular}{|l|l|}
hline multicolumn{1}{|c|} { Capacitor } & Values after Plates are Moved Closer Together \
hline Charges on Plates & larger \
Voltage Across Plates & same \
Capacitance & larger \
hline
end{tabular}
E begin{tabular}{|l|l|}
hline multicolumn{1}{|c|} { Capacitor } & Values after Plates are Moved Closer Together \
hline Charges on Plates & larger \
Voltage Across Plates Capacitance & larger larger \
hline
end{tabular}
12
310A condenser is charged and then battery is removed. A dielectric plate is put
between the plates of condenser, then correct statement is
A. Q is constant, v and U decrease
B. Q is constant, V increases U decreases
c. Q increases, v decreases U increases
D. ( Q, v ) and ( U ) increase
12
311in fig consists of two horizontal
conducting plates of equal area A. The
bottom plate rests on a fixed support and the top plate is suspended by four springs with spring constant ( mathrm{k} )
positioned at each of the four corners of
the plate as shown in Fig. When uncharged, the plates are separated by
a distance ( z_{0} . ) A battery is connected to the plates and produces a potential difference V between them. This causes
the plate separation to decrease to z.
Neglect any fringing effects. Find the condition of stable equilibrium:
A. z shall have positive root
B. z shall negative root
c. no dependence on value of ( z )
D. none of these
12
312Define the term electric potential. State
its S.I. unit.
12
313Which of the following is not showing the essential difference between
electrostatic shielding by a conducting shell and magnetostatic shielding?
A. Electrostatic field lines can end on charges and conductors have free charges
B. Magnetic field lines can end but conductors cannot end them.
c. Lines of magnetic field cannot end on any material and perfect shielding is not possible.
D. shells of high permeability materials can be used to divert lines of magnetic field from the interior region
12
314The capacitance of a capacitor becomes ( frac{7}{6} ) times its original value if a dielectric slab of thickness, ( t=frac{2}{3} d ) is introduced in
between the plates. ( d ) is the separation
between the plates. The dielectric
constant of the dielectric slab is:
( mathbf{A} cdot frac{14}{11} )
B. ( frac{11}{14} )
( c cdot frac{7}{11} )
D. ( frac{11}{7} )
12
315A spherical body P has a positive charge on it. It attracts an another sphere ( mathrm{Q} )
placed near it. The sphere ( Q ) is
A. negatively charge
B. positively charge
c. neutral
D. may be negative or neutral
12
316See the diagram. Area of each plate is
( 2.0 m^{2} ) and ( d=2 times 10 times 10^{-3} m . )
charge of ( 8.85 times 10^{-8} C ) is given to ( Q )
Then the potential of ( Q ) becomes:
( mathbf{A} cdot 13 V )
B. 10v
c. ( 66.7 mathrm{V} )
D. ( 8.825 v )
12
317A capacitor of capacitance ( C=4 mu F ) is
connected as shown in figure. If internal resistance of the cell is ( 0.5 . ) The charge
on the capacitor plates is
A. zero
3. ( 8 mu ) C
( c cdot 4 mu C )
( D cdot 6 mu C )
12
318A metallic sphere of radius ( 18 mathrm{cm} ) has
been given a charge of ( 5 times 10^{-6} ) C. The
energy of the charged conductor is:
A. 0.25
J ( J )
в. 0.6 .5
c. ( 1.2 J )
D. 2.4J
12
319Three identical capacitors, each of capacitance ( C, ) are connected in series
with a battery of emf ( V ) and get fully charged. Now, the battery is removed and the capacitors are connected in
parallel with positive terminals are one point and negative terminals at other point. Then, the common potential will be :
A. ( V )
в. ( 3 V )
c. ( frac{V}{3} )
D.
12
320Given that ( boldsymbol{E}=left(left(mathbf{3} boldsymbol{x}^{2}+boldsymbol{y}right) hat{boldsymbol{i}}+right. )
( boldsymbol{x} hat{boldsymbol{y}}) boldsymbol{k} boldsymbol{V} / boldsymbol{m}, ) find the work done in
moving a ( -2 mu C ) charge from (0,5,0) to (2,-1,0) by taking the path:
( boldsymbol{y}=mathbf{5}-mathbf{3} boldsymbol{x} )
A . ( 12 J )
в. ( 12 m J )
( mathbf{c} cdot 12 k J )
D. ( 12 mu J )
12
321Three particles, each having a charge of ( 10 mu C ) are placed at the corners of an
equilateral triangle of side ( 10 mathrm{cm} ). The electronic potential energy of the system is: ( left(text { Given } frac{1}{4 pi varepsilon_{0}}=9 times 10^{9} N-right. )
( left.m^{2} / C^{2}right) )
A. Zero
B. Infinite
c. 27
D. ( 100 J )
12
322Which of the following statements is
false for a perfect conductor?
A. The surface of the conductor is an equipotential surface.
B. The electric field just outside the surface of a conductor is perpendicular to the surface.
C. The charge carried by a conductor is always uniformly distributed over the surface of the conductor
D. None of these
12
323Calculate the ratio of the equivalent capacitance of the circuit when two identical capacitors are in series to that when they are in parallel?
A ( cdot frac{1}{4} )
B. ( frac{1}{2} )
c.
D. 2
E . 4
12
324A quantity ( X ) is given by ( epsilon_{0} L frac{Delta V}{Delta T} ) where so is the permittivity of the free space, is a length. ( Delta V ) is a potential difference
and ( Delta t ) is a time interval. The
dimensional formula for ( X ) is the same
as that of
A . resistance
B. charge
c. voltage
D. current
12
325Two circular plates of radius ( R ) are kept
at distance ( h ) to make a parallel plate capacitor as shown in the figure. Then the capacitance of this capacitor is:
A ( cdot frac{varepsilon_{0} pi R^{2}}{h} )
B. ( frac{varepsilon_{0} 2 pi R}{h} )
c. ( frac{2 varepsilon_{0} 2 pi R^{2}}{h} )
D. none of these
12
326In order to increase the capacity of
parallel plate condenser one should introduce between the plates, a sheet of
A . mica
B. tin
c. copper
D. stainless steel
12
327The electric potential at a point in free space due to a charge ( Q ) coulomb is ( Q times 10^{11} mathrm{V} . ) The electric field at that
point is:
A . 12 ( pi varepsilon_{0} Q times 10^{22} mathrm{Vm}^{-1} )
В . ( 4 pi varepsilon_{0} Q times 10^{22} V m^{-1} )
C . ( 12 pi varepsilon_{0} Q times 10^{20} mathrm{Vm}^{-1} )
D. ( 4 pi varepsilon_{0} Q times 10^{20} V m^{-1} )
12
328Four charges, all of the same magnitude placed at the four corners of a square. At centre of the square, the
potential is ( V ) and the field is ( E . B y ) suitable choices of the signs of four charges, which of the following can be obtained?
This question has multiple correct options
A. ( V=0, E=0 )
B. ( V=0, E neq 0 )
c. ( V neq 0, E=0 )
D. ( V neq 0, E neq 0 )
12
329In hydrogen atom electron of charge ( -e ) and mass m revolves round the nucleus
in a circular orbit of radius r. The
electrostatic potential energy of the electron is ( frac{1}{4 pi varepsilon_{0}} ) times
A ( cdot frac{-e}{r} )
B. ( frac{-e^{2}}{r} )
c. ( frac{e^{2}}{r} )
D. ( frac{-m e^{2}}{r} )
12
330An elliptical cavity is carved out in a
perfect conductor. A positive charge q is placed at the centre of the cavity. The points ( A ) and ( B ) are shown in figure. Then
This question has multiple correct options
A. electric field near A in the cavity = electric field near in the cavity
B. charge density at ( A= ) charge density at ( B )
C. potential at ( A= ) potential at ( B )
D. total electric field flux through the surface of the cavity ( =frac{q}{varepsilon_{0}} )
12
331Identical metal plates are located in air at equal distance ( d ) from one another
The area of each plate is equal to ( A ). If
the capacitance of the system between ( P ) and ( Q ) if the plates are interconnected
as shown in the figure is given as ( frac{x}{3} varepsilon_{0} frac{A}{d} ) Find ( x: )
12
332True or False :
Three positive (red) and three negative
(blue) point charges are arranged
symmetrically around a circle centered
on point ( P ) as shown in the diagram. Al
point charges are of the same
magnitude.
Electric Field at ( mathrm{P} ) will be zero while
electric potential at point ( P ) will be non
zero.
A. True
B. False
12
below. All point charges are of the same
magnitude.

Which table gives the best description
of the electric field at point ( P ) and the
electric potential at point P?
A. Electric Field at ( mathrm{P} ) – Electric Potential at ( mathrm{P} ), zero – zero
B. Electric Field at ( P ) – Electric Potential at ( P ), zero –
negative
C. Electric Field at ( P ) – Electric Potential at ( P ), downward
downward
D. Electric Field at ( P ) – Electric Potential at ( P ), downward
negative
E. Electric Field at ( mathrm{P} ) – Electric Potential at ( mathrm{P} ), negative –
zero

12
334For an irregularly shaped charged
conductor the potential is :
A. more at the flat parts
B. more at the spherical parts
C. more at the sharp edges
D. same everywhere
12
335A parallel plate capacitor with circular
plates and a capacitance ( C ) has the
radius of each plate doubled and the
distance between the plates doubled.
What is the new capacitance?
( ^{A} cdot frac{C}{2} )
в. ( C )
( c cdot 2 C )
D. ( 4 C )
12
336Air filled capacitor of capacitance ( 2 mu boldsymbol{F} )
is filled with three dielectric material of
dielectric constants ( boldsymbol{K}_{mathbf{1}}=mathbf{4}, boldsymbol{K}_{mathbf{2}}= )
4 and ( K_{3}=6 ) as shown in the figure.
The new capacitance of the capacitors
is
( mathbf{A} cdot 50 mu F )
в. ( 2 mu F )
( c cdot 20 mu F )
D. ( 10 mu F )
12
337:12
338The potential at ( P ) due to induced
charge is
( ^{text {A }} cdot_{K q}left(frac{1}{r_{1}}-frac{1}{r_{2}}right) )
в. ( _{K q}left(frac{1}{r_{1}}+frac{1}{r_{2}}right) )
( ^{text {c. }} K qleft(-frac{1}{r_{1}}+frac{1}{r_{2}}right) )
D. ( frac{K q}{r_{1}} )
12
339Figure shows three circular arcs, each of radius ( R ) and total charge as
indicated. The net electric potential at
the center of curvature is :
( ^{A} cdot frac{Q}{2 pi varepsilon_{0} R} )
( B )
c. ( frac{3 Q}{32 pi varepsilon_{0} R} )
D. none of these
12
340On moving a charge of 20 coulombs by ( 2 mathrm{cm}, 2 mathrm{J} ) of work is done, then the potential difference between the points is:
A . ( 0.1 mathrm{v} )
B. 8
( c cdot 2 v )
D. 0.5
12
341(a) A conductor ( A ) with a cavity as
shown in Fig. ( (a) ) is given a charge ( Q ) Show that the entire charge must
appear on the outer surface of the
conductor.
(b) Another conductor ( B ) with charge ( q )
is inserted into the cavity keeping ( boldsymbol{B} )
insulated from ( A . ) Show that the total
charge on the outside surface of ( boldsymbol{A} ) is
( boldsymbol{Q}+boldsymbol{q} )
(c) A sensitive instrument is to be
shielded from the strong electrostatic fields in its environment.
Suggest a possible way.
( (mathbf{a}) )
( mathbf{b} )
12
342A charge ( +q ) is fixed at each of the
points ( boldsymbol{x}=boldsymbol{x}_{0}, boldsymbol{x}=mathbf{3} boldsymbol{x}_{0}, boldsymbol{x}=mathbf{5} boldsymbol{x}_{0} dots dots ) up
to infinity on ( x ) axis and a charge ( (-q) ) is
fixed on each of points of ( boldsymbol{x}=mathbf{2} boldsymbol{x}_{0}, boldsymbol{x}= )
( mathbf{4} boldsymbol{x}_{0}, boldsymbol{x}=boldsymbol{6} boldsymbol{x}_{0} ldots ldots . . ) up to infinity, here ( boldsymbol{x}_{mathbf{0}} )
is a positive constant. Take the potential at a point due to a charge ( Q ) at a distance ( r ) from it ( frac{Q}{4 pi varepsilon_{0} r}, ) then the potential at the origin due to above
system of charges will be :
A . 0
B. ( infty )
c. ( frac{q log _{e} 2}{4 pi varepsilon_{a}} )
D. ( frac{q}{8 pi varepsilon_{0} x_{0} log _{e} 2} )
12
343On removing the dielectric from a charged condenser, its energy
A. increase
B. remains unchanged
c. decreases
D. none of these
12
344A capacitor acquires a potential
difference of ( 200 mathrm{V} ) when ( 10^{12} ) electrons
are taken from one plate and placed
on the other plate. Its capacitance is:
A ( cdot 2 times 10^{-10} F )
В. ( 4 times 10^{-10} F )
c. ( 8 times 10^{-10} F )
D. ( 12 times 10^{-10} F )
12
is earthed. ( C ) is the common center of ( A )
and ( B . ) Study the following statements.
Which of the following statements are
correct?

The potential at a distance ( r ) from ( C ) where ( a leq r leq b, i s frac{1}{4 pi varepsilon_{0}}left(frac{Q}{r}right) )
i. The potential difference between ( A ) and
( B ) is ( frac{1}{4 pi varepsilon_{0}} Qleft(frac{1}{a}-frac{1}{b}right) )
iii. The potential at a distance ( r ) from ( C ) where ( a leq r leq b, i s frac{1}{4 pi varepsilon_{0}} Qleft(frac{1}{a}-frac{1}{b}right) )
A. Only (i) and (ii)
B. Only (ii) and (iii)
c. only (i) and (iii)
Dhe above

12
346Assertion
Two equipotential surfaces cannot cut
each other.
Reason
Two equipotential surfaces are paralle
to each other.
A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
C. If Assertion is correct but Reason is incorrect.
D. If Assertion is incorrect but Reason is correct.
12
347An alpha particle of ( 5 mathrm{MeV} ) at a large
distance proceeds towards a gold nucleus ( (Z=79) ) to make a head on
collision. The closest distance of
approach from the centre of gold nucleus
is:
A. ( 20 f m )
B. 15 fm
c. ( 10 f m )
D. 45 fm
12
348Two circular plates of radius ( 0.1 mathrm{m} ) are used to form a parallel plate capacitor
if displacement current between the
plates is ( 2 pi ) ampere, then find
magnetic field produced by
displacement current ( 4 mathrm{cm} ) from the
axis of the plates.
12
349Charges of ( +frac{10}{3} times 10^{-9} C ) are placed at each of the four corners of a square of
side ( 8 mathrm{cm} . ) The potential at the intersection of the diagonals is
A. ( 150 sqrt{2} ) volt
в. ( 1500 sqrt{2} ) volt
c. ( 900 sqrt{2} ) volt
D. 900 volt
12
350A capacitor of ( 10 mu F ) charged upto ( 250 mathrm{V} ) is connected in parallel with another capacitor of ( 5 mu F ) charged upto ( 100 mathrm{V} ) The common potential is :
A . 200
B. 300
c. ( 400 mathrm{v} )
D. 500
12
351Find identical capacitor plates, each of
area ( A, ) are arranged such that adjacent
plates are at a distance ( ^{prime} d^{prime} ) apart, the
plates are connected to a source of emf
( V ) as shown in figure. The charge on
plate 1 is and that on
plate 4 is
12
352Three charges ( +q,-q ) and ( -q ) are kept at
the vertices of an equilateral triangle of ( 10 mathrm{cm} ) side. The potential at the mid point in between ( -q,-q, ) if ( q=5 mu C ) is :
A . ( -6.4 times 10^{5} V )
B. ( -12.8 times 10^{4} V )
c. ( -6.4 times 10^{4} V )
D. ( -12.8 times 10^{5} V )
12
353Two conducting spheres, each given a
charge ( q ) are kept far apart as shown. The amount of charge that crosses the
switch ( S_{1}, ) where it is closed, is (the
connection between the spheres is
conducting)
A . ( underline{q} ) 3
в. ( frac{2 q}{3} )
( c cdot frac{3 q}{4} )
D. Zero
12
354Two positive charges ( q ) and ( q ) are placed at
the diagonally opposite corners of a square and two negative charges ( -q ) and
( -q ) are placed at the other two corners of the square. Then at the centre of the square the resultant electric intensity and the net electric potential Vare
A. ( E neq 0, V=0 )
в. ( E=0, V=0 )
c. ( E=0, V neq 0 )
D. ( E neq 0, V neq 0 )
12
355The maximum and minimum resultant
capacity that can be obtained with ( 2 mu F, 3 mu F ) and ( 6 mu F ) are respectively:
A. ( 11 mu F, 1 mu F )
в. ( 11 mu F, 6 mu F )
c. ( 11 mu F, 2 mu F )
D. ( 11 mu F, 4 mu F )
12
356What amount of work is done in moving a charge of 4 coulombs from a point 220 volts to a point at 230 volts?12
357A parallel plate capacitor of capacitance ( 6 mu F ) in air and ( 60 mu F ) When dielectric is introduced. What is
the dielectric constant of the medium.?
A . 0.4
в. 0.1
c. 0.77
D. 0.25
12
358In the electric field of charge ( Q, ) another charge is carried from ( A ) to ( B . A ) to ( C, A ) to
Dand A to E, then work done will be
A. minimum along path AB
c. minimum along path AE
D. zero along all the paths
12
359The capacitors of three capacities are in
the ratio ( 1: 2: 3 . ) Their equivalent capacity when connected in parallel is ( frac{60}{11} mu F ) more
than that when connected in series. The
individual capacities are :
( A cdot 4,6,7 )
B. 1,2,3
c. 2,3,4
D. 1,3,6
12
360The electric field at a distance ( frac{3 R}{2} ) from
the centre of a charged conducting spherical shell of radius ( mathrm{R} ) is ( mathrm{E} ). The electric field at a distance ( frac{boldsymbol{R}}{mathbf{2}} ) from the centre of the sphere is :
A. zero
B. E
c. ( frac{E}{2} )
D. ( frac{E}{3} )
12
361Equipotentials surfaces are shown in
figure a and b. The field is uniform in
A . a only
B. b only
( c cdot a ) and ( b )
D. none
12
362A dense sphere of mass ( M ) is placed at
the centre of a circle of radius ( R ). Find
the work done, when a particle of mass
( m ) is brought from ( A ) to ( B ) along a circle
as shown in the figure.
A . zer
в. ( frac{G M m}{R} )
c. ( -frac{G M m}{R} )
D. ( frac{2 G M m}{B} )
12
363Two condensers of capacities ( 10 mu F ) and ( 20 mu F ) have potential differences of ( 20 mathrm{V} )
and ( 10 mathrm{V} ) respectively. The total charge is
A ( .200 mu C )
в. ( 600 mu C )
c. ( 400 mu C )
D. zero
12
364An isolated conducting sphere whose radius ( R=1 m ) has a charge ( q=frac{1}{9} n C )
The energy density at the surface of the
sphere is:
A ( cdot frac{varepsilon_{0}}{2} J / m^{3} )
B . ( varepsilon_{0} J / m^{3} )
( mathbf{c} cdot 2 varepsilon_{0} J / m^{3} )
D. ( frac{varepsilon_{0}}{3} J / m^{3} )
12
365In the arrangement shown in fig. plate has a charge equal to ( 60 mu C ) The ratio
( d_{1} / d_{2} ) is ( 2 . ) Then
( q_{1}=_{-} )
( q_{2}=_{-}– )
( mathbf{q}_{3}=_{-}- )
( boldsymbol{q}_{4}=_{-}– )
( boldsymbol{q}_{5}=– )
( boldsymbol{q}_{6}=_{-}- )
12
366In the given circuit the potential at
point ( boldsymbol{E} ) is:
A. Zero
B. ( -8 V )
( c cdot-frac{4}{3} V )
( D cdot underline{4}-v )
12
367Two points ( P ) and ( Q ) are maintained at
the potential of ( 10 ~ V ) and ( -4 V )
respectively. The work done in moving
100 electrons from ( P ) to ( Q ) is:
A. ( -19 times 10^{-7} J )
( J )
В. ( 9.60 times 10^{-17} J )
c. ( -2.24 times 10^{-16} J )
D. 2.24 ( times 10^{-16} mathrm{J} )
12
368Three capacitances, each of ( 3 mu F, ) are provided. These cannot be combined to
provide the resultant capacitance of :
A ( .1 mu F )
в. ( 2 mu F )
c. ( 4.5 mu F )
D. ( 6 mu F )
12
369For the given circuit, select the correct
alternative(s)
This question has multiple correct options
A. The equivalent capacitance between points ( 1 & 2 ) is
( frac{15 C}{11} )
B. The equivalent capacitance between points ( 3 & 6 ) is ( frac{5 C}{3} )
C. The equivalent capacitance between points ( 1 & 3 ) is ( frac{15 C}{14} )
D. The equivalent capacitance between points 3 & 5 is
( frac{14 C C}{15} )
12
370Figure shows equi-potential surfaces
for a two charges system. At which of
the labeled points point will an electron
have the highest potential energy?
A. Point ( A )
B. Point ( B )
( c . ) Point ( C )
D. Point ( D )
12
371Three identical large metal plates of
area ( A ) are small at distances ( d ) and ( 2 d )
from each other. Top metal plate is
uncharged, while the other metal plates
have charges ( +Q ) and ( -Q . ) Top and
bottom metal plates are connected by
switch ( S ) through a resistor of unknown
resistance. What energy (in mJ) is dissipated in the resistor when switch
is closed?
(given: ( left.frac{epsilon_{0} A}{d}=6 mu F, Q=60 mu Cright) )
12
372When a dielectric slab of thickness ( 4 mathrm{cm} )
is introduced between the plates of parallel plate condenser, it is found that
the distance between the plates has to be
increased by ( 3 mathrm{cm} ) to restore the capacity to it’s original value. The dielectric
constant of the slab is
A ( cdot frac{1}{4} )
B. 4
( c .3 )
D.
12
373joule coulomb ( ^{-1} ) is same as12
374When an additional charge of ( 2 C ) is given to a capacitor, energy stored in it is increased by ( 21 % ). The original charge of the capacitor is :
A . ( 30 mathrm{c} )
B. ( 40 mathrm{c} )
c. ( 10 c )
D. ( 20 mathrm{c} )
12
375In the electric field due to a point
charge ( boldsymbol{q}, ) a test charge is carried from
( A ) to the points ( B, C, D ) and ( E ) lying on
the same circle around ( q ). The work done
is
A. the least along ( A B )
B. the least along ( A D )
C. zero along any one of the paths ( A B, A D, A C ) and ( A E )
D. the least along ( A E ).
12
376Given the arrangement of charge below and the point ( P, ) what do we know for sure?
The distance between adjacent charges is the same for all and the same as the
distance from the nearest charges to
point ( P )
A. The electric potential at point ( P ) is positive.
B. The electric potential at point ( P ) is negative.
c. The electric potential at point ( P ) is directed down and to the right.
D. The electric potential at point P is directed up and to the left
E. The electric potential at point P is zero.
12
377To obtain ( 3 mu F ) capacity from three
capacitors of ( 2 mu F ) each, they will be
arranged as follows:
A. all the three in series
B. all the three in parallel
C. two capacitors in series and the third in parallel with the combination of first two
D. two capacitors in parallel and the third in series with the combination of first two
12
378Three charges ( Q,+q ) and ( +q ) are placed
at the vertices of a right-angled
isosceles triangle as shown.The net
electrostatic energy of the
configuration is zero if ( Q ) is equal to :
A ( cdot frac{-q}{1+sqrt{2}} )
B. ( frac{-2 q}{2+sqrt{2}} )
( c cdot-2 q )
( D cdot+a )
12
379Now consider two identical infinite
cylinders, parallel to each other, posed at a distance ( d>2 a ). Find the potential
energy of the system (per unit length)
( ^{mathrm{A}} cdot frac{-pi rho^{2} a^{4}}{2 epsilon_{0}}left(log frac{d}{a}+0.25right) )
( ^{mathbf{B}} cdot frac{-pi rho^{2} a^{4}}{2 epsilon_{0}}left(log frac{d}{a}+0.5right) )
( ^{mathbf{C}} cdot frac{-pi rho^{2} a^{4}}{2 epsilon_{0}}left(log frac{d}{a}+0.75right) )
( ^{mathrm{D} cdot} frac{-pi rho^{2} a^{4}}{2 epsilon_{0}}left(log frac{d}{a}+1right) )
12
380When a ( 2 mu mathrm{C} ) charge is carried from point ( A ) to point ( B, ) the amount of work done by the electric field is ( 50 mu ). What
is the potential difference and which point is at a higher potential?
A ( .25 V, B )
в. ( 25 V, A )
( c cdot 20 V, B )
D. Both are at same potential
12
381A variable air capacitor has 11 movable plates and 12 stationary plates, The
area of each plate is ( 0.0015 m^{2} ) and
separation between opposite plates is ( 0.001 m . ) The maximum capacitance of
the capacitor is
A . ( 292.2 F )
В. ( 292.2 mathrm{mF} )
c. ( 292 mu F )
D. 292 p
12
382A positively charged sphere suspended with a silk thread is slowly pushed in a
metal bucket. After its insertion the lid
is closed. What will be the electric field
intensity inside when the sphere has touched the bucket?
( (sigma ) is the surface charge density of sphere)
A. zero
в. ( frac{sigma}{2 varepsilon_{0}} )
c. ( frac{sigma}{varepsilon_{0}} )
D. None of these
12
383A silicon diode has a “knee voltage of
threshold voltage” value of ( 0.7 mathrm{V} ). This ( mathrm{Si} )
diode is connected in a circuit as shown
in the figure

Potential ( V_{0} ) of point ( p ) in the circuit will
be:
A . ( -0.44 v )
B. 0.44V
c. ( 4.4 v )
( D,-4,4rangle )

12
384What is the capacity of a conductor?
Explain the principle of a capacitor
12
385Three charges, each ( +q ), are placed at
the corners of an isosceles triangle
( A B C ) of sides ( B C ) and ( A C, 2 a . D ) and ( E )
are the mid points of ( B C ) and ( C A ). The
work done in taking a charge ( Q ) from ( D )
to ( boldsymbol{E} ) is :
A ( cdot frac{e q Q}{8 pi epsilon_{0} a} )
в. ( frac{q Q}{4 pi epsilon_{0} a} )
c. zero
D. ( frac{3 q Q}{4 pi epsilon_{n} a} )
12
386The figure shows two identical paralle plate capacitors connected to a battery
with the switch ( S ) closed. The switch is
now opened and the free space between
the plates of the capacitors is filled with
a dielectric of dielectric constant (or
relative permittivity) 3.Find the ratio of
the total electrostatic energy stored in both capacitors before and after the
introduction of the dielectric.
( A cdot frac{2}{3} )
B . 5 ( overline{3} )
( c cdot 3 )
( overline{5} )
( D cdot 3 )
( overline{2} )
12
387The negative charge ( -q_{2} ) is fixed while
positive charge ( q_{1} ) as well as the
conducting sphere ‘S’ is free to move. If
the system is released from rest (the
total charge on ( mathrm{S} ) being zero.
A. Both S and ( q_{1} ) move towards left
B. ( q_{1} ) moves towards right while ( S ) moves towards left.
C ( cdot q_{1} ) remains at rest, ( S ) moves towards left
D. Both ( q_{1} ) and ( S ) remain at rest
12
388An electric dipole is placed at the centre of a sphere, choose the correct options:
A. electric field is zero at every point on the surface
B. flux is zero across the surface
C. no circle is present in the sphere which is equipotentia
D. none of the above
12
389In the given figure, the work done in taking the charge q from M to N is
( mathbf{A} cdot frac{2 k q Q}{a} )
B. ( frac{2 sqrt{2} k q Q}{a} )
c. ( frac{sqrt{2} k q Q}{a} )
D. zer
12
390Define electric potential due to a point charge and arrive at the expression for the electric potential at a point due to a point charge in its vicinity.12
391The equivalent capacitance between ( mathrm{P} )
and ( Q ) of the given figure is (the capacitance of each capacitor is1 ( mu F ) ):
( A cdot 2 mu F )
B. ( 0.5 mu F )
( c cdot 5 mu F )
D. ( 0.2 mu F )
12
392The electrostatic potential energy of two point charges, ( 1 mu C ) each, placed 1 meter apart in air is?
( begin{array}{l}text { A } cdot 9 times 10^{3} \ text { j }end{array} times 10^{times 10} )
В. ( 9 times 10^{9} ),
12
393Five identical conducting plates, 1.2,3,4 and 5 are fixed parallel plates equidistant from each other (see
figure). A conductor connects plates 2
and 5 while another conductor joins 1
and 3. The junction of 1 and 3 and the plate 4 are connected to a source of
constant emf ( V_{o} ). Find the effective
capacitance of the system between the terminals of source where ( d ) is the
distance between any two successive
plates
12
394Four metallic plates are arranged as
shown in the figure. If ( d ) is the distance
between each plate then capacitance of
the given system between points ( A ) and
( B ) is :
( (operatorname{given} boldsymbol{d}<<boldsymbol{A}) )
( mathbf{A} cdot frac{epsilon_{0} A}{d} )
B. ( frac{2 epsilon_{0} A}{d} )
c. ( frac{3 epsilon_{0} A}{d} )
D. ( frac{4 epsilon_{0} A}{d} )
12
395If two electric charges ( q ) and ( -2 q ) are
placed at distance ( 6 a ) apart, then locus
of point in the plane of charges, where electric potential is zero is: (Take
charge ( q ) at origin and ( -2 q ) lies on positive ( x ) -axis
A. ( x^{2}+y^{2}+4 a x-6 a^{2}=0 )
B . ( x^{2}+y^{2}+4 a x-12 a^{2}=0 )
c. ( x^{2}+y^{2}+2 a x-12 a^{2}=0 )
D. ( x^{2}+y^{2}-4 a x+12 a^{2}=0 )
12
396Assertion
A point charge ( q ) is placed in front of a
solid conducting sphere. Electric field due to induced charges at the centre of
sphere is zero.
Reason
Electric field at point inside the solid
body of conductor is zero.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
12
397When dielectric medium of constant
is filled between the plates of a charged parallel-plate condenser, then the energy stored becomes, as compared to its previous value,
( mathbf{A} cdot K^{-3} )times
B. ( K^{-2} )times
c. ( K^{-1} )times
D. Ktimes
12
398If electric intensity ( vec{E} ) is along the ( X )
axis, then the equipotential surfaces are parallel to
A. xor plane
B. x0Z plane
c. YOZ plane
D. None of these
12
399A parallel-plate air condenser of plate
area ( A ) and separation d is charged to
potential ( V ) and then the battery is
removed. Now a slab of dielectric
constant ( k ) is introduced between the
plates. If ( Q, E ) and ( W ) denote respectively the magnitude of charge on each plate, the electric field between the plates
(after introduction of dielectric slab)
and work done on the system in the process of introducing the slab, then This question has multiple correct options
A ( cdot W=frac{varepsilon_{0} A V h^{2}}{2 d}(1-1 / k) )
( ^{mathbf{B}} cdot Q=frac{varepsilon_{0} K A V}{d} )
( ^{mathbf{C}} cdot Q=frac{varepsilon_{0} A V}{d} )
D. ( quad E=frac{V}{k d} )
12
400A positive point charge q is carried from a point B to a point A in the electric field of a point charge ( +mathrm{Q} ) held at ( 0 . ) If the
permittivity of free space is ( epsilon_{0} ) and ( 0 A=a ) and ( 0 mathrm{B}=mathrm{b}, ) the work done in the process is given by :
A. ( frac{q Q}{4 pi epsilon_{0}}left(frac{1}{a}+frac{1}{b}right) )
в. ( frac{q Q}{4 pi epsilon_{0}}left(frac{1}{a}-frac{1}{b}right) )
c. ( frac{q Q}{4 pi epsilon_{0}}left(frac{1}{a^{2}}-frac{1}{b^{2}}right) )
D. ( frac{q Q}{4 pi epsilon_{0}}left(frac{1}{a^{2}}+frac{1}{b^{2}}right) )
12
401A parallel plate capacitor is to be designed with a voltage rating ( 1 mathrm{kV} ) using a material of dielectric constant
3 and dielectric strength about ( mathbf{1 0}^{mathbf{7}} boldsymbol{V} boldsymbol{m}^{-1} . ) (Dielectric strength is the
maximum electric field a material can
tolerate without breakdown, i.e., without
starting to conduct electricity through partial ionisation.) For safety, we should like the field never to exceed, say ( 10 % ) of the dielectric strength.What minimum area of the plates is required to have a capacitance of 50 pF ?
12
402The electric field due to the electric
potential ( V=left(2 x^{2}-4 xright) ) is
( mathbf{A} cdot(4 x+4) hat{i} )
B. ( (4 x-4) hat{i} )
c. ( (-4 x+4) hat{i} )
D. ( (-4 x-4) hat{i} )
12
403A uniform electric field of magnitude ( mathbf{1 0 0} V / boldsymbol{m} ) in space is directed along the
line ( y=3+x . ) Find the electric
potential difference between (1,3) and (3,1)
A. ( 100 V )
в. ( 200 sqrt{2} V )
c. ( 200 V )
D.
12
404Find ( left|V_{B A}right| ) if ( 12 J ) of work has to be done
against an electric field to take a
charge of ( 10^{-2} C ) from ( a ) to ( b )
12
405A point charge ( q ) is brought form infinity
and is placed at the centre of a
conducting neutral spherical shell of
inner radius ( a ) and outer radius ( b, ) then
work done by external agent is:
( A )
B. ( frac{k q^{2}}{2 b} )
c. ( frac{k q^{2}}{2 b}-frac{k q^{2}}{2 a} )
D. ( frac{k q^{2}}{2 a}-frac{k q^{2}}{2 b} )
12
406Two identical air filled parallel plate
capacitors are charged to the same
potential in the manner shown by closing the switch S. If now the switch is opened and the space between the plates is filled with a dielectric of
relative permittivity ( varepsilon_{r}, ) then :
A. The potential difference as well as charge on each capacitor goes up by a factor ( varepsilon_{r} )
B. The potential difference as well as charge on each capacitor goes down by a factor ( varepsilon_{r} )
c. The potential difference across A remains constant and the charge on B remains unchanged
D. The potential difference across B remains constant while the charge on A remains unchanged
12
407Two point charges ( 2 C ) and ( -1 C ) are
placed at ( boldsymbol{x}=mathbf{0} ) and ( boldsymbol{x}=boldsymbol{6} ) respectively.
The potential will be zero at points:
A. ( x=2,-2 )
в. ( x=1,5 )
c. ( x=4,12 )
D. ( x=2,9 )
12
408Three charges ( 2 q,-q ) and ( -q ) are located at the vertices of an equilateral triangle. At the centre of the triangle:
A. the field is zero but potential is non-zero
B. the field is non-zero, but potential is zero
c. both field and potential are zero
D. both field and potential are non-zero
12
409A capacitor of capacitance ( C ) is charged to a potential difference V from a cell and
then disconnected from it. A charge +Q is now given to its positive plate. The potential difference across the capacitor
is now:
A. ( V )
B. ( V+frac{Q}{C} )
( c cdot V+frac{Q}{2 C} )
D. ( V-frac{Q}{C}, ) if ( V<C V )
12
410Write the definition of electric potential. Calculate the electric potential due to a point charge ( Q ) at a distance ( r ) from it. Draw a graph between electric potential Vand distance r for a point charge ( Q )12
411A spark is produced between two insulated surfaces maintained at a
potential difference of ( 5 times 10^{6} V . ) If the
energy output is ( 10^{-5} J ), the charge
transferred during the spark is :
A ( cdot 5 times 10^{11} C )
В. ( 5 times 10^{-11} C )
C ( cdot 2 times 10^{12} C )
D. ( 2 times 10^{-12} C )
12
412A hexagon of side ( 8 mathrm{cm} ) has a charge 4
( mu C ) at each of its vertices. The potentia
at the centre of the hexagon is
A ( cdot 2.7 times 10^{6} mathrm{v} )
B ( .7 .2 times 10^{11} mathrm{v} )
C ( .2 .5 times 10^{12} mathrm{v} )
D. ( 3.4 times 10^{4} mathrm{v} )
12
413A parallel plate capacitor of plate area ( A ) and plate separation ( d ) is charged to
potential difference ( V ) and then the battery is disconnected. A slab of
dielectric constant ( k ) is then inserted
between the plates of the capacitor so as to fill the space between the plates. If
( Q, E ) and ( W ) denote respectively, the magnitude of charge on each plate, the electric field between the plates (after
the slab is inserted) and the work done
on the system, in question, in the process of inserting the slab, then:
This question has multiple correct options
A ( cdot Q=frac{epsilon_{0} A V}{d} )
в. ( Q=frac{epsilon_{0} k A V}{d} )
c. ( quad E=frac{V}{k d} )
D. ( W=-frac{epsilon_{0} A V^{2}}{2 d}left(1-frac{1}{k}right) )
12
414An infinitely long straight conductor is uniformly charged with charge density ( lambda ) per meter. The work done to bring a
charge ( q_{0} ) at perpendicular distance ( b ) to
( a ) perpendicular distance ( a(a<b) ) from
the conductor is :
A. zero
в. ( frac{q_{0} lambda}{2 pi_{0}} )
c. ( frac{q_{0} lambda}{2 pi varepsilon_{0}} log _{0}left(frac{b}{a}right) )
D. ( frac{q_{0} lambda}{2 pi varepsilon_{0}} log _{0}left(frac{a}{b}right) )
12
415You are given an arrangement of three point charges ( q, 2 q ) and ( x q ) separated by equal finite distances so that electric potential energy of the system is zero. then the values of ( x ) is:
( A cdot-2 / 3 )
B. -1/3
( c cdot 2 / 3 )
D. 3/2
12
416Two point charges, each of charge ( q, ) are
placed at a separation of ( 2 a ). The
electric potential at their midpoint will
be :
A. zero
в. ( frac{q}{2 pi varepsilon_{0} a} )
c. ( frac{q}{8 pi varepsilon_{0} a} )
D. ( frac{q}{2 pi varepsilon_{0} a^{2}} )
12
now-famous oil-drop experiment. In that experiment, tiny oil drops were sprayed into a uniform electric field between a
horizontal pair of oppositely charged plates.The drops were observed with a magnifying eyepiece, and the electric field was adjusted so that the upward force on some negatively charged oil drops was just sufficient to balance the
downward force of gravity. That is, when suspended, upward force qE just equaled mg. Millikan accurately measured the charges on many oil drops and found the values to be whole number multiples of ( 1.6 times 10^{-19} C ) the
charge of the electron. For this, he won the Nobel prize. If a drop of mass ( 1.08 times )
( 10^{-14} k g ) remains stationary in an
electric field of ( 1.68 times 10^{5} N C^{-1} ), then
the charge of this drop is :
A. ( 6.40 times 10^{-19} mathrm{C} )
B . ( 3.2 times 10^{-19} C )
c. ( 1.6 times 10^{-19} C )
D. ( 4.8 times 10^{-19} mathrm{C} )
12
418Two equal charges ( q ) are placed at a
distance ( 2 a ) and a third charge ( -2 q ) is
placed at the midpoint. The potential energy of the system is
A ( cdot frac{9 q^{2}}{8 pi epsilon_{0} a} )
В. ( frac{q^{2}}{8 pi epsilon_{0} a} )
c. ( frac{-7 q^{2}}{8 pi epsilon_{0} a} )
D. ( frac{6 q^{2}}{8 pi epsilon_{0} a} )
12
419The potential difference between the two plates of a parallel plate capacitor
is constant. When air between the
plates is replaced by dielectric material, the electric field intensity:
A. Decreases
B. Remains unchanged
c. Becomes zero
D. Increases
12
420A right isosceles triangle of side ( a ) has
charges ( boldsymbol{q},+boldsymbol{3} boldsymbol{q} ) and ( -boldsymbol{q} ) arranged on its
vertices as shown in the figure. What is
the electric potential at point ( boldsymbol{P} ) midway
between the line connecting the ( +q ) and
( -q ) charges?
A ( cdot frac{3 q}{r epsilon_{6} a} )
В. ( frac{3 q}{sqrt{2} pi epsilon a a} )
c. ( frac{q}{pi epsilon_{a} a} )
D. ( frac{3 q}{2 sqrt{2} pi epsilon_{0} a} )
12
421The figure shows the field lines of a
positive point charge. The work done by
the field in moving a small positive
charge from ( Q ) to ( P ) is:
A. zero
B. Positive
c. Negative
D. Data insufficient
12
422If a charge is shifted from a high potential region to low potential region, the electrical potential energy
A. Increses
B. Decreses
c. May increase or decrease
D. Remains constant
12
423The two capacitors ( 2 mu F ) and ( 6 mu F ) are put in series, the effective capacity of
the system is ( mu boldsymbol{F} ) is:
( A cdot 8 mu F )
в. ( 2 mu F )
c. ( 3 / 2 mu F )
D. ( 2 / 3 mu F )
12
424( A . ) another positively charged particle of
mass ( m ) and charge ( +q ) is projected
from a point ( B ) with velocity ( u ) as shown
in figure. The point ( B ) is at the lage distance from ( A ) and at distance ( d ) from
the line ( A C . ) The initial velocity is
parallel to the line ( A C . ) The point ( C ) is at
very large distance from ( A ). The minimum distance (in meter) of ( +boldsymbol{q} )
from ( +Q ) during the motion is ( d(1+ ) ( sqrt{A}) . ) Find the value of ( A )
(Take ( boldsymbol{Q} boldsymbol{q}=boldsymbol{4} boldsymbol{pi} varepsilon_{0} boldsymbol{m} boldsymbol{u}^{2} boldsymbol{d} ) and ( boldsymbol{d}=(sqrt{mathbf{2}}- )
1) meter)
A . 3
B. 2
( c cdot 4 )
( D )
12
425A parallel-plate capacitor with plate
area ( A ) and separation between the
plates ( d, ) is charged by a constant
current ( i . ) Consider a plane surface of area ( A / 2 ) parallel to the plates and drawn symmetrically between the plates. Find the displacement current through this area.
12
426Assertion
Dielectric material (dielectric for short)
is an electrical insulator that can be
polarized by an applied electric field.
Reason

Electric field attracts the polarised or
even non polarised atoms in a element
and those atoms get collected on the
Surface
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect

12
427A number of capacitors, each of equal
capacitance ( C, ) are arranged as shown
in the figure. The equivalent
capacitance between ( A ) and ( B ) is :
A ( cdot n^{2} C )
B. ( (2 n+1) C )
c. ( frac{(n-1) n}{2} C )
D. ( frac{(n+1) n}{2} C )
12
428Four electric charges ( +boldsymbol{q},+boldsymbol{q},-boldsymbol{q} ) and
( -q ) are placed at the corners of a square
of side ( 2 L ) (see figure). The electric
potential at point ( A, ) midway between
the two charges ( +boldsymbol{q} ) and ( +boldsymbol{q} ), is
A ( cdot frac{1}{4 pi epsilon_{0}} frac{2 q}{L}(1+sqrt{5}) )
в. ( frac{1}{4 pi epsilon_{0}} frac{2 q}{L}left(1+frac{1}{sqrt{5}}right) )
c. ( frac{1}{4 pi epsilon_{0}} frac{2 q}{L}left(1-frac{1}{sqrt{5}}right) )
D. zero
12
429( boldsymbol{n} ) small drops of small size are charged
to ( V ) volt each. If they collapse to form a
single large drop, then its potential will be
( mathbf{A} cdot(V / n) )
в. ( V n )
( mathbf{c} cdot V n^{2 / 3} )
D. None of these
12
430Five capacitors of ( 10 mu F ) capacity each
are connected to a d.c. potential of 100
volts as shown in the adjoining figure.
The equivalent low capacitance
between the points ( A ) and ( B ) will be
equal to:
( mathbf{A} cdot 40 mu F )
B. ( 20 mu F )
c. ( 30 mu F )
( mathbf{D} cdot 10 mu F )
12
431Figure shows some equipotential lines distributed in space. A charged object
is moved from point ( A ) to point ( B )
A. The work done in figure (i) is the greatest.
B. The work done in figure (ii) is the least.
C. The work done is the same in figure (i), (ii) and (iii)
D. The work done is the same in figure (iii) is greater than figure
(ii) but equal to that in figure (i).
12
432The electric potential due to charges ( 2 q )
and ( -3 q, ) fixed at points ( (4 m, 0,0) ) and
( (9 m, 0,0) ) respectively, is zero on:
A ( cdot ) a spherical surface ( x^{2}+y^{2}+z^{2}=36 )
B. a parabola ( y^{2}=36 z )
c. an ellipsoidal ( frac{x^{2}}{16}+frac{y^{2}}{81}+z^{2}=1 )
D. a spherical surface ( (x-4)^{2}+y^{2}+z^{2}=81 )
12
433Three charges ( +boldsymbol{q},+boldsymbol{q} ) and ( -boldsymbol{q} ) are situated in ( x ) -y plane at the point ( (0, a),(0,0),(0,-a) . ) Then, the electric potential at a point in first quadrant
whose position vector makes an angle ( theta ) with the ( y ) -axis and at a distance ( r(r> ) ( >a) ) from the origin is :
A ( cdot frac{q a cos theta}{2 pi varepsilon_{0} r^{2}} )
в. ( frac{q}{4 pi varepsilon_{0} r}left(1+frac{2 a cos theta}{r}right) )
c. ( frac{q}{4 pi varepsilon_{0} r} )
D. ( frac{q}{4 pi varepsilon_{0} r}left(1-frac{2 a cos theta}{r}right) )
12
434Which of the following is not a unit for electric potential?
A. volt
B. Joule/coulomb
c. Erg/stat coulomb
D. None of these
12
435In an electric field of a point charge ( boldsymbol{q}, ) a
certain charge is carried from point ( boldsymbol{A} )
to ( B, C, D, E . ) Then, the work done
( A ). is least along path ( A B )
C. is zero along all paths
D. is least along path ( A E )
12
436A sliding rod ( A B ) of resistance ( R ) is shown in the figure. Here magnetic field ( B ) is constant and is Out of the
paper. Parallel wires have no resistance and the rod is moving with Constant velocity v. The current in the sliding rod AB in the function of ( t, ) when
switch ( mathrm{S} ) is closed at time ( mathrm{t}=0 ) is
( ^{A} cdotleft(frac{v B d}{R}right) e^{-t / c} )
( ^{mathbf{B}} cdotleft(frac{v B d}{R}right) e^{-t / R C} )
( ^{mathrm{c}} cdotleft(frac{v B d}{R}right) e^{R t C} )
D. ( left(frac{v B d}{R}right) e^{t / R C} )
12
437The plate separation in a parallel plate capacitor is ( d ) and plate area is ( A ). If it is charged to ( V ) volts then calculate the work done in increasing the plate separation to ( 2 d ) then12
438In a uniform electric field, equipotential
surfaces must:
This question has multiple correct options
A. be plane surfaces
B. be normal to the direction of the field
C. be placed such that surfaces having equal differences in potential are separated by equal distances
D. have decreasing potentials in the direction of the field
12
439The equivalent capacitance of
capacitors ( 6 mu F ) and ( 3 mu F ) connected in
series is
( mathbf{A} cdot 3 mu f )
B. ( 2 mu f )
c. ( 4 mu f )
D. ( 6 mu f )
12
440Four large parallel identical conducting
plates of area A are arranged as shown
in fig. The charges on each plate are
given in the figure and the separation between the plates is d(d is very small). The surfaces of the plates are numbered (1), (2),
(1)
12
441A parallel plate air condenser has capacity of ( 20 mu F ). If the distance between two plates is doubled, then new
capacity will be
A ( .5 mu F )
B. ( 10 mu F )
( mathbf{c} cdot 15 mu F )
D. ( 20 mu F )
12
442Define electric potential and write down its dimension.12
443Assertion
A polarised atom can be approximated as a dipole.
Reason
Electric field induces the charge separation in the atom.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
12
444Which of the following statements is
correct?
A. The balls will execute simple harmonic motion between the two plates
B. The balls will bounce back to the bottom plate carrying the same charge they went up with
C. The balls will stick to the top plate an remain there
D. The balls will bounce back to the bottom plate carrying the opposite charge they went up with
12
445A conducting rod of resistance is
moving with constant velocity ( v_{1} ) then
the force required to keep rod moving is
( frac{v B^{2} l^{2}}{R} )
в. ( frac{2 v B^{2} l^{2}}{R+r} )
c. ( frac{v B^{2} l^{2}}{R+r} )
D. zer
12
446Identical charges q each are placed at
the eight corners of a cube of side ( b )
Find the electrostatic potential energy of a charge ( +q ) placed at the center of the cube
12
447A method for charging a conductor without bringing a charged body in contact with it is called:
A. Magnetization
B. Electrification
c. Electrostatic induction
D. Electromagnetic induction
12
448Potential difference is also called
A. voltage
B. Biot
c. coulomb
D. Ampere
12
449Surface charge density of the plate is
equal to
( mathbf{A} cdot 8.85 times 10^{-10} mathrm{C} / mathrm{m}^{2} )
B . ( -8.85 times 10^{-10} C / m^{2} )
C ( cdot 17.7 times 10^{-10} mathrm{C} / mathrm{m}^{2} )
D. ( -17.7 times 10^{-10} C / m^{2} )
12
450A metal plate of thickness half the
separation between the capacitor plates of capacitance ( C ) is inserted. The new
capacitance is:
A .
B. ( frac{c}{2} )
c. zero
D. 2C
12
451Prove that the electric potential at a point in broad side on position due to an electric dipole is zero.12
452A parallel plate capacitor is given a
definite potential difference. Keeping the potential difference same, a slab of
thickness ( 3 mathrm{mm} ) is placed between the plates. To do this, the distance between the plates is increased by ( 2.4 mathrm{mm} )
Calculate the dielectric constant of the
slab.
( (mathbf{a}) )
(b)
( A cdot 10 )
В. 15
( c .5 )
( D )
12
453Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of ( 30^{0} ) with each other. When suspended in a liquid
of density ( 0.8 mathrm{gcm}^{-3}, ) the angle remains
the same. If density of the material of
the sphere is ( 1.6 mathrm{gcm}^{-3} ), the dielectric
constant of the liquid is :
( A cdot 4 )
B. 3
( c cdot 2 )
( D )
12
454The capacity of a parallel plate capacitor with no dielectric substance
but with a separation of ( 0.4 mathrm{cm} ) is ( 2 mu F )
If the separation is reduced to half and it is filled with a dielectric substance of
value ( 2.8, ) then the final capacity of the
capacitor is
A ( .11 .2 mu F )
в. ( 15.6 mu F )
c. ( 19.2 mu F )
D. 22.4 ( mu F )
12
455coordinates as ( boldsymbol{v}=left(boldsymbol{x}^{2}-boldsymbol{y}^{2}right) )
Corresponding electric field lines in ( x-y )
plane as shown in the figure are
( A )
B.
( mathbf{c} )
D.
12
equipotential surfaces.
A. It is a surface over which the potential is constant
B. The electric field is parallel to the equipotential surface
C. The electric field is perpendicular to the equipotential surface
D. The electric field is in the direction of steepest decrease of potential
E. They are concentric spheres for a point charge
12
457Capacity of a parallel plate condenser is ( 10 mu F ) when the distance between its
plates is ( 8 mathrm{cm} ). If the distance between the
plates is reduced to ( 4 mathrm{cm} ), its capacity will
be:
A. ( 10 mu F )
B. ( 15 mu F )
c. ( 20 mu F )
D. ( 40 mu F )
12
458A capacitor has a capacitance of 27.0 microfarads
If we triple the area of the plates of the capacitance and cut the distance between the plates to ( 1 / 3 ) of its original value, what is the new capacitance of the capacitor?
12
459Three charges ( Q, q,-q ) are placed at the vertices of an equilateral triangle. If
the net electric potential energy of the
system is ( 0, ) then ( Q ) is
( A cdot-q )
B. ( q )
( c cdot 0 )
D. None of the above
12
460A charge ( +q ) is fixed at each of the
points ( boldsymbol{x}=boldsymbol{x}_{0}, boldsymbol{x}=mathbf{3} boldsymbol{x}_{0}, boldsymbol{x}=mathbf{5} boldsymbol{x}_{0}, dots ) upto
( infty ) on ( mathrm{X} ) -axis and charge -q is fixed on
each of the points ( boldsymbol{x}=mathbf{2} boldsymbol{x}_{0}, boldsymbol{x}= )
( mathbf{4} boldsymbol{x}_{0}, boldsymbol{x}=boldsymbol{6} boldsymbol{x}_{0}, ldots boldsymbol{u} boldsymbol{p} boldsymbol{a} )
positive constant. Take the potential at a point due to a charge ( Q ) at a distance ( r ) from it to be ( frac{Q}{4 pi epsilon_{0} r} . ) Then the potentia at the origin due to above system of
charges will be :
A . zero
в. ( frac{q}{8 pi epsilon_{0} x_{0} log _{e} 2} )
c. inifinty
D. ( frac{q log _{e} 2}{4 pi epsilon_{6} x_{0}} )
12
461A point charge ( q ) is rotated along a circle in the electric field generated by another point charge ( Q ). The work done by the electric field on the rotating charge in one complete revolution
is
A . zero
B. positive
c. negative
D. zero if the charge ( Q ) is at the center and nonzero otherwise
12
462The current through the ammeter
shown in the figure is ( 1 A ). If each of the
4 resistor is replaced by 2 resistor, the
current in the circuit will become
( A cdot(a) frac{10}{9} A )
( mathbf{B} cdot(mathbf{b}) frac{5}{4} A )
( mathbf{c} cdot(mathrm{c}) frac{9}{8} A )
( mathbf{D} cdot(mathrm{d}) frac{5}{8} A )
12
463Two capacitors of capacitance ( C ) are
connected in series. If one of them is
filled with a substance of dielectric
constant ( K, ) what is the effective
capacitance?
( ^{A} cdot frac{K C}{(1+k)} )
в. ( C(K+1) )
c. ( frac{2 K C}{(1+k)} )
D. None of these
12
464A parallel-plate air capacitor of
capacitance ( C_{0} ) is connected to a cell of emf ( V ) and then disconnected from it. ( A )
dielectric constant ( K, ) which canjust fill the air gap of capacitor, is now inserted in it. Which of the following is incorrect?
A. The potential difference between the plates decreases ( K ) times
B. The energy stored in the capacitor decreases ( K ) times.
C ‘ the change in energy is ( frac{1}{2} C_{0} varepsilon^{2}(K-1) )
D. The change in energy is ( frac{1}{2} C_{0} varepsilon^{2}left(1-frac{1}{k}right) )
12
465A parallel plate capacitor with plates separated by air acquires ( 1 mu mathrm{C} ) of charge
when connected to a battery of ( 500 mathrm{V} ). The
plates still connected to the battery are then immersed in benzene ( (k=2.25) )
Then a charge flows from the battery is :
A. ( 1.25 mu ) С
B. ( 2.28 mu ) С
c. ( 1 / 4 mu ) с
D. ( 4.56 mu ) С
12
466Surface charge density of a sphare of a radius ( 10 mathrm{cm} ) is ( 8.85 times 10^{-8} c / m^{2} )
Potential at the centre of the sphare is
A . ( 1000 V )
B. ( 885 V )
( c cdot 10^{-3} )
D. ( 442.5 V )
12
467Two capacitors of capacities ( 3 mu mathrm{F} ) and ( 6 mu F ) are connected in series and connected to
120V. The potential differences across ( 3 mu )
( mathrm{F} ) is ( V_{0} ) and the charge here is ( q_{0} . ) We have :
A) ( q_{0}=40 mu C )
B) ( V_{0}=60 V )
( left.mathrm{C}) V_{0}=80 mathrm{V} quad mathrm{D}right) q_{0}=240 mu C )
( A cdot A, C ) are correct
B. A, B are correct
c. ( B, ) D are correct
D. ( c, ) D are correct
12
468Electric potential is the force experienced by a unit positive charge placed at a point
A. True
B. False
12
469Deduce an expression for the effective
capacitance of capacitors of ( C_{1}, C_{2} ) and
( C_{3} ) connected in series
12
470There are two concentric spherical
shells of radii ( r ) and ( 2 r . ) Initially a
charge ( Q ) is given to the inner shell and
both the switches are open. If switch ( S_{1} ) is closed and then opened, charge on
the outer shell will be
( A cdot Q )
в. ( frac{Q}{2} )
c. ( -Q )
D. ( frac{-Q}{2} )
12
471Two positive charges ( Q ) and ( 4 Q ) are placed at points ( A ) and ( B ) respectively where ( mathrm{B} ) is at a distance ‘d’ units to the
right of A. The total electric potential due to these charges in minimum at ( mathrm{P} ) on the line through ( A ) and ( B ), What is (are) the distance(s) of P from A?
A. ( d ) ( frac{d}{3} ) units to the right of ( A )
B. ( frac{d}{3} ) units to the left of
c. ( frac{d}{5} ) units to the right of
D. d units to the left of A
12
472Explain the concept of a parallel plate capacitor. State its any ‘two’ applications.12
473In Milikan’s oil drop experiment, an oil
drop of radius ( r ) and charge ( q ) is held in equilibrium between the plates of a charged parallel plate capacitor when
the potential difference is ( V . ) To keep a
drop of radius ( 2 r ) and with a charge ( 2 q )
in equilibrium between the plates the
potential difference ( boldsymbol{V} ) required is :
A. ( V )
B. ( 2 V )
( c .4 V )
D. ( 8 V )
12
474Calculate the work done by electric field
when a point charge q is moved from
point ( mathrm{B} ) to ( mathrm{A} ) along the curved path. Given that electric field is created by the
stationary charge ( mathrm{Q} ) and ( V_{A}= )
( 200 V, V_{B}=100 V, q=0.05 C, ) length of line
segment ( A B=10 mathrm{cm}, ) length of curved
path ( =20 mathrm{cm} )
A . O
B. 5
c. 10
D. 15 J
E. 20
12
475A charge of ( 10 mathrm{C} ) is brought from infinity to a point near a charged body and in
this process, 200 J of work is done
Calculate the electric potential at that point near the charged body
A . ( 20 mathrm{v} )
B. ( 10 mathrm{v} )
( c .5 v )
D. 15 v
12
476The slight separation of charge, or
polarization
A. reduces the electric field within the dielectric.
B. increases the electric field within the dielectric.
C. doesn’t effect the electric field within the dielectric.
D. none of the above
12
477A capacitor has a capacitance of
( 7.28 mu F . ) What amount of charge in ( (mu C ) must be placed on the plates to make the potential difference between its
plates equal to ( 25.0 mathrm{V} ? )
12
478A charge of ( 5 mu mathrm{C} ) is placed at the center
of a square ( A B C D ) of side ( 10 mathrm{cm} . ) Find the work done (in ( mu ) ) in moving a charge of
( 1 mu C ) from ( A ) to ( B )
12
479Consider two concentric spherical
metal shells of radii ( r_{1} ) and ( r_{2}left(r_{2}>r_{1}right) )
If the outer shell has a charge q and the inner one is grounded, the charge on the
inner shell is :
A ( cdot frac{-r_{2}}{r_{1}} q )
B. Zero
c. ( frac{-r_{1}}{r_{2}} q )
D. ( -q )
12
480Equipotential lines are shown, what is
the approximate voltage at point ( P ) in the diagram?
A . 12 ( v )
B. ( 8.0 mathrm{v} )
( c cdot 8.5 v )
D. ( 6.0 mathrm{v} )
12
481Electric field intensity is the strength of an electric field at any point which is the electric force per unit
charge experienced by a test charge placed at that point.
A. Greater than
B. Lesser than
c. Equal to
D. None
12
482The electric potential at a point in free
space due to a charge ( Q ) coulomb is ( Q times 10^{11} V . ) The electric field at that
point is
A ( cdot 12 pi varepsilon_{0} Q times 10^{22} V m^{-1} )
B . ( 4 pi varepsilon_{0} Q times 10^{22} V m^{-1} )
C ( .12 pi varepsilon_{0} Q times 10^{20} mathrm{Vm}^{-1} )
D. ( 4 pi varepsilon_{0} Q times 10^{20} V m^{-1} )
12
483A parallel plate condenser with oil between the plates (dielectric constant of oil ( K=2 ) ) has a capacitance ( C . ) If the oil is removed, then capacitance of the capacitor becomes:
A ( cdot sqrt{2} C )
в. ( 2 C )
c. ( frac{C}{sqrt{2}} )
D. ( frac{c}{2} )
12
484Which of the following can be used as
dielectric?
This question has multiple correct options
A. Mineral oil
B. Electrets
C. Sulfur hexafluoride
D. None of the above
12
485The capacity of a parallel plate condenser is ( C . ) Its capacity when the separation between the plates is halved will be :
A . ( 4 C )
в. ( 2 C )
c. ( frac{c}{2} )
D. ( frac{C}{4} )
12
486If an earthed plate is brought near a positively charged plate, the potential and capacity of charged plate respectively:
A. increases, decreases
B. decreases, increases
c. decreases, decreases
D. increases, increases
12
487(a) Obtain a relation for equivalent capacitance of the series combination
of capacitors. Draw a circuit diagram
(b) 10 capacitors each of capacity ( 10 mu F ) are joined first in series and then
in parallel. Write the value of product of equivalent capacitances.
(c) What will be the value of
capacitance of a ( 4 mu F ) capacitor if a
dielectric of dielectric constant 2 is
inserted fully between the plates of parallel plate capacitor.
12
488Draw a plot showing the variation of (i)
electric field ( (boldsymbol{E}) ) and (ii) electric
potential ( (V) ) with distance ( r ) due to a
point charge ( Q )
12
489Find the charge appearing on capacitor
of capacitance ( 4 mu F )
A ( .32 mu C C )
B. ( 96 mu C )
c. ( 12 mu C )
12
490In an hydrogen atom, the electron
revolves around the nucleus in an orbit
of radius ( 0.53 times 10^{-10} m . ) Then the
electrical potential produced by the nucleus at the position of the electron is
12
491Find out the points on the line joining two charges ( +boldsymbol{q} ) and ( boldsymbol{3} boldsymbol{q} ) (kept at a
distance of ( 1.0 m ) in that order), where
electric potential is zero. This question has multiple correct options
A. ( 0.5 m ) to the left of ( q )
B. ( 0.5 m ) to the right of ( q )
c. ( 0.25 m ) to the right of ( q )
D. ( 0.75 m ) to the right of ( q )
12
492When no current is passed through a
conductor
A. the free electrons do not move
B. the average speed of a free electrons over a large speed of time is zero
C. the average velocity of a free electron over a large period of time is zero
D. the average of the velocities of all the free electrons at an instant is zero
12
493A spherical metal shell A of radius ( boldsymbol{R}_{boldsymbol{A}} )
and a solid metal sphere ( B ) of radius
( R_{B}left(Q_{B} )
C ( frac{sigma_{A}}{sigma_{B}}=frac{R_{B}}{R_{A}} )
D. ( E_{A}^{text {onsurface }}<E_{B}^{text {onsurface }} )
12
494A particle with a charge of 3 coulombs is taken from a point at a potential of 50 V to another point at a potential of ( 120 mathrm{V} ) Calculate the work done.
A . 23.33 J
B. 2.4 J
c. 210
D. 40 J
12
495The figure shows a capacitor having three layers of equal thickness and same area as that of plate. the layer
first is vaccum, second is conductor
and third is dielectric of dielectric
constant ( K . ) The ratio of energy stored
in region three to total energy stored in capacitor three is :
A ( cdot frac{1}{K+1} )
в. ( frac{3}{K+1} )
( c cdot frac{4}{K+3} )
D. ( frac{4}{K+1} )
12
496Which of the following is/are polar
dielectric molecules?
This question has multiple correct options
A ( . N H_{3} )
B. Benzene
c. Methane
D. ( H C L )
12
497The kinetic energy of an electron, which is accelerated in the potential
difference of ( 100 V, ) is
A . ( 1.6 times 10^{-10} mathrm{J} )
в. ( 1.6 times 10^{8} mathrm{J} )
c. ( 1.6 times 10^{-17} J )
D. ( 1.6 times 10^{-18} mathrm{J} )
12
498The plates of a parallel plate capacitor
have an area of ( 90 mathrm{cm}^{2} ) each and are
separated by ( 2.5 m m . ) The capacitor is
charged by a 400 volt supply. How much electrostatic energy is stored by the capacitor?
A ( .2 .55 times 10^{-6} J )
В. ( 1.55 times 10^{-6} J )
c. ( 8.15 times 10^{-6} J )
D. ( 5.5 times 10^{-6} J )
12
499Two equal point charges are fixed at ( x= )
( -a ) and ( x=+a ) on the ( x ) -axis. Another
point charge ( Q ) is placed at the origin. The change in the electrical potential energy of ( mathrm{Q}, ) when it is displaced by a smal distance ( x ) along the ( x ) -axis, is approximately proportional to :
( A cdot x )
B . ( x^{2} )
c. ( x^{3} )
D. ( 1 / x )
12
500A parallel plate capacitor has 91 plates all are identical and arranged with same spacing between them. If the capacitance between adjacent plates is ( 3 p F . ) What will be the resultant
capacitance?
A . 273 pF
B . ( 30 p F )
c. ( 94 p F )
D. 270 ( p F )
12
501A conductor A with a cavity as shown in the figure is given a charge ( Q . ) Find net charge appear on the inner surface of
the cavity.
( mathbf{A} cdot+Q )
B. – ( Q )
c. ( -Q / 2 )
D. zero
12
502A spherical volume contains a
uniformly distributed charge density of
( 2 times 10^{-4} mathrm{Cm}^{-3} . ) The electric field at a
distance of ( 4 mathrm{cm} ) from the centre is :
A . ( 3 times 10^{5} )
B . ( 3 times 10^{4} )
( c cdot 2 times 10^{5} )
D. ( 3 times 10^{6} )
12
503Two point charges ( 2 q ) and ( 8 q ) are placed at a distance r apart. Where should a third charge -q be placed between them so that the electrical potential energy of the system is a minimum.
A. At a distance of r/3 from 2 q.
B. At a distance of 2 r/3 from 2 2
c. At a distance of r/16 from 2q.
D. There is no such position
12
504Three mass points each of mass ( m ) are
placed at the vertices of an equilateral
triangle of side ( 1 . ) What is the
gravitational potential at the centroid of
the triangle.
12
505What is the work done in moving a
charge of ( 50 n C ) between two points on an equipotential surface?
12
506Suppose that you are in a cave deep
within the earth. Are you safe from thunder and lightning? Justify your
12
507An infinite number of charges, each
equal to q, are placed along the x-axis
at ( x=1, x=2, x=4, x=8 ) and so on
What is the potential at ( x=0 ) due to
this set of charges?
12
508Two identical condensers M and N are
connected in series with a battery. The space between the plates of M is
completely filled with a dielectric medium of dielectric constant 8 and a
copper plate of thickness ( frac{d}{2} ) is introduced between the plates of ( mathrm{N}(d ) is
the distance between the plates). Then
potential differences across ( mathrm{M} ) and ( mathrm{N} ) are, respectively, in the ratio:
( mathbf{A} cdot 1: 4 )
B . 4: 1
( mathbf{c} cdot 3: 8 )
D. 1: 6
12
509The capacitance of a capacitor is ( 10 F )
The potential difference on it is ( 50 V ). If the distance between its plate is halved, What will be the potential difference
now?
( mathbf{A} cdot 100 V )
в. ( 50 V )
( c .25 V )
D. ( 75 V )
12
510Across the surface of a charged
conductor, the electric:

This question has multiple correct options
A. field id continuous
B. potential is continuous
C. field is discontinuous
D. potential is discontinuous

12
511Two electric charges ( q ) and ( -2 q ) are placed at a distance 3a apart. The locus of points in the plane of the charges where the field potential is zero is:
A. straight line
B. circle
c. ellipse
D. hyperbola
12
512A thin metallic spherical shell contains
a charge ( Q ) on its surface. A point
charge ( q_{1} ) is placed at the center of the
shell, and another charge ( q_{2} ) is placed
outside the shell. All the three charges
are positive. Then the force on charge ( boldsymbol{q}_{1} )
is :
A. toward right
B. toward left
c. zero
of these
12
513When a dielectric slab is introduced
between the two plates of condenser then its capacity
A. remains constant
B. increases
c. decreases
D. may increase or decrease depending on the material of dielectric slab
12
514Why are equipotential surfaces perpendicular to field lines?12
515Charges ( 5 mu mathrm{C} ) and ( 10 mu mathrm{C} ) are placed ( 1 mathrm{m} )
a part. Workdone to bring these charges
at a distance ( 0.5 mathrm{m} ) from each other is
( left(k=9 times 10^{9} S Iright) )
( mathbf{A} cdot 9 times 10^{4} J )
B . ( 18 times 10^{4} J )
c. ( 45 times 10^{2} J )
D. ( 9 times 10^{-1} J )
12
516An infinite sheet carrying a uniform surface charge density ( sigma ) lies on the ( x y- ) plane. The work done to carry a charge ( q ) from the point ( vec{A}=a(hat{i}+2 j+3 hat{k}) ) to point ( vec{B}=a(hat{i}-2 hat{j}+6 hat{k}) ) (where a is
constant with the dimension of length
and ( varepsilon_{0} ) is the permittivity of free space)
is :
A. ( frac{3 sigma a q}{2 varepsilon_{0}} )
В ( cdot frac{2 sigma a q}{varepsilon_{0}} )
c. ( frac{5 sigma a q}{2 varepsilon_{0}} )
D. ( frac{3 sigma a q}{varepsilon_{0}} )
12
517Potential difference between two points is 60 V. How much work will done on
bringing charge of ( 3 times 10^{-5} ) Coulomb
from one point to another point.
12
518Determine the electrostatic potential energy of a system consisting of two charges ( 7 mu C ) and ( -2 mu C ) (and with no
external field) placed at ( (-9 c m .0 .0) ) and ( (9 c m, 0.0) ) respectively.
12
519A lamp is connected in series with a
capacitor and an AC source. What
happens if the capacity of the capacitor
is reduced?
A. The lamp shines more brightly
B. The lamp shines less brigthly
C. There is no change in the brightness of the lamp
D. Brightness may increase or decrease depending on the frequency of the ( A C )
12
520Three charges each ( 20 mu C ) are placed at
the corners of an equilateral triangle of side of ( 0.4 m . ) The potential energy of the
system is :
( mathbf{A} cdot 18 times 10^{-6} J )
B. ( 9 J )
c. ( 9 times 10^{-6} J )
D. 27J
12
521The parallel plate capacitor on the left ( C L ) has a separation distance of ( 1 mathrm{cm} )
and the sides of the square plate are each ( 0.5 m . ) While the smaller paralle
plate capacitor on the right ( C R ) has a
separation distance of ( 0.2 mathrm{cm} ) and each
side of the square plate is ( 0.1 m ) in length. Determine the ratio of capacitance
( boldsymbol{C} boldsymbol{L}: boldsymbol{C} boldsymbol{R} )
A . 1:
B. 5:
( c .1: 5 )
( D .3 )
12
522At the corners of an equilateral triangle
of side a ( (1 text { metre }), ) three point charges
are placed (each of ( 0.1 C ) ). If this
system is supplied energy at the rate of
1 kw, then calculate the time required
to move one of the mid-point of the line
joining the other two.
A . ( 50 h )
B. ( 60 h )
( mathbf{c} cdot 48 h )
( mathbf{D} cdot 54 h )
12
523The equi-potential surface in the region
are
A. planes parallel to ( X Y ) plane
B. planes parallel to ( Z Y ) plane
C. planes parallel to ( X Z ) plane
D. None of the above
12
524I nree laentıcal square metal plates
( M_{1}, M_{2} ) and ( M_{3} ) of side ( 10 mathrm{cm} & 5 mathrm{mm} )
thick are arranged as shown in figure.
The plates are separated by sheets of
paper ( 0.5 mathrm{mm} ) thick ( & ) of dielectric
constant ( 5 . ) The outer plates are
connected together ( & ) connected to
lower potential while inner plate to higher potential terminal of a battery. Capacitance between the terminals of
the battery is : ( left(epsilon_{0}=8.910^{-12} C^{2} / N-right. )
( left.boldsymbol{m}^{2}right) )
A. ( 1780 p F )
В. ( 890 p F )
( mathbf{c} .445 p F )
D. ( 222.5 p F )
12
5253. The velocity factor of a transmission line x. If dielectric
constant of the medium is 2.6, the value of x is
(a) 0.26
(b) 0.62
(c) 2.6
(d) 6.2
12
526The electric potential at a point in free space due to a charge ( Q ) coulomb is
( Q times 10^{11} ) volts. The electric field at that
point is –
( mathbf{A} cdot 4 pi epsilon_{0} times 10^{20} ) volt ( / mathrm{m} )
B . ( 12 pi epsilon_{0} times 10^{22} )volt( / m )
C . ( 4 pi epsilon_{0} times 10^{22} ) volt ( / m )
D . ( 12 pi epsilon_{0} times 10^{20} ) volt ( / m )
12
527Two equal charges ( A ) and ( B ) each of ( 1 / 3 times 10^{-6} C ) are placed ( 200 mathrm{cm} ) apart
in air. A particle carrying a charge of ( -1 / 3 times 10^{-6} C ) is projected along the
perpendicular bisector from the point 0 midway between ( A ) and ( B ) with a kinetic
energy of ( 10^{-3} J . ) Before the particle
starts to return it will cover a distance
A. ( 1 m )
B. ( sqrt{2} mathrm{m} )
c. ( sqrt{3} mathrm{m} )
D. ( 1 / sqrt{3} mathrm{m} )
12
528How does the magnitude of the electric
field at ( mathrm{B} ) compare for these three cases
в. ।>॥>॥||
D. II>1>11
( E cdot 1=11=11 )
12
529The displacement of a charge ( Q ) in the
electric field ( boldsymbol{E}=boldsymbol{e}_{1} boldsymbol{l}+boldsymbol{e}_{2} boldsymbol{j}+boldsymbol{e}_{3} boldsymbol{k} ) is
( boldsymbol{r}=boldsymbol{a} boldsymbol{i}+boldsymbol{b} boldsymbol{j} . ) The work done is
A ( Qleft(a e_{1}+b e_{2}right) )
() ( aleft(a_{1}+b_{2}right)+b_{2}+b_{2} )
в. ( Q overline{a e_{1}^{2}+b e_{2}^{2}} )
c. ( Qleft(e_{1}+e_{2}right) overline{a^{2}+b^{2}} )
D. ( Q overline{e_{1}^{2}+e_{1}^{2}} a+b )
12
530( 4 mu F ) and ( 6 mu F ) capacitors are joined in series and ( 500 v ) are applied between
the outer plates of the system. What is the charge on each plate?
A ( cdot 1 cdot 2 times 10^{3} C )
в. ( 6 cdot 0 times 10^{3} C )
( mathrm{c} cdot 5 cdot 0 times 10^{-3} mathrm{C} )
D. ( 2 cdot 0 times 10^{-3} C )
12
531You measure the capacitor and inductor voltages in a driven RLC circuit, and find 10V for the rms capacitor voltage and ( 15 V ) for the ( r m s ) inductor voltage.
A ( cdot omega=omega_{r e s} )
В. ( omegaomega_{r e s} )
D. can’t be said
12
532The potential at a point due to a charge
of ( 5 times 10^{-7} ) C located ( 10 mathrm{cm} ) away is:
A. ( 3.5 times 10^{5} mathrm{V} )
B. 3.5 ( times 10^{4} mathrm{v} )
c. ( 4.5 times 10^{4} v )
D. ( 4.5 times 10^{5} mathrm{v} )
12
533When a steady current ( I ) flows through
a resistor of resistance ( boldsymbol{R} ) under
a constant potential difference ( V ) for
time ( t, ) the electrical work done
by charge carrier is ( W= )
A . ( V I t )
в. ( I^{2} R t )
( c cdot frac{V^{2} t}{R} )
D. Any of these
12
534Find equivalent capacitance between
points ( A ) and ( B: )
( ^{A} cdot frac{5 C}{3} )
в. ( frac{4 C}{3} )
( c cdot 2 C )
( D . C )
12
535What are polar and non polar dielectric
give one example each other ?Define dielectric constants.
12
536Three charges ( -2 q, q, q ) are placed on the vertices of an equilateral triangle. At the incentre of the triangle,
A. the field is zero but the potential is non-zero.
B. the field is non-zero but the potential is zero.
c. both the field and the potential is zero.
D. both the field and the potential is non-zero
12
537The capacitance of a capacitor
A. filled with a dielectric is lesser than it would be in a
vacuum
B. filled with a dielectric is greater than it would be in a vacuum
c. filled with a dielectric is same as it would be in a
vacuum.
D. none of the above
12
538The charge stored in a capacitor is ( 20 mu C ) and the potential difference across the plates is ( 500 mathrm{V} ). Its capacity is :
A. ( 0.04 mu F )
B . ( 10^{-2} mu F )
c. ( 2 times 10^{-6} mu F )
D. 250 muF
12
539( frac{bar{k}}{k} )12
540How does the amount of work needed to
move this charge compare for these
three cases?
A. Most work required in
B. Most work required in II
C. Most work required in III
D. I and II required the same amount of work but less than III
E. All three would require the same amount of work
12
541n identical capacitors are connected in parallel to a potential difference ( V ) These capacitors are then reconnected
in series, their charges being left undisturbed. The potential difference obtained is:
A . zero
B. (n-1)V
( c cdot n v )
D. ( n^{2} V )
12
542For high frequency a capacitor offer
A. more reactance
B. less reactance
c. zero reactance
D. inifinite reactance
12
543Charges +50,+20,+30 and -100 nano coulomb are placed at the four corners of a square of side ( 5 sqrt{2} mathrm{cm} . ) The potential at
the intersection of diagonals is :
A ( cdot 1.8 sqrt{2} times 10^{4} V )
( V )
B. ( 3.6 times 10^{4} V )
c. ( 1.8 times 10^{4} V )
D. Zero
12
544Which of the following is correct
statement:
A. Equipotential lines are always perpendicular to the electric field
B. Work done for moving a charge along the conducting surface (closed and containing charge) very close to it may be negative or positive
C. Electric field may cross each other
D. None of the above
12
545A metal rod of length ( 10 mathrm{cm} ) and a rectangular cross section of ( 1 mathrm{cm} times frac{1}{2} ) ( mathrm{Cm} ) is connected to a battery across opposite faces. The resistance will be.
A. Maximum when the battery is connected cross ( 1 mathrm{cm} ) ( times frac{1}{2} mathrm{cm} ) faces
B. Maximum when the battery is connected across ( 10 mathrm{cm} ) ( times 1 mathrm{cm} ) faces
c. Maximum when the battery is connected across ( 10 mathrm{cm} ) ( times frac{1}{2} mathrm{cm} ) faces
D. Same irrespective of the three faces
12
546The quantity of heat generated in a
conductor depends on
A. square of the current ( left(I^{2}right) )
B. resistance of the conductor ( (R) )
c. time for which the mean flows ( (t) )
D. ( I^{2} R t )
12
547Four charges, all of the same magnitude, are placed at the four corners of a square. At the centre of the
square, the potential is ( mathrm{V} ) and the field
is E. With suitable choices of the signs of the four charges, which of the following can be obtained? This question has multiple correct options
A. ( V=0, E=0 )
B. ( V=0, E neq 0 )
c. ( V neq 0, E=0 )
D. ( V neq 0, E neq 0 )
12
548Two capacitors ( C_{1} ) and ( C_{2} ) are
connected in parallel. Assume that
( C_{1}<C_{2} . ) The equivalent capacitance of
this arrangement is ( C, ) where
A. ( C<C_{1} / 2 )
в. ( C_{1}<C<C_{1} )
c. ( C_{1}<C<C_{2} )
D. ( C_{2}<C<2 C_{2} )
12
549Two parallel plate capacitors of
capacitances ( C_{1} ) and ( C_{2} ) such that
( C_{1}=2 C_{2} ) are connected across a
battery of ( V ) volts as shown in the
figure. Initially the key ( ( k ) ) is kept closed
to fully charge the capacitors. The key is
now thrown open and a dielectric slab of
dielectric constant ‘ ( K^{prime} ) is inserted in the
two capacitors to completely fill the gap between the plates. The ratio of the energies stored in the combination, before and after the introduction of the
dielectric slab:
12
550A parallel plate capacitor has a uniform electric field ( E ) in the space between the
plates. If the distance between the plates is ( d ) and area of each plate is ( A )
the energy stored in the capacitor is :
A ( cdot E^{2} A d / varepsilon_{0} )
в. ( frac{1}{2} varepsilon_{0} E^{2} A d )
( mathbf{c} cdot varepsilon_{0} E A d )
D ( cdot frac{1}{2} varepsilon_{0} E^{2} )
12
551Electric field inside the capacitor is 100 ( mathrm{V} / mathrm{m} ) and dielectric constant ( =5.5 )
What is the polarization?
12
552There is an infinite straight chain
of alternating charges ( q ) and ( -q )
The distance between the two
neighbouring charges is equal to a. Find the interaction energy of any charge with all the other charges.
A ( cdot frac{2 q^{2}}{4 pi varepsilon_{0} a} )
B ( cdot frac{2 q^{2} log _{e} 2}{4 pi varepsilon_{0} a} )
( ^{mathbf{C}}-frac{2 q^{2} log _{e} 2}{4 pi varepsilon_{0} a} )
D. none of these
12
553There are four concentric shells ( A, B, C )
and D of radii a, ( 2 a, 3 a ) and ( 4 a ) respectively. Shells B and D are given charges ( +q ) and ( -q ) respectively. Shell ( C ) is now earthed. The potential difference ( V_{A}-V_{c} ) is ( k=frac{1}{4 pi varepsilon_{0}} )
A ( cdot frac{k q}{2 a} )
в. ( frac{k q}{3 a} )
( c cdot frac{k q}{4 a} )
D. ( frac{k q}{6 a} )
12
554A parallel-plate capacitor has
capacitance of ( 1.0 mathrm{F} ). If the plates are 1.0 ( mathrm{mm} ) apart, what is the area of the
plates?
12
555Three capacitors each of capacitance
( 9 p F ) are connected in series as shown
in figure.
(a) What is the total capacitance of the
combination?
(b) What is the potential difference across each capacitor, if the
combination is connected to a 120 volt
supply?
12
556Determine ( boldsymbol{V}(boldsymbol{x}) )
A . ( 20 x )
B . ( -20 x )
c. ( 10 x )
D. ( -10 x )
12
557There are four large parallel conducting
plates each of Area A, placed parallel to
each other. Plates 1,2,3,4 are given
charges equal to ( boldsymbol{q}_{1}, boldsymbol{q}_{2}, boldsymbol{q}_{3} ) and ( boldsymbol{q}_{4} )
respectively:
This question has multiple correct options
A. Charge appearing on the left hand side of plate 1 will be ( frac{q_{1}+q_{2}+q_{3}+q_{4}}{2} )
B. Electric field intensity at the point ( P ), towards right, will be ( frac{q_{1}+q_{2}-q_{3}-q_{4}}{2 A varepsilon_{0}} )
C. Electric field intensity at the point ( Q ), towards right, will be ( frac{q_{1}-q_{2}+q_{3}+q_{4}}{2 varepsilon_{0}} )
D. Electric field at P will be equal to that at Q, for any
values of ( q_{1}, q_{2}, q_{3} ) and ( q_{4} )
12
558Two conducting plates ( A ) and ( B ) are placed parallel to each other at a small
distance between them. Plate A is given
a charge ( q_{1} ) and plate ( B ) is given a
charge ( boldsymbol{q}_{2} . ) Then :

This question has multiple correct options
A. the outer surfaces of ( A ) and ( B ) (not facing each other) get no charge
B. the inner surfaces of ( A ) and ( B ) (facing each other) get al the charge
C. the inner surfaces of ( A ) and ( B ) (facing each other) get equal and opposite charge of magnitude ( left|frac{q_{1}-q_{1}}{2}right| )
D. the outer surfaces of ( A ) and ( B ) (not facing each other) get charge of the same polarity and of magnitude
( frac{q_{1}+q_{2}}{2} )
2

12
559The electric potential at a distance of ( 3 m ) on the axis of a short dipole of dipole moment ( 4 times 10^{-12} ) coulomb-
metre is
A ( cdot 1.33 times 10^{-3} V )
( V )
B. ( 4 m V )
c. ( 12 m V )
D. ( 27 mathrm{mV} )
12
560Which of the following statement is not
true?
A. Electrostatic force is a conservative force.
B. Potential at a point is the work done per unit charge in bringing a charge from infinity to that point in an electric field.
C. Electrostatic force is non-conservative.
D. Potential is the ratio of work to charge.
12
561Consider the situation shown in the
figure. The capacitor A has a charge ( q ) on
it, whereas ( mathrm{B} ) is uncharged. The charge
appearing on the capacitor ( mathrm{B} ), after a long time of closing the switch is:
A. zero
B. ( frac{q}{2} )
( c cdot q )
D. ( 2 q )
12
562A ( 1 mu F ) capacitor is charged to 200 V and then connected in parallel (+ve to +ve) with a ( 4 mu F ) capacitor charged to ( 100 mathrm{V} ) The resultant potential difference is :
A. ( 120 mathrm{V} )
B. 60
c. ( 180 v )
D. ( 150 mathrm{v} )
12
563A hollow insulated conduction sphere is
given a positive charge of ( 10 mu C . ) What
will be the electric field at the centre of
the sphere if its radius is 2 metres?
A. zero
в. ( 5 mu C m^{-2} )
( c cdot 20 mu C m^{-2} )
D. ( 8 mu C m^{-2} )
12
564Two charges ( +6 mu C ) and ( -4 mu C ) are
placed ( 15 c m ) a part as shown. At what
distances from ( A ) to its right, the
electrostatic potential is zero?
( mathbf{A} cdot 4,9,60 )
B. 9,15,45
( mathrm{C} cdot 20,30,40 )
D. ( 9,45, ) infinity
12
565The plates of a parallel-plate capacitor are made of circular discs of radii 5.0
( mathrm{cm} ) each. If the separation between the plates is ( 1.0 mathrm{mm}, ) what is the capacitance?
12
between its plates that covers ( 1 / 3 ) of the
area of its plates, as shown in the figure. The total capacitance of the capacitor is ( C ) while that of the portion
with dielectric in between is ( mathrm{C}_{1} ). When
the capacitor is charged, the plate area
covered by the dielectric gets charge ( Q_{1} )
and the rest of the area gets charge ( Q_{2} )
The electric field in the dielectric is ( mathrm{E}_{1} )
and that in the other portion is ( mathrm{E}_{2} )
Choose the correct option/options, ignoring edge effects:
This question has multiple correct options
A ( cdot frac{E_{1}}{E_{2}}=1 )
В. ( frac{E_{1}}{E_{2}}=frac{1}{K} )
C. ( frac{Q_{1}}{Q_{2}}=frac{3}{K} )
D. ( frac{C}{C_{1}}=frac{2+K}{K} )
12
567A ( 4 mu F ) capacitor is charged to ( 400 V . ) If its plates are joined through a resistance ( 2 k Omega, ) then heat produced in the resistance is
( mathbf{A} cdot 0.16 J )
в. ( 0.32 J )
c. ( 0.64 J )
D. ( 1.28 J )
12
568Two charges – ( q ) and ( +q ) are located at points ( (0,0,-a) ) and ( (0,0, a) ) respectively.
(a) What is the electrostatic potential at the points ( (0,0, z) ) and ( (x, y, 0) ? )
(b) Obtain the dependence of potential on the distance r of a point from the origin when ( r / a>>1 )
(c) How much work is done in moving a small test charge from the point (5,0,0) to (-7,0,0) along the ( x ) -axis? Does the answer change if the path of the test charge between the same points is not along the x-axis?
12
569With ( V=0 ) at infinity, what is the
electric potential at corner A?
A ( cdot 6 times 10^{4} V )
В. ( -7.8 times 10^{5} V )
c. ( 8.4 times 10^{5} V )
D. None of these
12
570The electric potential decreases uniformly from ( 120 mathrm{V} ) to ( 80 mathrm{V} ) as one
moves on the X-axis from ( x=-1 c m ) to
( boldsymbol{x}=+1 mathrm{cm} . ) The electric field at the
origin.
A. must be equal to ( 20 V / c m )
B. must be equal to ( 2.0 mathrm{V} / mathrm{cm} )
c. must be greater than ( 20 V / mathrm{cm} )
D. must be less than ( 20 mathrm{V} / mathrm{cm} )
12
571Positive and negative point charges of equal magnitude are kept at ( left(0,0, frac{a}{2}right) ) and ( left(0,0, frac{-a}{2}right), ) respectively. The work done by the electric field when another
positive point charge is moved from ( (-a, 0,0) ) to ( (0, a, 0) ) is:
A. positive
B. negative
c. zero
D. depends on the path connecting the initial and final positions
12
572Find the charge appearing on the inner face of the left plate:
A ( cdot C V-Q_{1} )
в. ( C V+Q_{1} )
c. ( _{C V}-frac{Q_{1}}{2} )
D. ( C V )
12
573Two point charges ( q_{1} ) and ( q_{2} ) are located
at ( overrightarrow{r_{1}} ) and ( overrightarrow{r_{2}} ) respectively in an external
electric field ( E ).Total work done
in assembling this configuration ( frac{boldsymbol{E}left(boldsymbol{q}_{1}+boldsymbol{q}_{2}right)}{boldsymbol{delta l}} . ) Type 1 for true and 0 for false
12
574A parallel plate condenser with oil (dielectric constant 2 ) between the
plates has capacitance ( C . ) If the oil is removed, the capacitance of capacitor becomes:
A. ( sqrt{2 C} )
B. 2C
c. ( frac{c}{sqrt{2}} )
D. ( frac{c}{2} )
12
575In a parallel plate capacitor, the region between the plates is filled by a delectric slab. The capacitor is connected to a cell and the slab is taken
out.
A. Some charge is drawn from the cell
B. Some charge is returned to the cell
c. The potential difference across the capacitor is reduced
D. No work is done by an external agent in taking the slab out
12
576TWO point charges ( +2 n c ) and ( -4 n c ) are
1 ( m ) apart in air. Find the positions along the line joining the two charges at which resultant potential is zero.
12
577Assertion
For practical purposes, the earth is
used as a reference at zero potential in
electrical circuits.
Reason
The electric potential of a sphere of
radius ( R ) with charge ( Q ) uniformly distributed on the surface is given by
( frac{Q}{4 pi varepsilon_{0} R} )
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect and Reason are correct
12
578Four identical plates each of area a are separated by a distance d. The connection is shown below. What is the
capacitance between ( mathrm{P} ) and ( mathrm{Q} ) ?
A ( cdot 2 a in_{0} / d )
B ( cdot a epsilon_{0} /(2 d) )
( mathrm{c} cdot a epsilon_{0} / d )
D. ( 4 a in_{0} / d )
12
579Two parallel plate air capacitors of
same capacity’ ( C^{prime} ) are connected in
series to a battery of emf ‘ ( E^{prime} . ) Then one
of the capacitors is completely filled
with dielectric material of constant ( ^{prime} boldsymbol{K}^{prime} )
The change in the effective capacity of
the series combination is
A ( cdot frac{C}{2}left[frac{K-1}{K+1}right] )
B ( cdot frac{2}{C}left[frac{K-1}{K+1}right] )
c. ( frac{C}{2}left[frac{K+1}{K-1}right] )
( ^{mathrm{D}} cdot frac{C}{2}left[frac{K-1}{K+1}right]^{2} )
12
580As shown in the figure, charges ( +q ) and ( q ) are placed at the vertices ( B ) and ( C ) of
an isosceles triangle. The potential at
the vertex ( A ) is
( A )
в. ( frac{1}{4 pi varepsilon_{0}} cdot frac{q}{sqrt{a^{2}+b^{2}}} )
( c )
D. zero
12
581The electrostatic potential due to the
charge configuration ot point ( P ) as
shown in figure for ( b<<a ) is
( A )
[
frac{2 q}{4 pi varepsilon_{0} a}
]
B.
[
frac{2 q b^{2}}{4 pi varepsilon_{0} a^{3}}
]
( c )
[
frac{q b^{2}}{4 pi varepsilon_{0} a^{3}}
]
D. zero
12
582A spherical drop of water carrying a charge of 0.032 nC has a potential of 512 V at its surface. If two such drops with the same radius and charge were to combine to form a single drop, what would be the potential at the surface of the new drop?
A . 136.2 ( v )
в. 113 v
c. ( 999.08 mathrm{v} )
D. 812.756 V
12
583The charge on solid sphere is
A ( cdot-9 / 2 )
B. – -व/4
( c cdot-q / 8 )
D. – q/16
12
584The capacity between two adjacent plates of parallel plate condenser is ( 5 mu F ). The number of plates used if we want to get a capacity of ( 40 mu F ) are (alternate plates are connected together):
( A cdot 8 )
B. 9
( c cdot 7 )
D. 10
12
585A parallel plate capacitor has a
dielectric (of dielectric constant ( k ) )
between the plates. The plates are
charged to a surface charge density ( sigma_{0} ) What is the density of the polarized charge that appear on the surface of the dielectric.
12
586Four identical plates each of area ( a ) are
separated by a distance ( d ). The
connection is shown below. What is the
capacitance between ( P ) and ( Q ? )
A ( cdot frac{2 a varepsilon_{0}}{d} )
B. ( frac{a varepsilon_{0}}{2 d} )
c. ( frac{varepsilon_{0}}{d} )
D. ( frac{4 a varepsilon_{0}}{d} )
12
587Two concentric conducting shells A and
B are of radii Rand 2 R. A charge ( + ) q is placed at the centre of the shells Shell B is earthed and a charge q is given to shell A. The charge on outer surface of A is ( n q ), find ( n )
12
588Eight identical spherical mercury drops charged to a potential of 20 v each are coalesced into a single spherical drop:
A. The internal Energy of the system remains the same
B. The new potential of the drop is 80 v
c. Internal Energy of he system decreases
D. The potential remains the same i.e. ( 20 mathrm{v} )
12
589Four metallic plate each with a surface
area of ( A ) are placed at a distance ( d )
from each other. The plates are
connected as shown in the circuit
diagram. Then the capacitance of the
system between a and b is-
( mathbf{A} cdot frac{3 epsilon_{0} A}{d} )
В. ( frac{2 epsilon_{0} A}{d} )
( mathbf{c} cdot frac{2 epsilon_{0} A}{3 d} )
D. ( frac{3 epsilon_{0} A}{2 d} )
12
590A capacitor, as shown in figure has
square plates of length land are inclined
at an angle ( theta ) with one another. For small
value of ( theta, ) capacitance is given by:
( ^{mathbf{A}} cdot frac{epsilon_{0} l^{2}}{d}left(1-frac{theta l}{2 d}right) )
( ^{mathbf{B}} cdot frac{epsilon_{0} l^{2}}{2 d}left(1-frac{theta l}{d}right) )
c. ( frac{epsilon_{0} l^{2}}{d}left(1+frac{theta l}{d}right) )
D ( cdot frac{epsilon_{0} l^{2}}{2 d}left(1+frac{theta l}{d}right) )
12
591The work done in bringing a unit positive charge from infinite distance to a point at distance ( x ) from a positive charge ( Q ) is ( W ). Then the potential ( phi ) at that point is:
A. ( frac{W Q}{x} )
B. ( W )
c. ( frac{W}{x} )
D. ( W Q )
12
592The plates of a parallel plate condenser are pulled apart with a velocity v. If at any instant their mutual distance of
separation is ( x, ) the magnitude of the time of rate of change of capacity depends on ( x ) as follows:
( A cdot 1 / x )
B . ( 1 / x^{2} )
c. ( x^{2} )
D.
12
593Calculate the amount of work done in
carrying a charge of ( 5 mathrm{mC} ) against a potential difference of ( 100 V )
A. ( 0.5 . )
J
в. ( 50 J )
c. ( 5 J )
D. None
12
594What is the electric potential at the
center of the triangle in figure
12
595The equivalent capacitance between ( mathrm{P} )
and ( Q ) is
( A cdot frac{C}{3} )
в. ( 3 C )
( c .2 C )
D.
12
596The velocity factor of a transmission
line is ( 0.62 . ) Calculate dielectric
constant of the insulation used
A . 2.6
B. 3
( c cdot 4 )
D. 5
12
597Which of the following quantities are independent of the choice of zero
potential or zero potential energy? This question has multiple correct options
A. Potential at a point
B. Potential difference between two points.
c. Potential energy of a two charge system.
D. change in potential energy of a two charge system.
12
598A capacitor of capacitance ( C ) is charged
to a potential difference ( V ) from a cell and then disconnected from it. A charge
( +Q ) is now given to its positive plate. The potential difference across the capacitor is now
A. ( V )
B. ( V+frac{Q}{C} )
c. ( _{V}+frac{Q}{2 C} )
D. ( V-frac{Q}{C}, ) if ( Q<C V )
12
599Three particles, each having a charge of
( 10 C ) are placed at the corners of an
equilateral triangle of side ( 10 mathrm{cm} ). The
electrostatic potential energy of the system is :
A . ( 100 J )
В. ( 27 times 10^{12} J )
c. 0
( D cdot infty )
12
600( frac{sqrt{x}}{frac{x}{3}} )12
601The equivalent capacitance between AB of the combination shown in figure is
( A )
B. 2C
( c cdot c / 2 )
D. none of thes
12
602State whether true or false:
The unit of voltage is ( J C^{-1} )
12
603How much work is done moving an electron from a potential of ( 2 mathrm{V} ) to ( 5 mathrm{V} ) ?
A . 2ev
B. 3ev
c. ( 5 mathrm{ev} )
D. 10ev
12
604A metal sphere of ( 4 mathrm{cm} ) radius is suspended within a hollow sphere of 6 cm radius. The inner sphere is charged
to potential 3 esu and the outer sphere is earthed. The charge on the inner sphere is
A . 54 esu
B. 1/4 esu
( c . ) 30 esu
D. 36 esu
12
605A ( 5.80 mu F ) parallel-plate air capacitor
has a plate separation of ( 5.00 mathrm{mm} ) and is charged to a potential difference of ( 400 mathrm{V} . ) Calculate the energy density in
the region between the plates, in ( J / m^{3} )
12
606The separation between the plates of a charged parallel plate capacitor is increased. The force between the plates
A. increases
B. decreases
c. remains same
D. first increases then decreases
12
607No charge will flow when two conductors having the same charge are connected to each other
Given statement is:
A. True
B. False
12
608The work done in carrying 20 coulomb charge through a distance of ( 5 mathrm{m} ) is ( 2 J )
The potential difference between these
two points will be:
( mathbf{A} cdot 2 times 10^{-1} V )
B. ( 1 times 10^{-2} V )
c. ( 2 times 10^{-2} V )
D. ( 1 times 10^{-1} V )
12
609toppr
lower half. The electric field lines around
the cylinder will look like figure given in
(figures are schematic and not drawn to scale)
( A )
B.
( c )
( D )
12
610The equivalent capacitance between ( x )
and ( y ) is :
( A cdot 5 / 6 mu F )
B. ( 7 / 6 mu F )
( c cdot 8 / 3 mu F )
D. ( 1 mu F )
12
611(a) Deduce the expression for the
potential energy of a system of two
charges ( q_{1} ) and ( q_{2} ) located ( overrightarrow{r_{1}} ) and ( overrightarrow{r_{2}} )
respectively, in an external electric
field.
(b) Three point charges, ( +Q+2 Q ) and
( 3 Q ) are placed at the vertices of an equilateral triangle ABC of side I. If these charges are displaced to the mid-
point ( A_{1}, B_{1} ) and ( C_{1}, ) respectively, find
the amount of the work done in shifting
the charges to the new locations.
12
612On what factors does the capacitance of
a parallel plate capacitors depends?
12
613Three concentric spherical conductors
are shown in figure. Determine the
equivalent capacitance of the system
between ( B ) and ( C ).
12
614The diagrams below show regions of equipotentials. A positive charge is moved from ( A ) to ( b ) in each diagram.
A. Maximum work is required to move ( q ) in figure (b)
B. Maximum work is required to move ( q ) in figure(c)
( mathrm{c} . ) In all the cases the work done is the same
D. Minimum work is required to move ( q ) in figure(a)
12
615Two capacitors of ( 1 mu F ) and ( 2 mu F ) are connected in series and this
combination is changed upto a potential difference of 120 volt. What will be the potential difference across ( 1 mu F ) capacitor:
A . ( 40 v o l t )
B. 60 volt
c. ( 80 v ) olt
D. ( 120 v o l t )
12
616A parallel plate capacitor is made of two
square plates of side ‘ ( a ) ‘, separated by a
distance ( d(d<<a) ). The lower
triangular portion is filled with a
dielectric of dielectric constant ( boldsymbol{K}, ) as
shown in the figure. The capacitance of this capacitor is :
( mathbf{A} cdot frac{1}{2} frac{k in_{0} a^{2}}{d} )
B. ( frac{k in_{0} a^{2}}{d} ln K )
c. ( frac{k in_{0} a^{2}}{d(K-1)} ln K )
D. ( frac{k in_{0} a^{2}}{2 d(K+1)} )
12
617A parallel plate capacitor of capacitance C consists of two identical plates ( A ) and ( B ). A charge ( q ) is given to plate ( A ) and charge ( -2 q ) is given to plate
B. The space between plates is vacuum. The separation between plates is d. The electric intensity at a point situated between plates is?
A ( cdot frac{q}{C d} )
в. ( frac{q}{2 C d} )
c. ( frac{3 q}{2 C d} )
D. None of these
12
618A parallel plate condenser is immersed
in an oil of dielectric constant 2. The
field between the plates is :
A ( cdot ) increased, proportional to ( frac{1}{2} )
B. decreased, proportional to – 2
c. increased, proportional to – 2
D. decreased, proportional to ( -frac{1}{2} )
12
619What is the potential difference across
a 64.0 microfarad capacitor if the
charge on the positive plate is +16.0 microcoulombs?
A. ( 4.0 V )
B. ( 0.25 V )
( c .1024 V )
D. ( 2.0 V )
E . ( 32.0 V )
12
620Assertion: Two concentric charged
shells are given. The potential difference between the shells depends on
charge of inner shell.
Reason: Potential due to charge of outer
shell remains same at every point
inside the sphere.
A. Both Assertion and Reason are true and the Reason is the correct explanation of the Assertion
B. Both Assertion and Reason are true but the Reason is not the correct explanation of the Assertion
c. Assertion is true statement but Reason is false
D. Both Assertion and Reason are false statements
12
621Three point charges ( +boldsymbol{q},+mathbf{2} boldsymbol{q} ) and ( -mathbf{4 q} )
where ( boldsymbol{q}=mathbf{0 . 1} boldsymbol{mu} boldsymbol{C}, ) are placed at the
vertices of an equilateral triangle of
side ( 10 mathrm{cm} ) as shown in figure. The potential energy of the system is
A ( cdot 3 times 10^{-3} J )
В. ( -3 times 10^{-3} J )
( mathbf{c} cdot 9 times 10^{-3} J )
( mathbf{D} cdot-9 times 10^{-3} mathbf{J} )
12
622The amount of work done in moving a unit positive charge from infinity to a given point is known as:
A. Nuclear potential
B. Potential energy
c. Electric potential
D. Gravitational potential
12
623Three charged particles are initially in position-1. They are free to move and they come to position – 2 , after some
time.Let ( U_{1} ) and ( U_{2} ) be the electrostatic
potential energies in position-1 and
2.Then
A ( cdot U_{1}=U_{2} )
в. ( U_{2} geq U_{1} )
c. ( U_{2}>U_{1} )
D. ( U_{1}>U_{2} )
12
624Two capacitators having capacitances
( C_{1} ) and ( C_{2} ) are charged with ( 120 V ) and
( 200 V ) batteries respectively. When they
are connected in parallel now, it is found that the potential on each one of them is zero. Then:
A ( cdot 8 C_{1}=5 C_{2} )
В. ( 9 C_{1}=5 C_{2} )
( mathbf{c} cdot 3 C_{1}=5 C_{2} )
D. ( 5 C_{1}=3 C_{2} )
12
625toppr
by
( A )
B.
( mathbf{c} )
( D )
12
626When a small uncharged conducting ball of radius ( a=1 c m ) and mass ( m=50 ) g
is dropped from a height h above the
center of another large conducting sphere of radius b ( (=1 mathrm{m}) ) having charge
( Q(=100 mu C), ) it rises to a height ( h_{1} in )
( 2 m ) ) after the collision. The value of h is
( mathbf{1 0} )
Find ( x )
Assume that during the impact there is no dissipation of energy.
12
627A parallel plate capacitor is charged and
the charging battery is then
disconnected. If the plates of the
capacitor are moved further apart by means of insulating handles, then:
A. the charge in the capacitor becomes zero
B. the capacitance becomes infinite
C. the charge in the capacitor increases
D. the voltage across the plates increases
12
628An electric dipole is kept in the origin
with charges along the ( x ) axis, now choose the correct option,
A. equipotential surface is on ( x y ) plane
B. equipotential surface is on ( x z ) plane
c. equipotential surface is on ( y z ) plane
D. none of the above
12
629Derive an expression for effective
capacitance of three capacitors
connected in parallel
12
630Out of the given statements which of the
following are true:
A) Work done in moving a charge on equipotential surface is zero.
B) Electric lines of force are always
normal to equipotential surface.
C) When two like charges are brought closer, the electrostatic potential energy of the system is decreased.
D) Electric lines of force converge at
positive charge and diverge at negative charge.
( A cdot A, B, C, D ) are true
B. ( A, B, C ) are true
c. ( A, B ) are true
D. A only true
12
631A dielectric of thickness ( 5 mathrm{cm} ) and a
dielectric constant 10 is introduced
between the plates of a parallel plate capacitor having plate area 500 sq. ( mathrm{cm} ) and separation between the plates ( 10 mathrm{cm} )
The capacitance of the capacitor with the dielectric slab is ( varepsilon_{0}=8.8 times 10^{-12} C^{2} / N- )
( m^{2} )
A ( .4 .4 p F )
B. ( 6.2 p F )
c. ( 8 p F )
D. ( 10 p F )
12
6321 volt is equal to
A .1 Joule
B. ( frac{1 text { Joule}}{1 text { Coulomb }} )
c. ( frac{1 text { Joule}}{1 text { meter }} )
D. ( frac{1 text { Newton }}{1 text { Coulomb }} )
12
633The radius of a hypothetical nucleus (atomic number= 79 ) is about ( 7 times )
( 10^{-15} mathrm{m} . ) Assuming that charge
distribution is uniform, the electric
field at the surface of the nucleus is :
A. ( 2.9 times 10^{-21} )
B. ( 2.32 times 10^{21} )
C. ( 4.64 times 10^{21} )
D.
12
634Two metal spheres (radii ( r_{1}, r_{2} ) with
( left.r_{1}<r_{2}right) ) are very far apart but are
connected by a thin wire. If their combined charge is ( Q ), then what
is their common potential?
A ( cdot k Q /left(r_{1}+r_{2}right) )
B . ( k Q /left(r_{1}-r_{2}right) )
( mathbf{c} cdot-k Q /left(r_{1}+r_{2}right) )
D. ( -k Q / r_{1} r_{2} )
12
635Which of the particles would move to
the right?
A. I and II only
B. I and III only
c. II and III only
D. II only
E. I only
12
636Fill in the blank:
In order to increase the capacity of a parallel plate condenser, one should
introduce a sheet of between
the plates (assume that the space is completely filled).
A. Mica
B. Tin
c. copper
D. Stainless Steel
12
637A hollow closed conductor of irregular shape is given some charge. Which of
the following statements are correct? This question has multiple correct options
A. The entire charge will appear on its outer surface
B. All points on the conductor will have the same potential
c. All points on its surface will have the same charge density
D. All points near its surface and outside it will have the same electric intensity
12
638A dielectric with a dielectric constant of
( k ) is inserted between the plates of the
capacitor of capacitance ( C ) having
a potential difference of ( Delta V ) between
the two plates. Calculate the energy
stored in the capacitor?
A ( cdot frac{1}{2}(C / k)(Delta V)^{2} )
B ( cdot frac{1}{2}(k / C)(Delta V)^{2} )
( ^{mathrm{c}} cdot frac{1}{2} k C(Delta V)^{2} )
D. ( frac{1}{2} k C Delta V )
E ( cdot frac{1}{2}(C / k) Delta V )
12
639The potential across a 25.0 microfarad capacitor is ( 5.0 V . ) What is the charge on
the capacitor?
A. 0.20 microcoulombs
B. 5.0 microcoulombs
c. 125 microcoulombs
D. 30.0 microcoulombs
E. We cannot determine the charge on the capacitorwith the given information
12
640Relation between relative permitivity
( left(mu_{r}right) ) and magnetic susceptibility ( left(X_{m}right) )
12
641The amount of work done in joules, when one unit electric charge moves from one point to another point in an electric circuit is called:
A . electric current
B. electric resistance
c. electric conductance
D. potential difference
12
642Why must the electrostatic potential
inside a hollow charged conductor be
the same at every point?
12
643The top of the atmosphere is about 400
kV with respect to the surface of earth,
corresponding to an electric field that
decreases with altitude. Near the
surface of the earth the field is about
( 100 mathrm{V} mathrm{m}^{-1}, ) but still dont get an electric
shock, as we set out of our houses in to
open because : (assume the house is
free from electric field)
A. Our body is a perfect insulator
B. Our body and ground form an equipotential surface
C. The original equipotential surfaces of open air remain same
D. None of the above
12
644Two points ( A ) and ( B ) are located in diametrically opposite directions of a
point charge of ( +2 mu mathrm{C} ) at distances ( 2 mathrm{m} ) and ( 1 mathrm{m} ) respectively from it. The potential difference between ( A ) and ( B ) is
A. ( 3 times 10^{3} vee )
В. ( 6 times 10^{4} mathrm{V} )
( mathbf{c} cdot-9 times 10^{3} mathbf{v} )
D. ( -3 times 10^{3} mathrm{v} )
12
645A point-charge of ( 6.0 times 10^{-8} mathrm{C} ) is
situated at the coordinate origin. How much work will be done in taking an electron from the point ( x=3 mathrm{m} ) to ( x=6 )
( mathrm{m} ? )
B . ( 1.44 times 10^{-27} ) J
c. ( 1.44 times 10^{-37} ) J
D. ( 1.44 times 10^{-7} ).
12
646Two capacitors of capacitance ( C_{1} ) and
( C_{2} ) are connected in parallel across a
battery. If ( Q_{1} ) and ( Q_{2} ) respectively be the charges on the capacitors, then ( frac{Q_{1}}{Q_{2}} ) will be equal to :
A. ( frac{C_{2}}{C_{1}} )
в. ( frac{C_{1}}{C_{2}} )
c. ( frac{C_{1}^{2}}{C_{2}^{2}} )
D. ( frac{C_{2}^{2}}{C_{1}^{2}} )
12
647Three charges ( 2 q,-q,-q ) are located at the vertices of an equilateral triangle. At the centre of the triangle :
A. the field is zero but potential is nonzero
B. the field is nonzero but potential is zero
c. both field and potential are zero
D. both field and potential are nonzero
12
648An ( alpha ) -particle of charge ( 2 e ) is projected with high speed towards two protons (each of charge ( e ) ) kept at a distance
( 4 m ) apart, along a perpendicular passing through the mid-point of the line joining the protons. Initially, ( alpha ) particle starts very far away from the protons. The change In potential energy of the system, when the ( alpha ) -particle undergoes the greatest repulsion, in terms of ( frac{mathbf{e}^{2}}{pi epsilon_{0}} ) will be:
A ( cdot frac{1}{sqrt{3}} )
B. ( sqrt{2} )
c. ( frac{1}{sqrt{6}} )
D. ( sqrt{3} )
12
649The particle of mass ( m ) and charge ( q ) will touch the infinitely large plate of uniform charge density ( sigma ) if its velocity ( v ) is more than:(Given that ( sigma q>0 ) )
A . 0
в. ( sqrt{frac{4 sigma q d}{m varepsilon_{0}}} )
c. ( sqrt{frac{sigma q d}{m varepsilon_{o}}} )
D. none of these
12
650The electric potential at a certain
distance from a point charge ( Q ) is ( 810 V ) and electric field is ( 300 N / C ). The minimum speed with which a particle of charge ( -Q ) and mass ( m=6 x )
( 10^{-16} k g ) should be projected from that
point so that it moves into the field free region is:
A ( cdot 9 times 10^{6} m / s )
в. ( 81 times 10^{6} mathrm{m} / mathrm{s} )
c. ( 81 times 10^{4} m / s )
D. ( 9 times 10^{4} m / s )
12
651Highlousuelto thaligic ul olut ( u ) lias
charges ( boldsymbol{q},+2 boldsymbol{q} ) and ( -boldsymbol{q} ) arranged on its
vertices, as shown.What does the sign
of ( U ) signify?
A. The negative sign means that work was done on the agent who assembled these charges in moving them in from infinity.
B. The positive sign means that work was done on the agent who assembled these charges in moving them in from infinity
C. The negative sign means that work was done by the agent who assembled these charges in moving them in from infinity
D. The positive sign means that work was done by the agent who assembled these charges in moving them in from infinity
12
652Dimension of capacitance is?
A ( cdot M^{-1} L^{-2} A^{2} T^{4} )
B. ( M L^{2} A^{-2} T^{-4} )
c. ( M L A^{-1} T^{4} )
D. ( M^{-1} L^{-1} A^{2} T^{2} )
12
653Capacity of a parallel capacitor with dielectric constant 5 is ( 40 mu F . ) Calculate
the capacity of the same capacitor when dielectric material is removed.
12
654Find ( C_{A B} ) in the given circuit of given
figure. Assume each capacitor is ( mathrm{C} )
A ( cdot frac{15 C}{8} )
B. ( frac{15 C}{7} )
c. ( frac{3 C}{2} )
D. ( 2 C )
12
655The figure shows an infinite line charge of density ( C / m . ) The work done by the
electrostatic force on a unit charge,
when it is moved along the path ( boldsymbol{A B C} )
is (plane of the curve ( A B C ) contains the
line charge)
( A cdot ) zero
B. ( frac{-sigma}{2 pi epsilon_{o}} ln 2 )
c. ( frac{-sigma}{2 pi epsilon_{o}} ln 3 )
D. ( frac{sigma}{2 pi epsilon_{o}} ln 2 )
12
656A parallel plate capacitor of capacitance ( 5 mu F ) and plate separation ( 6 mathrm{cm} ) is connected to a ( 1 mathrm{V} ) battery and charged. A dielectric of dielectric
constant 4 and thickness ( 4 mathrm{cm} ) is
introduced between the plates of the
capacitor. The additional charge that flows into the capacitor from the battery is
A. ( 2 mu C )
в. ( 3 mu C )
( c cdot 5 mu C )
D. 10 ( mu C )
12
657In the circuit shown in figure charge stored in the capacitor of capacity
5 muf is
( A cdot 60 mu C )
В. ( 20 mu C )
( c .30 mu C )
( D )
12
658Calculate the work done to move a
charge 5 C between two points ( A ) and ( B ), if both the points are maintained at same potential of ( 6 mathrm{V} )
A. zero
B . 6 J
c. 3 J
D. 12 J
12
changes that will take place as a result
of the increased plate separation?
( mathbf{A} )
begin{tabular}{|l|l|}
hline multicolumn{1}{|c|} { Capacitor Property } & Effect of Increased Plate Separation \
hline Charge on Plates & increase \
Voltage Across Plates & no effect \
Capacitance & increase \
hline
end{tabular}
B.
begin{tabular}{|l|l|}
hline Capacitor Property & Effect of Increased Plate Separation \
hline Charge on Plates & no effect \
Voltage Across Plates & increase \
Capacitance & decrease \
hline
end{tabular}
( c )
begin{tabular}{|l|l|}
hline multicolumn{1}{|c|} { Capacitor Property } & Effect of Increased Plate Separation \
hline Charge on Plates & increase \
Voltage Across Plates & decrease \
Capacitance & no effect \
hline
end{tabular}
D. begin{tabular}{|l|l|}
hline Capacitor Property & Effect of Increased Plate Separation \
hline Charge on Plates & decrease \
Voltage Across Plates & increase \
Capacitance & no effect \
hline
end{tabular}
( E )
begin{tabular}{|l|l|}
hline Capacitor Property & Effect of Increased Plate Separation \
hline Charge on Plates & no effect \
Voltage Across Plates & decrease \
Capacitance & increase \
hline
end{tabular}
12
660Let ( U_{a} ) and ( U_{d} ) be the energy densities in air and in a dielectric of constant k for
same field. Then
( mathbf{A} cdot U_{a}=U_{d} )
в. ( U_{a}=k U_{d} )
( mathbf{c} cdot U_{d}=k U_{a} )
D. ( U_{a}=(k-1) U_{d} )
12
661The resultant capacity between the terminals ( P ) and ( Q ) of the given figure is :
A ( .37 mu F )
в. ( frac{15}{7} mu F )
( c .3 mu F )
D. ( frac{30}{9} mu F )
12
662Charge ( Q ) taken from the battery of 12 V in
the circuit is :
( mathbf{A} cdot 72 mu C )
B. ( 36 mu C )
( c cdot 156 mu C )
D. ( 20 mu C )
12
663Two capacitors of unknown
capacitances ( C_{1} ) and ( C_{2} ) are connected
first in series and then in parallel across a battery of ( 100 mathrm{V} ). If the energy stored in two combinations is 0.045
and 0.25 J respectively, determine the
value of ( C_{1} ) and ( C_{2} . ) Also calculate the
charge on each capacitor in parallel combination.
12
664Three charges ( 1 mu C, 2 mu C, ) and ( 3 mu C ) are kept at vertices of an equilateral triangle of side ( 1 mathrm{m} ). If they are brought nearer, so that they now form an
equilateral triangle of side ( 0.5 m, ) then
work done is :
A. ( 0.11 J )
( J )
в. ( 11 J )
c. ( 0.01 J )
D. ( 1.1 mathrm{J} )
12
665When an ideal capacitor is charged by dc battery, no current flows, However, When an ac source is used, the current
flows continuously. How does one explain this, based on the concept of displacement current?
12
666Force between two plates of a capacitor
is :
A. ( frac{Q}{epsilon_{0} A} )
В. ( frac{Q^{2}}{2 epsilon_{0} A} )
c. ( frac{Q^{2}}{epsilon_{0} A} )
D. none of these
12
667A parallel plate capacitor is filled by a di-electric whose relative permitivity varies with the applied voltage according to the law ( =alpha V ), where ( alpha=1 )
per volt. The same (but containing no dielectric) capacitor charged to a voltage ( V=156 ) volt is connected in parallel to
the first “non-linear” uncharged capacitor. Determine the final voltage (in volts) ( V_{f} ) across the capacitors.
12
668Assertion
Two charges ( -q ) each are fixed at points
( A ) and ( B . ) When a third charge ( -q ) is
moved from ( boldsymbol{A} ) to ( boldsymbol{B} ), electrical potential
energy first decreases, then increases.
Reason

Along the line joining ( A ) and ( B ), the third charge is in stable equilibrium position
at centre.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect

12
669Which of the following is/are non-polar dielectrics?
( mathbf{A} cdot H C L )
B. water
c. Benzene
D. ( N H_{3} )
12
670A parallel plate capacitor is made by placing n equally spaced plates connected alternatively. If the
capacitance between any two adjacent plates is ( C ) then the resultant capacitance is:
A . nc
в. ( frac{C}{n} )
( c cdot(n+1) c )
D. ( (n-1) C )
12
671Assertion
If a dielectric is placed in external field then field inside dielectric will be less
than applied field.
Reason
Electric field will induce dipole moment
opposite to field direction.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
12
672If the capacitance between two successive plates is ( C, ) then the capacitance of the equivalent system between ( A ) and ( B ) is
A ( cdot frac{C}{3} )
в. ( 3 C )
c. ( frac{2 C}{3} )
D. ( frac{3 C}{2} )
12
673A thin metallic spherical shell contains
a charge ( Q ) on its surface. A point
charge ( q_{1} ) is placed at the centre of the
shell and another charge ( q_{2} ) is placed
outside the shell. All the three charges
are positive. Then, the force on charge ( boldsymbol{q}_{1} )
is
A. Towards left
B. Towards right
D. zero
12
674Calculate the capacitance (in farads) of
a charged, parallel-plate capacitor. Given the potential difference between
the plates is equal to ( X ) volts and the
amount of charge on the POSITIVE plate
is equal to ( Y ) coulombs.
A ( cdot frac{X}{2 Y} )
в. ( frac{Y}{2 X} )
( c cdot frac{Y}{X} )
D. ( frac{2 Y}{X} )
E ( cdot frac{2 X}{Y} )
12
675Two vertical metallic plates carrying equal and opposite charges are kept parallel to each other like a paralle plate capacitor. A small spherical metallic ball is suspended by a long insulated thread such that it hangs
freely in the center of the two metallic plates. The ball, which is uncharged, is taken slowly towards the positively charged plate and is made to touch that
plate. Then the ball will :
A. stick to the positively charged plate
B. come back to its original position and will remain there
c. oscillate between the two plates touching each plate in turn
D. oscillate between the two plates without touch them
12
676Figure shows three circular arcs, each
of radius ( R ) and total change as
indicated. The net electric potential at
the center of curvature is :-
( A )
в. ( frac{Q}{2 pi epsilon_{0} R} )
с. ( frac{2 Q}{pi epsilon_{0} R} )
D. ( frac{Q}{pi epsilon_{0} R} )
12
677Three charges ( Q,+q ) and ( +q ) are placed
at the vertices of a right angle triangle (isosceles triangle) as shown. If the net electrostatic potential energy of the
configuration is zero, value of ( Q ) is:
A ( cdot frac{+q}{2+sqrt{2}} )
B. ( frac{-q}{2+sqrt{2}} )
c. ( frac{+2 q}{2+sqrt{2}} )
D. ( frac{-2 q}{2+sqrt{2}} )
12
678Two positive point charges of ( 12 mu C ) and
( 8 mu C ) are ( 10 c m ) apart. The work done in
bringing them ( 4 c m ) closer is
A . ( 5.8 . J )
B. ( 5.8 e V )
c. ( 13 . J )
D. ( 13 e V )
12
679Three concentric spherical shells have radii ( a, b ) and ( c(a<b<c) ) and have
surface charge densities ( +boldsymbol{sigma},-boldsymbol{sigma},+boldsymbol{sigma} )
respectively. If ( V_{A}, V_{B} ) and ( V_{C} ) denote the potentials of three shells, then for ( c=a+b, ) we have
A. ( V_{C}=V_{B}=V_{A} )
B. ( V_{C}=V_{B} neq V_{A} )
c. ( V_{C} neq V_{B}=V_{A} )
D. ( V_{C} neq V_{B} neq V_{A} )
12
680A point charge ( -q ) is carried from a
point ( A ) to another point ( B ) on the axis of a charged ring of radius ‘r’ carrying a charge ( +q / ) If the point ( A ) is at ( a ) distance ( frac{4}{3} r ) from the centre of the ring and the point ( mathrm{B} ) is ( frac{3}{4} r ) from the centre but on the opposite side, what is the net work that need to be done for this?
( ^{mathrm{A}} cdot-frac{7}{5} frac{q^{2}}{4 pi varepsilon_{0} r} )
В. ( -frac{1}{5} frac{q^{2}}{4 pi varepsilon_{0} r} )
c. ( frac{q^{2}}{54 pi varepsilon_{0} r} )
D. ( frac{q^{2}}{54 pi varepsilon_{e} r} )
12
681The value of the dielectric constant at
room temperature ( (25 mathrm{C}, text { or } 77 mathrm{F}) ) for air is
A. 1.00059
в. 2.00059
c. 0.0009
D. 0.00059
12
682A parallel plate capacitor having plates
of area ( mathrm{S} ) and plate separation ( mathrm{d}, ) has
capacitance ( C_{1} ) in air. When two
dielectrics of different relative
permittivities ( left(varepsilon_{1}=2 text { and } varepsilon_{2}=4right) ) are
introduced between the two plates as
shown in the figure, the capacitance becomes ( C_{2} . ) The ratio ( frac{C_{2}}{C_{1}} ) is
A . ( 6 / 5 )
B. ( 5 / 3 )
( c cdot 7 / 5 )
( 0.7 / 3 )
12
683The conducting sphere of radii ( r_{1} ) and ( r_{2} ) are at the same potential. What is the ratio of their charges?
B . ( r_{2}: r_{1} )
C ( cdot r_{1}^{2}: r_{2}^{2} )
D ( cdot r_{2}^{2}: r_{1}^{2} )
12
684In a quark model of elemetary particles, a neutron is made of one up quark of charge ( frac{2}{3} e ) and two down quark of charges ( left(-frac{1}{3} eright) . ) If they have a triangle configuration with side length of the order of ( 10^{-15} ) m. The electrostatic
potential energy of neutron in ( M e V ) is
A. 7.68
B . -5.21
c. -.048
D. 9.34
12
685A parallel plate capacitor is charged by a battery and the battery remains connected, a dielectric slab is inserted
in the space between the plates. Explain what changes if any, occur in the values of the
(i) potential difference between the plates
(ii) electric field between the plates
(ii) energy stored in the capacitor
12
686In a parallel plate condenser if the distance between the plates is made half and the dielectric constant is doubled,
then the capacity increases by a factor:
A. 2 times
B. 4 times
( c .8 ) times
D. 16 times
12
687A parallel-plate capacitor has plates of unequal area. The larger plate is connected to the positive terminal of the battery and the smaller plate to its
negative terminal. Let ( Q_{+} ) and ( Q_{-} ) be
the charges appearing on the positive and negative plates respectively. Calculate the potential difference between the two plates.
12
688Four charges ( 10^{-8} ;-2 times 10^{-8} ;+3 times 10^{-8} )
and ( 2 times 10^{-8} ) coulombs are placed at the
four corners of a square of side ( 1 mathrm{m} ). The
potential at the centre of the square is
A . zero
B. 360volt
c. ( 180 v o l t )
D. ( 360 sqrt{2} ) volt
12
689A network of four ( 10 mu F ) capacitors is
connected to a ( 500 V ) supply, as shown
in fig. Determine
(a) the equivalent
capacitance of the network and
(b) the
charge on each capacitor.(Note, the
charge on a capacitor is the charge on
the place with higher potential, equal
and opposite to the charge on the plate
with lower potential)
12
690A capacitor of capacitance ( 10, mathrm{f} ) is charged to a potential of ( 100 mathrm{V} ) Now connecting it in parallel with an uncharged capacitor, the resultant potential difference becomes 40 volt.The capacitance of this capacitor is
A ( .2 .5, mathrm{F} )
в. ( 5, ) F
( c .10, F )
D. ( 15, ) F
12
691Three capacitors ( boldsymbol{C}_{mathbf{1}}=boldsymbol{6} boldsymbol{mu} boldsymbol{F}, boldsymbol{C}_{2}= )
( 12 mu F ) and ( C_{3}=20 mu F ) are connected to
a ( 100 V ) battery, as shown following
figure below:
Calculate:
Charge on each plate of capacitor ( C_{1} )
12
692Charges of ( q ) coulomb but of alternately
opposite signs are placed along the ( x- ) axis at ( x=1, x=2, x=4, ldots ) and so on. The
electric potential at the point ( x=0 ) due to
all these charges will be
A ( cdot frac{q}{2 pi epsilon_{0}} )
в. ( frac{q}{3 pi epsilon_{0}} )
c. ( frac{2 q}{3 pi epsilon_{0}} )
D. ( frac{q}{6 pi epsilon_{0}} )
12
693Two materials of dielectric constants
( k_{1} ) and ( k_{2} ) are introduced to fill the
space between the two parallel plates of
a capacitor as shown in the figure. The
capacitance of the capacitor is :
A ( cdot frac{A in_{0}left(k_{1}+k_{2}right)}{2 d} )
в. ( frac{2 A in_{0}}{d}left(frac{k_{1} k_{2}}{k_{1}+k_{2}}right) )
c. ( frac{A in_{0}}{d}left(frac{k_{1} k_{2}}{k_{1}+k_{2}}right) )
( frac{A epsilon_{0}left(k_{1}+k_{2}right)}{2 d k_{2} k} )
12
694If ‘Q’ is the quantity of charge, ‘V’ the potential and ‘C’ the capacity of a conductor, they are related as:
A. ( C=Q V )
в. ( Q=V C )
c. ( V=C Q )
D. ( C V Q= ) costant
12
695A parallel plate air capacitor has a
initial capacitance ( C . ) If plate
separation is slowly increased from ( boldsymbol{d}_{1} )
to ( d_{2} ), then mark the correct
statement(s). (Take potential of the
capacitor to be constant, i.e. throughout the process it remains connected to battery.) This question has multiple correct options
A. Work done by electric force= negative of work done by the external agent.
B. Work done by external force ( -int vec{F} . overrightarrow{d x} ), where ( vec{F} ) is the electric force of attraction between the plates at plate separation ( x )
c. work done by electric force ( neq ) negative of work done by external agent
D. work done by battery = two times the change in electric potential energy stored in capacitor.
12
696A parallel plate capacitor is charged by a battery. The battery is disconnected and a
dielectric slab is inserted to completely fill the space between the plates. How will
(i) its capacitance,
(ii) electric
field between the plates and (iii) energy stored in the capacitor be affected? Justify your answer giving necessary mathematical expressions for each
case.
12
697If two similarly charged particles are brought near one another, the potential energy of the system will:
( A ). increase
B. decrease
c. remains the same
D. equal to the K.E.
12
698In the rectangle shown below, the two
corners have charges ( q_{1}=-5 mu C ) and
( q_{2}=+2.0 mu C . ) The work in moving a charge
( +3.0 mu C ) from ( B ) to ( A ) is:
12
69912
700The capacitance ( C_{A B} ) in the given network
is:
( mathbf{A} cdot 7 mu F )
B. ( frac{50}{7} mu F )
( mathbf{c} .7 .5 mu F )
D. ( frac{7}{50} mu F )
12
701Two plates (area ( =5 ) ) charged to ( +q_{1} )
and ( +q_{2}left(q_{2}<q_{1}right) ) are brought closer to
form a capacitor of capacitance ( C ). The potential difference across the plates is
A ( cdot frac{q_{1}-q_{2}}{2 C} )
в. ( frac{q_{1}-q_{2}}{C} )
c. ( frac{q_{1}-q_{2}}{4 C} )
D. ( frac{2left(q_{1}-q_{2}right)}{C} )
12
702Six point charges are kept at the
vertices of a regular hexagon of side ( boldsymbol{L} )
and centre ( O ), as shown in the figure. Given that ( K=frac{1}{4 pi epsilon_{0}} frac{q}{L^{2}}, ) which of the following statement(s) is(are) correct?
This question has multiple correct options
A. The electric field at ( O ) is ( 6 K ) along ( O D )
B. The potential at ( O ) is zero
c. The potential at all points on the line ( P R ) is same
D. The potential at all points on the line ( S T ) is same
12
703The energy stored in magnetic field
produced by a metal sphere is 4.5 J. If the sphere contains ( 4 mu C ) charge, its
( left[text { Take }: frac{1}{4 pi epsilon_{0}}=9 times 10^{9} N-m^{2} / C^{2}right] )
A. 32 mm
B. ( 16 mathrm{mm} )
c. ( 20 mathrm{mm} )
D. 28 mm
12
704Assertion
Physically, if a dielectric with a high value of ( mathrm{k} ) is placed in an electric field, the electric field will be greatly reduced
inside.
Reason
Dielectrics are very useful in modern electronics as it is possible to to precisely control their permittivity by doping them with other types of
materials.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
12
705Pick up the correct statement
A. Charge on surface of inner sphere is non-uniformly distributed
B. Charge on inner surface of outer shell is non-uniformly distributed
C. Charge on outer surface of outer shell is nonuniformly distributed
D. All the above statements are false
12
706At a point in space, the electric field points toward north. In the region surrounding this point, the rate of change of potential will be zero along
A. north
B. south
c. north-south
D. east-west
12
707A parallel-plate air capacitor is connected to a battery. The quantities charge, voltage, electric field and energy associated with this capacitor are given
by ( Q_{0}, V_{0}, E_{0} ) and ( U_{0} ) respectively. ( A ) dielectric slab is now introduced to fill
the space between the plates with battery still in connection. The corresponding quantities now given by Q, ( V ), E and ( U ) are related with previous
ones as:
This question has multiple correct options
A. ( V>V_{0} )
в. ( U>U_{0} )
c. ( Q>Q_{0} )
D. ( E>E_{0} )
12
708A hollow charged conductor has a tiny hole cut into its surface. Show that the
electric field in the hole is ( left(sigma / 2 epsilon_{0}right) hat{n} )
where ( hat{boldsymbol{n}} ) is the unit vector in the
outward normal direction, and ( sigma ) is the
surface charge density near the hole.
12
709( A, B ) and ( C ) are three large, paralle
conducting plates, placed horizontally
( A ) and ( C ) are rigidly fixed and earthed. ( B )
is given some charge. Under
electrostatic and gravitational forces, ( boldsymbol{B} )
may be :
This question has multiple correct options
A. in equilibrium midway between ( A ) and ( C )
B. in equilibrium if it is closer to ( A ) than to ( C )
c. in equilibrium if it is closer to ( C ) than to ( A )
D. ( B ) can never be in stable equilibrium
12
710Two metal spheres of radii a and b are connected by a thin wire. Their separation is very large compared to their dimensions. The capacitance of
this system is?
( mathbf{A} cdot 4 pi varepsilon_{0}(a b) )
В . ( 2 pi varepsilon_{0}(a+b) )
C ( .4 pi varepsilon_{0}(a+b) )
D. ( 4 pi varepsilon_{0}left(frac{a^{2}+b^{2}}{2}right)^{2} )
12
711A potential difference of 300 volts is applied to a combination of ( 2.0 mu mathrm{F} ) and ( 8.0 mu mathrm{F} ) capacitors connected in series. The charge on the ( 2.0 mu mathrm{F} ) capacitor is :
A . ( 2.4 times 10^{-4} ) coulomb
B. ( 4.8 times 10^{-4} ) coulomb
c. ( 7.2 times 10^{-4} ) coulomb
D. ( 9.6 times 10^{-4} ) coulomb
12
712The electronic potential ( V ) at a point on the circumference of a thin non-
conducting disk of radius r and uniform charge density ( sigma ) is given by equation ( boldsymbol{V}=mathbf{4} boldsymbol{sigma} boldsymbol{r} . ) Which of the following
expression correctly represents
electrostatic energy store in the electric
field of a similar charge disk of radius
R?
12
713What is E in the outer region of the first
plate?
A ( cdot frac{1}{2} times 10^{-10} N / C )
B . ( 2 times 10^{-10} N / C )
c. ( 0 N / C )
D . ( 5 times 10^{-10} mathrm{N} / mathrm{C} )
12
714A parallel plate capacitor is charged and the charging battery is then
disconnected. If the plates of the
capacitor are moved farther apart by
means of insulating handle:
This question has multiple correct options
A. the charge on the capacitor increases
B. the voltage across the plates increases
C. the capacitance increases
D. the electrostatic energy stored in the capacitor increases
12
715Identical metal plates are located in air at equal distance ( d ) from one another.
The area of each plate is equal to ( A ). If
the capacitance of the system between ( P ) and ( Q ) if the plates are interconnected
as shown in the figure ( boldsymbol{x} varepsilon_{0} frac{boldsymbol{A}}{boldsymbol{d}} ). Find ( boldsymbol{x} )
12
716A charge ( +q ) is fixed at each of the
points ( boldsymbol{x}=boldsymbol{x}_{0}, boldsymbol{x}=mathbf{3} boldsymbol{x}_{0}, boldsymbol{x}=mathbf{5} boldsymbol{x}_{0} dots dots, infty )
on the ( x ) -axis and charge ( -q ) is fixed at
each of the points ( boldsymbol{x}=mathbf{3} boldsymbol{x}_{0}, boldsymbol{x}= )
( mathbf{4} boldsymbol{x}_{0}, boldsymbol{x}=boldsymbol{6} boldsymbol{x}_{0}, ldots ldots, infty . ) Here, ( boldsymbol{x}_{0} ) is a
positive quantity. Take the electric potential at a point due to charge ( Q ) at a distance ( r ) from it to be ( frac{Q}{4 pi varepsilon_{0} r} . ) Then the potential at origin due to the above system of charges is:
A . zero
B. infinity
c. ( frac{q}{8 pi varepsilon_{0} x_{0} text { In2 }} )
D. ( frac{q operatorname{In} 2}{4 pi varepsilon_{0} x_{0}} )
12
717Two identical plane metallic surface ( boldsymbol{A} )
and ( B ) parallel to each other in air
separated by a distance of 1 cm let
surface ( A ) as given a position potential
of ( 10 mathrm{V} ) and surface ( B ) is earthed.
12
718A charge ( q_{1}=2 mu C ) is located at the
origin and a charge ( boldsymbol{q}_{2}=-boldsymbol{6} boldsymbol{mu} boldsymbol{C} ) is
located at ( (0,3 m) . ) Find the total
electric potential due to the charges at point ( (4 m, 0) )
( mathbf{A} cdot-6.29 e V )
В. ( -6.29 m V )
( mathbf{c} .-6.29 M V )
D. – ( 6.29 V )
12
719A regular hexagon of side ( 10 mathrm{cm} ) has a charge ( 5 mu C ) at each of its vertices.
Calculate the potential at the centre of the hexagon.
12
720(a) Explain why, for a charge configuration, the equipotential surface through a point is normal to the electric
field at that point?

Draw a sketch of equipotential surfaces
due to a single charge ( (-q) ) depicting the electric field lines due to the charge.
(b) Obtain an expression for the work done to dissociate the system of
three charges placed at the vertices of an equilateral triangle of side ‘a’ as shown in the figure.

12
721Obtain the formula for the capacitance
of a parallel plate capacitor.
12
722Assertion
Positive charge always moves from a higher potential point to lower potential point
Reason
Electric potential is a vector quantity
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
12
723If you have several ( 2.0 mu F ) capacitors,
each capable of withstanding 200 volts without breakdown how would you
assemble a combination having minimum number of capacitors and of given equivalent capacitance which capable of withstanding 1000 volts
( (A) 0.40 mu F )
(B) ( 1.2 mu F, ) capable of withstanding
( mathbf{1 0 0 0} ) volts.
12
724Which graph best illustrates the electric potential along the ( x ) axis, from ( x=-a operatorname{tox}=a ? )
( A )
B. I
c. ॥॥
D. IV
12
725Fig shows some of the equipotential
surfaces of the magnetic scalar potential
The magnetic field ( B ) at a point in the
region is:
A ( cdot 2 times 10^{-3} T )
B . ( 4 times 10^{-4} T )
c. ( 2 times 10^{-4} T )
D. ( 4 times 10^{-3} T )
12
726The potential energy of a proton is ( 3.2 times 10^{-18} J ) at a particular point. The
electric potential at this point is:
(Given charge on a proton is ( 1.6 times )
( left.mathbf{1 0}^{-mathbf{1 9}} boldsymbol{C}right) )
A . ( 5 V )
B. ( 10 V )
( c .20 V )
D. ( 15 V )
12
727Electric charge given to the hollow conductors resides
A. On the outer surface
B. At the centre
c. on the inner surface
D. Uniformly on the outer as well as on the inner surface
12
728In the given figure each capacitor is
equal to ( 45 mu F ) then the equivalent
capacity between ( A ) and ( B ) in the given circuit is:
( mathbf{A} cdot 15 mu F )
в. ( 10 mu F )
c. ( 40 mu F )
D. ( 135 mu F )
12
729Initially the spheres ( A ) and ( B ) are at
potential ( V_{A} ) and ( V_{B} ) respectively. Now
sphere ( mathrm{B} ) is earthed by closing the
switch. The potential of ( A ) will now
become:
( A )
B. ( V_{A} )
( mathbf{c} cdot V_{A}-V_{B} )
D. ( V_{B} )
12
730The electric field at a distance ( 2 mathrm{cm} ) from the centre of a hollow spherical conducting shell of radius ( 4 mathrm{cm} ) having a charge of ( 2 times 10^{-3} mathrm{C} ) on its surface is :
This question has multiple correct options
A . ( 1.1 times 10^{10} V / m )
B . ( 4.5 times 10^{-10} V / m )
C ( .4 .5 times 10^{10} V / m )
D. zero
12
731If the capacity of a spherical conductor is 1 picofarad, then its diameter would
be
A ( cdot 1.8 times 10^{-3} mathrm{m} )
B . ( 18 times 10^{-3} m )
c. ( 1.8 times 10^{-5} m )
D. ( 18 times 10^{-5} m )
12
732A plane electromagnetic wave in a non magnetic dielectric medium is given by ( overline{boldsymbol{E}}=overline{boldsymbol{E}}_{0}left(mathbf{4} times mathbf{1 0}^{-mathbf{7}} times-mathbf{5 0} boldsymbol{t}right) ) with
distance being in meter and time in seconds. The dielectric constant of the
medium is:
A . 2.4
в. 5.8
( c cdot 8.2 )
D. 4.8
12
733The potential in certain region is given
as ( V=2 x^{2}, ) then the charge density of
that region is
A ( cdot-frac{4 x}{varepsilon_{0}} )
в. ( -frac{4}{varepsilon_{0}} )
( mathbf{c} .-4 varepsilon_{0} )
D. ( -2 varepsilon_{0} )
12
734A body of ( 2 g ) carrying a charge of ( 0.1 times ) ( 10^{-6} C ) starts from rest from the positive
plate and moves to the negative plate of a parallel plate condenser connected to a voltage supply of ( 30 k V ). The final velocity
is:
A ( cdot sqrt{3} m s^{-1} )
B. ( frac{sqrt{3}}{12} m s^{-1} )
c. ( frac{1}{sqrt{2}} m s^{-1} )
D. zero
12
735In the arrangement shown in figure,
dielectric constant ( k_{1}=2 ) and ( K_{2}=3 . ) If
the capacitance across ( mathrm{P} ) and ( mathrm{Q} ) are ( C_{1} ) and ( C_{2} ) respectively, then ( frac{C_{1}}{C_{2}} ) will be (the gaps shown are negligible)
A . 1:
B. 2:
( c .9: 5 )
D. 25: 24
12
736Consider the situation shown in the
figure. The capacitor A has a charge q on it whereas ( mathrm{B} ) is uncharged. Find the
charge appearing on the capacitor ( mathrm{B} ) a long time after the switch is closed
A. zero
B. ( q / 2 )
( c cdot q )
D. ( 2 q )
12
737The net charge on a condenser is :
A . infinity
B. ( 9 / 2 )
( c cdot 29 )
D. zero
12
738Rank the following points from greatest to least Electric field.
( mathbf{A} cdot 1>2>3 )
B. ( 3>1>2 )
c. ( 3=2>1 )
D. ( 1=2=3 )
12
739A capacitor of ( 10 mu F ) capacitance is charged by a ( 12 V ) battery. Now the space
between the plates of capacitors is filled with a dielectric of dielectric constant
( K=3 ) and again it is charged. The
magnitude of the charge is :
A. ( 120 mu C )
в. ( 240 mu C )
c. ( 360 mu C )
D. ( 480 mu C )
12
740Two uniformly large parallel thin plates
having charge densities ( +sigma ) and ( -sigma ) are
kept in the ( X Z ) -plane at distance ( d ) apart. Sketch an equipotential surface due to electric field between the plates.
If a particle of mass ( m ) and charge ( -q ) remains stationary between the plates. What is the magnitude and direction of this field?
12
741Calculate the charge on the capacitor in coulombs if a 20 -F capacitor has a ( 30-v ) potential difference across it.
A. ( 6.7 times 10^{-7} mathrm{c} )
В. ( 6.0 times 10^{-4} mathrm{C} )
( c cdot 1.5 c )
D. ( 6.0 times 10^{2} mathrm{C} )
E . ( 1.5 times 10^{6} mathrm{C} )
12
742Two charges ( q ) and ( -q ) are kept apart.
Then at any point on the perpendicular bisector of line joining the two charges:
A. the electric field strength is zero
B. the electric potential is zero
c. both electric potential and electric field strength are zero
D. both electric potential and electric field strength are non-zero
12
743A non-conducting sphere has a total charge Q uniformly distributed throughout its volume. the centre of the sphere is at origin and its radius is ( mathrm{R} )
let ( U_{1} ) be the electrostatic potential energy in the region inside the sphere and ( U_{2} ) be the electrostatic potential energy in another imaginary spherical shell, having inner radius ( R ) and outer radius infinity, centred at origin. select the correct alternative(s)
( ^{mathrm{A}} cdot U_{1}=frac{Q^{2}}{8 pi varepsilon_{0} R} )
в. ( U_{2}=frac{Q^{2}}{8 pi varepsilon_{0} R} )
c. ( U_{1}+U_{2}=frac{3}{5} times frac{Q^{2}}{4 pi varepsilon_{0} R} )
D. ( U_{1}=frac{3 Q^{2}}{20 pi varepsilon_{0} R} )
12
744Two identical metal plates are given
positive charge ( Q_{1} ) and ( Q_{2}left(<Q_{1}right) )
respectively. If they are now brought close together to form a parallel plate
capacitor with capacitance ( C, ) the
potential difference between them is
( mathbf{A} cdotleft(Q_{1}+Q_{2}right) / 2 C )
B ( cdotleft(Q_{1}+Q_{2}right) / C )
c. ( left(Q_{1}-Q_{2}right) / C )
D ( cdotleft(Q_{1}-Q_{2}right) /(2 C) )
12
745Three condensers each of capacitance 2 ( F, ) are connected in series. The resultant
capacitance will be :
( A cdot 6 F )
B. 5
( c cdot 2 / 3 F )
D. 3/2
12
746Define linear charge density. Mention its ( S I ) unit.12
747n this diagram, the potential difference
( A ) and ( B ) is ( 60 V . ) The potential
difference across ( 6 mu F ) capacitor is:
( 4.4 V )
3. ( 10 V )
( c .5 V )
( 20 V )
12
748In electroplating, the metal to be used for coating is made the
A. Cathode (negative electrode)
B. Anode(positive electrode)
c. cathode(positive electrode)
D. Anode(negative electrode)
12
749There are six plates of equal are ( A ) and
separation between the plates is
( d(d<<A) ) are arranged as shown in
figure. The equivalent capacitance between points 2 and ( 5, ) is ( alpha frac{varepsilon_{0} A}{d} . ) Then
find the value of ( boldsymbol{alpha} )
12
750A charge ( 10 n C ) is situated in a medium
of relative permittivity 10. The potential due to this charge at a distance of ( 0.1 m )
is :
( mathbf{A} cdot 900 V )
в. ( 90 V )
( c .9 V )
D. ( 0.09 V )
12
751An equipotential surface is that surface
A. on which each and every point has the same potential
B. which has negative potential
C . which has positive potential
D. which has zero potential
12
752In the circuit shown, the potential
difference across the ( 3 mu F ) capacitor is
( mathrm{V}, ) and the equivalent capacitance
between ( A ) and ( B ) is ( C_{A B} )

This question has multiple correct options
( mathbf{A} cdot C_{A B}=4 mu F )
в. ( c_{A B}=frac{18}{11} mu F )
c. ( v=20 )
D. ( V=40 )

12
753A conducting shell ( S_{1} ) having a charge ( Q )
is surrounded by an uncharged concentric conducting spherical shell ( S_{2} ). Let the potential difference between
( S_{1} ) and that ( S_{2} ) be ( V ). If the shell ( S_{2} ) is now
given a charge ( -3 Q, ) the new potential difference between the same two shells
is :
( A cdot 1 v )
B. 2
( c cdot 4 v )
D. -2 v
12
754On changing a capacitor with charge ( mathrm{Q} ) stored energy is W. If charge is doubled then stored energy will be:-
A ( .2 W )
в. ( 4 W )
c. ( 8 W )
D. ( frac{1}{2} W )
12
755Mark the correct statment:
A. An electron and a proton when released from rest in a uniform electric field experience the same force and the same acceleration
B. Two equipotential surfaces may intersect.
C. A solid conducting sphere holds more charge than a hollow conducting sphere of the same radius.
D. No work is done in taking a positive charge from one point to another inside a negatively charged metallic sphere.
12
756The capacity of a parallel plate condenser is ( 10 mu F ) without the dielectric. Material with a dielectric
constant of 2 is used to fill half-
thickness between the plates. The new
capacitance is ( mu F )
A . 10
B . 20
c. 15
D. 13.33
12
757State whether the given statement is True or False:
A small isolated conductor has a large
positive charge. The electric field inside this conductor will be zero.
A. True
B. False
12
758The electric potential at 0 is :
A ( cdot frac{sqrt{2} q}{pi varepsilon_{0} a} )
В. ( frac{sqrt{3} q}{pi varepsilon_{0} a} )
c. ( frac{q}{pi varepsilon_{0} a} )
D. zero
12
759Two parallel plates have equal and opposite charge. When the space between them is evacuated. the electric
field between the plates ( 2 times 10^{5} V / m )
When the space is filed with dielectric
the electric field becomes ( 10^{5} V / m ) The
dielectric constant of he dielectric
material is
A . 2
B. 4
c. 5
D. 9
12
760uniformly charged in such a way that the potential difference between
them is ( V_{2}-V_{1}=120 V . ) (i.e. plate 2 is
at a higher potential). The plates are
separated by ( boldsymbol{d}=mathbf{0 . 1 m} ) and can be
treated as infinitely large. An electron is
released from rest on the inner surface
of plate ( 1 . ) What is its speed when it hits
plate ( 2 ?left(e=1.6 times 10^{-19} C, m_{e}=right. )
( left.9.11 times 10^{-31} k gright) )
( mathbf{A} cdot 32 times 10^{-19} mathrm{m} / mathrm{s} )
B . ( 6.49 times 10^{6} mathrm{m} / mathrm{s} )
C ( .7 .02 times 10^{12} mathrm{m} / mathrm{s} )
D. ( 1.87 times 10^{6} mathrm{m} / mathrm{s} )
12
761What is the shape of the equipotential surface for the line charge?
A. Sphere
B. Cylinder
c. It will depend upon the type of charge
D. can’t say
12
762Show that the effective capacitance, ( C ) of a series combination, of three
capacitors, ( C_{1}, C_{2} ) and ( C_{3} ) is given by
( boldsymbol{C}=frac{C_{1} C_{2} C_{3}}{left(C_{1} C_{2}+C_{2} C_{3}+C_{3} C_{1}right)} )
12
763The electric field in the dielectric slab
is:
A ( cdot frac{V}{K d} )
B. ( frac{K V}{d} )
c. ( frac{V}{d} )
D. ( frac{K V}{t} )
12
764The electric energy density between the plates of charged condenser is
A ( cdot q / 2 varepsilon_{0} A^{2} )
В ( cdot q / 2 varepsilon_{0} A )
( mathbf{c} cdot q^{2} /left(2 varepsilon_{0} A^{2}right) )
D. none of these
12
765An insulated charged conducting sphere of radius ( 5 mathrm{cm} ) has a potential of ( 10 mathrm{V} ) at
the surface. What is the potential at
centre?
A . ( 10 V )
в. zero
c. same as that at ( 5 mathrm{cm} ) from the surface
D. same as that at ( 25 mathrm{cm} ) from the surface
12
766A charged particle ( q ) is shot from a large
distance towards another charged particle ( Q ) which is fixed, with a speed ( v )
t approaches ( Q ) up to a closest distance ( r ) and then returns. If ( q ) were
given a speed ( 2 v, ) the distance of
approach would be
( A )
B. ( 2 r )
c. ( r / 2 )
D. ( r / 4 )
12
767Identical charges -q each are placed at 8 corners of a cube of each side ( b )
Electrostatic potential energy of a charge +q which is placed at the centre of cube will be :
( ^{mathbf{A}} cdot frac{-4 sqrt{2} q^{2}}{pi epsilon_{0} b} )
B. ( frac{-8 sqrt{3} q^{2}}{pi epsilon_{6} b} )
( ^{mathrm{c}} cdot frac{-4 q^{2}}{sqrt{3} pi epsilon_{0} b} )
D. ( frac{-8 sqrt{2} q^{2}}{pi epsilon_{0} b} )
12
768A uniformly charged solid sphere of
radius R has potential ( V_{0} ) (measured
with respect to ( infty ) ) on its surface. For
this sphere the equipotential surfaces with potentials ( frac{3 V_{0}}{2}, frac{5 V_{0}}{4}, frac{3 V_{0}}{4} ) and ( frac{V_{0}}{4} )
have radius ( boldsymbol{R}_{1}, boldsymbol{R}_{2}, boldsymbol{R}_{3} ) and ( boldsymbol{R}_{4} )
respectively. Then :
A ( . R_{1}=0 ) and ( R_{2}>left(R_{4}-R_{3}right) )
B . ( R_{1} neq 0 ) and ( left(R_{2}-R_{1}right)>left(R_{4}-R_{3}right) )
( mathbf{c} cdot 2 R<R_{4} )
D. None of the above
12
769Define electric potential.12
770A nucleus has charged of +50 e ( A ) proton is located at a distance of ( 10 mathrm{m} )
The potential at this point in volt will be-
12
771Pis a point on an equipotential surface
S. The field at Pis E.
This question has multiple correct options
A. E must be perpendicular to s in all cases
B. E will be perpendicular to S only if S is a plane surface.
C. E cannot have a component along a tangent to S.
D. E may have a nonzero component along a tangent to if ( mathrm{S} ) is a curved surface.
12
772For case III what is the direction of the
electric force exerted by the field on the
( +1 mu C ) charged object when at ( A ) and
when at ( B ? )
A. left at ( A ) and left at ( B )
B. right at ( A ) and right at ( B )
C. left at A and right at B
D. right at A and left at B
E. no electric force at either positions
12
773( frac{E}{L} )12
774Calculate the effective capacitance
( operatorname{across} X Y )
( A cdot frac{5}{2} C )
( B cdot frac{3}{E} C )
( c cdot frac{5}{2} c )
D. ( C )
12
775A hollow sphere of radius 5 cm is
charged such that the potential on its
surface is ( 10 mathrm{V} ). The potential at the
center of the sphere will be:
( mathbf{A} cdot 0 V )
B. ( 10 V )
C. same as at a point ( 5 mathrm{cm} ) away from the surface
D. same as at point ( 25 mathrm{cm} ) away from the center
12
776A battery of ( 100 mathrm{V} ) is connected to series combination of two identical parallel-
plate condensers. If dielectric of constant 4 is slipped between the plates of second condenser, then the potential difference on the condensers will respectively become:
( A cdot 80 vee, 20 v )
B. ( 75 vee, 25 mathrm{V} )
c. ( 50 v ), ( 80 v )
D. 20 V, 80 V
12
777A parallel plate air capacitor has
capacity ( ^{prime} C^{prime} ) farad, potential ( ^{prime} V^{prime} ) volt
and energy’ ( E^{prime} ) joule. When the gap
between the plates is completely filled
with dielectric.
( A . ) Both ( V ) and ( E ) increase
B. Both ( V ) and ( E ) decrease
c. ( V ) decreases, ( E ) increases
D. ( V ) increases, ( E ) decreases
12
778Three capacitance of capacity ( 10 mu F, 5 mu F ) are connected in parallel.
The total capacity will be :
( mathbf{A} cdot 10 mu F )
в. ( 5 mu F )
( mathbf{c} cdot 20 mu F )
D. None of the above
12
779Three capacitors of capacitance 1.0,2.0
and ( 5.0 mu F ) are connected in series to a
( 10 V ) source. The potential difference
across the ( 2.0 mu F ) capacitor is
A ( cdot frac{100}{17} )
в. ( frac{20}{17} v )
c. ( frac{50}{17} v )
D. ( 10 V )
12
780A parallel plate capacitor is first charged and then isolated, and a dielectric slab is
introduced between the plates. The quantity that remains unchanged is:
A. charge ( Q )
B. potential ( V )
c. capacity ( C )
D. energy ( U )
12
781Four point charges ( -Q,-q, 2 q ) and ( 2 Q ) are placed, one at each corner of the square. The relation between ( Q ) and ( q ) for
which the potential at the centre of the square is zero is
A. ( Q=-q )
в. ( Q=-frac{1}{q} )
c. ( Q=q )
( mathrm{D} cdot Q=frac{1}{q} )
12
782Two equal charges q of opposite sign are separated by a small distance ‘2l.’ The
electric potential at a point on the
perpendicular bisector of the line joining
the two charges at a distance r is:
( mathbf{A} cdot frac{1}{4 pi varepsilon_{0}} frac{q}{r} )
B. ( frac{1}{4 pi varepsilon_{0}} frac{2 q}{r} )
c. zero
D. ( frac{1}{4 pi varepsilon_{0}} frac{2 q}{r^{2}} )
12
783What is an equipotential surface?12
784What happens when a nonpolar
material is subjected to external electric field.
12
785In the following figure potential
difference between ( A ) and ( B ) is
( A )
B. 5 volt
( c cdot 10 ) volt
D. 15 volt
12
786A large conducting plane has surface charge density ( 10^{-2} C / m^{2} . ) Find the
electrostatic energy stored in a cubical volume of side ( 1 mathrm{cm} ) in the front plane.
A. 1.4
B. ( 2.8 J )
c. ( 5.6 J )
D. none of these
12
787The charge that will flow to earth when
only switch ( S_{1} ) is connected to earth is :
A . ( -(Q / 2) )
B. ( (Q / 2) )
c. ( 3 Q / 4 )
D. ( -Q )
12
788A solid conducting sphere of radius a
having a charge ( q ) is surrounded by
a concentric conducting spherical shell
of inner radius ( 2 a ) and outer radius ( 3 a )
as shown in figure. Find the amount of heat produced when switch is closed ( left(boldsymbol{K}=frac{mathbf{1}}{mathbf{4} boldsymbol{pi} varepsilon_{0}}right) )
( ^{mathrm{A}} cdot_{K}=frac{k q^{2}}{2 a} )
в. ( _{K}=frac{k q^{2}}{3 a} )
( ^{mathrm{c}} cdot_{K}=frac{k q^{2}}{4 a} )
D. ( _{K}=frac{k q^{2}}{6 a} )
12
789A potential difference is applied across the ends of a metallic wire. If the
potential difference is doubled, the drift
velocity will
A. Be doubled
B. Be halved
D. Remain unchanged
12
790The voltage can be increased, but
electric breakdown will occur if the
electric field inside the capacitor becomes too large. The capacity can be increased by
A. expanding the electrode areas
B. reducing the gap between the electrodes
c. expanding the gap between the electrodes
D. Both A and B
12
791A parallel plate capacitor with air between the plates is charged to a potential difference of ( 500 V ) and then
insulated. A plastic plate is inserted between the plates filling the whole gap. The potential difference between the plates now becomes ( 75 V . ) The dielectric
constant of plastic is :
A ( .10 / 3 )
B. 5
( c cdot 20 / 3 )
D. 10
12
792The equivalent capacitance ( C_{A B} ) of the
circuit shown in the figure is:
( A cdot frac{5}{1} )
( B cdot frac{4}{E} C )
( c cdot 2 C )
D. ( C )
12
793The equation of an equipotential line in an electric field is ( y=2 x, ) then the
electric field strenght vector at (1,2) may be:
A ( .4 hat{i}+3 hat{j} )
B. ( 4 hat{i}+8 hat{j} )
c. ( 8 hat{i}+4 hat{j} )
D. ( -8 hat{i}+4 hat{j} )
12
794The displacement of charge ( q ) in the electric field ( overrightarrow{boldsymbol{E}}=boldsymbol{e}_{1} hat{boldsymbol{i}}+boldsymbol{e}_{2} hat{boldsymbol{j}}+boldsymbol{e}_{3} hat{boldsymbol{j}} ) is ( overrightarrow{boldsymbol{r}}= )
( a hat{i}+b hat{j} . ) The work done is
A ( cdot Qleft(e_{1}+e_{2}right) sqrt{a^{2}+b^{2}} )
в. ( Q(a+b) sqrt{e_{1}^{2}+e_{2}^{2}} )
c. ( Qleft(a e_{1}+b e_{2}right) )
D. ( Q sqrt{left(a e_{1}right)^{2}+left(b e_{2}right)^{2}} )
12
795Two point charges ( -q ) and ( +q ) are located at points ( (0,0,-a) ) and ( (0,0, a) ) respectively. The electric potential at point ( (0,0, z) ) is :
A ( cdot frac{q a}{4 pi varepsilon_{0} z^{2}} )
в. ( frac{q}{4 pi varepsilon_{0} a} )
c. ( frac{2 q a}{4 pi varepsilon_{0}left(z^{2}-a^{2}right)} )
D. ( frac{2 q a}{4 pi varepsilon_{0}left(z^{2}+a^{2}right)} )
12
796Suppose Earth has a volume ‘V’ and surface area ‘A’; then its becomes a
large capacitor having the value of capacitance as
A ( cdot 12 pi in_{0} frac{V}{A} )
в. ( _{4 pi in_{0}} frac{V}{A} )
c. ( _{4 pi in_{0}} frac{A}{V} )
D. ( _{12 pi in_{0}} frac{A}{V} )
12
797The electric field at any point ( (x, y, z) ) is
( mathbf{A} cdot(8 x-3) hat{i} )
B . ( -(8 x-3) )
c. ( -8 x hat{i} )
D. ( 8 x hat{i} )
12
798A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy
is stored in the capacitor?
12
799Two concentric shells of radii ( d ) and ( 2 d )
respectively are placed far away from a parallel plate capacitor. Each plate of the capacitor is a square of side ( d ) and
separation between the plates is ( d / 4 pi )
The charge on the plates are ( q ) and ( -q )
Then the keys ( k_{1} ) and ( k_{2} ) are closed, find
the charges on the shells and electric
potential energy left in the parallel plate capacitor in equilibrium.
12
800Two identical charges, ( 5 mu C ), each are
fixed at a distance ( 8 mathrm{cm} ) and a charged particle of mass ( 9 times 10^{-6} k g ) and charge
( -10 mu C ) is placed at a distance ( 5 mathrm{cm} )
from each of them and is released. Find
the speed of the particle when it is
nearest to the two charges.
12
801Two point charges ( Q ) and ( -Q / 4 ) placed
along the ( x ) -axis are separated by a
distance ( r . ) Take ( -Q / 4 ) as origin and it
is placed at the right of ( Q . ) Then
the potential is zero.
( mathbf{A} cdot ) at ( x=r / 3 ) only
B. at ( x=-r / 5 ) only
C. both at ( x=r / 3 ) and at ( x=-r / 5 )
D. there exist two points on the axis where the electric field is zero
12
802The electric volt is a measure of
electrical potential. Identify which of the following can be defined as a volt.
A. Opposition to electrical motion
B. Number of particles in motion
c. work per unit charge
D. Field strength per unit of force
E. Electrostatic discharge
12
803In a conductor, a point ( P ) is at a higher potential than another point ( Q . ) In which
direction do the electrons move?
12
804Find the charge in steady state of the capacitor.
( A cdot 10 ) nC
B. 20 nC
( c .30 mathrm{nc} )
D. 40 nc
E. None of the above
12
805If ( mathrm{E} ) is the electric field intensity of an electrostatic field, then the
electrostatic energy density is proportional to:
( A cdot E )
B . ( E^{2} )
c. ( 1 / E^{2} )
D. ( E^{3} )
12
806A metallic sphere is placed in a uniform
electric field. Which one of paths ( a, b, c )
and ( d ) shown in the figure will be followed by the field lines and why?
12
i. If electrical resistivity of metal ( boldsymbol{X} ) is
lower than that of metal ( Y ), it means
metal ( X ) is better conductor
of electricity than metal ( Y )
ii. If a wire of resistance ( 8 Omega ) is doubled
on itself, the resistance of the new wire
will be ( 2 Omega )
iii. The coils of electric toasters and
irons are made of an alloy rather than a pure metal because resistivity of the alloy is higher than that of its constituent metals.
iv. If a conductor of length ( 65 mathrm{cm} ) has a
resistance of ( 4 Omega, ) the same conductor of
length ( 260 mathrm{cm} ) will have the resistance
of ( 16 Omega )
v. The maximum amount of current that
can pass through a conductor is ( 440 A )
A. i, iii and v
B. i, ii, iii and iv
c. iii, iv and ( v )
D. iii and iv only
12
808The equivalent capacitance between
the terminals ( X ) and ( Y ) in the figure
shown will be –
A ( .100 p F )
в. ( 200 p F )
c. ( 300 p F )
D. ( 400 p F )
12
809What is the shape of the equipotential surface for the line charge?
A. Sphere
B. cylinder
c. will depend upon the type of charge.
D. can’t say.
12
810What is the surface charge density on
the
(i) inner surface
(ii) outer surface of the shell
12
811Dielectric constant for a metal is:
A . zero
B. infinite
( c cdot 1 )
D. 10
12
812The capacity of a parallel plate condenser
consisting of two plates each of ( 10 mathrm{cm}^{2} )
separated by a distance of ( 2 mathrm{mm} ) is:
(Take air as the medium between the
plates
A ( cdot 8.85 times 10^{-13} F )
В. ( 4.42 times 10^{-12} mathrm{F} )
c. ( 44.25 times 10^{-12} F )
D. ( 88.5 times 10^{-13} F )
12
813The angle between electric lines of force and equipotential surface is :
( mathbf{A} cdot 0^{circ} )
B . ( 180^{circ} )
( c cdot 90^{circ} )
( D cdot 45^{circ} )
12
814A capacitor has some dielectric between its plates, and the capacitor is connected to a dc source. The battery is
now disconnected and then the
dielectric is removed, then
A. capacitance will increase
B. energy stored will decrease.
c. electric field will increase
D. Voltage will decrease
12
815A change of ( 2 x^{-7} C ) moves from the
origin to the point (4,4) with co-
ordinates measured in meters (see
figure). Calculate the work done by the
uniform electric field ( boldsymbol{E}=(mathbf{1} . mathbf{0} times )
( left.10^{4}right) hat{i} N / C ) for each of three paths:
(a) (0,0)( rightarrow(4,0) rightarrow(4,4) )
(b) ( (0,0) rightarrow(4,4), ) along the diagonal
( (c)(0,0) rightarrow(0,4) rightarrow(4,4) )
(d) What is the electrostatic potential
at point (4,4) relative to the origin?
12
816Charges are placed on the vertices of a square as shown. Let ( overrightarrow{boldsymbol{E}} ) be the electric
field and ( V ) be the potential at the
centre. If the charges on ( A ) and ( B ) are interchanged with those on D and ( mathbf{C} )
respectively, then:
A ( . vec{E} ) remains unchanged, ( V ) changes
B. Both ( vec{E} ) and ( V ) change
C ( . vec{E} ) and ( V ) remain unchanged
D. ( vec{E} ) changes, ( V ) remains unchanged
12
817Two fixed charges ( -2 Q ) and ( +Q ) are located at points ( (-3 a, 0) ) and ( (+3 a, 0) ) respectively, Then which of the following statement is correct?
A. Points where the electric potential due to the two charges is zero in ( x ) -y plane, lie on a circle of radius 42 and centre (5a, 0)
B. Potential is zero at ( x=a ) and ( x=9 a )
c. Both (a) and
(b) are wrong
D. Both (a) and (b) are correct
12
818Two identical positive charges are 0.6
meters apart. Which of the following is true about the electric field and
potential at the point which is directly in-between the two?
A. The electric field and potential both are zero
B. The electric field and potential both are positive numbers
C. The electric field is a positive number while the potential is zero
D. The electric field is zero while the potential is a positive number
12
819The radius of a hypothetical nucleus (atomic number ( =mathbf{7} 9 ) ) is about ( mathbf{7} times )
( 10^{-15} mathrm{m} . ) Assuming that charge
distribution is uniform, the electric
field at distance of ( 3.5 times 10^{-15} ) of the
nucleus is :
A ( cdot 3 times 10^{20} )
В. ( 1.7 times 10^{21} )
c. ( 3.5 times 10^{20} )
D. ( 3.5 times 10^{21} )
12
820Six capacitors each of capacitance of
( 2 mu F ) are connected as shown in the
figure. The effective capacitance
between ( A ) and ( B ) is
( mathbf{A} cdot 12 mu F )
B. ( -mu F )
( F F )
( c .3 mu F )
D. ( 6 mu F )
12
821Assertion: Two equipotential surfaces
cannot cut each other.

Reason: Two equipotential surfaces are
parallel to each other.
A. Both Assertion and Reason are true and the Reason is
the correct explanation of the Assertion
B. Both Assertion and Reason are true but the Reason is
not the correct explanation of the Assertion
C. Assertion is true statement but Reason is false
D. Both Assertion and Reason ale false statements

12
822Three charges ( -q, Q,-q ) are placed at equal distance on a straight line. If the total potential energy of the system is zero, then ( Q: q ) is:
A .1: 4
B. -1: 4
c. 1: 2
D. 2: 1
12
823A charged parallel plate capacitor of
distance
(d) has ( U_{0} ) energy. A slab of
dielectric constant (K) and thickness
(d) is then introduced between the
plates of the capacitor. The new energy of the system is given by:
A ( . ) к ( U_{0} )
B. ( K^{2} U_{0} )
( c cdot frac{U_{0}}{K_{0}} )
D. ( frac{U_{0}}{K^{2}} )
12
824How much work is required to slowly
move a ( 1 mu C ) charge from ( E ) to D?
A ( cdot 2 times 10^{-5} J )
B . ( -2 times 10^{-5} J )
C ( cdot 4 times 10^{-5} J )
D. ( -4 times 10^{-5} J )
12
825Define the following term. Surface charge density.12
826The electric potential inside a conductor:
A . is zero
B. increases with distance from center
c. is constant
D. decreases with distance from center
12
827A lightning conductor is a
A. piece of wire with spikes through which current can flow
B. sbstance that can be charged by clouds
C. metal rod with spikes, ending in a copper plate buried in the ground, fixed to a building to protect it from lightning
D. copper plate buried in the ground below a building to protect it from lightning.
12
828Assertion
When a charge is brought near a
conductor then a very small value
current is established in the conductor
Reason
since electric field inside the conductor
has to be zero so to overcome the
electric field of the external charge,
internal charge of conductor is
collected all accross the surface.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
12
829The top of the atmosphere is about
( 400 k V ) with respect to the surface of earth, corresponding to an electric field that decreases with altitude. Near the
surface of earth the field is about
( 100 V m^{-1}, ) but still don’t get an electric
shock, as we set out of our houses in to open because (assume the house is
free from electric field)
A. our body is a perfect insulator
B. our body and ground form an equipotential surface
c. the original euipotential surfaces of open air remain same
D. none of these
12
830Find the electric potential at an
arbitrary point on the ( x ) axis? ( left(V_{o}=frac{boldsymbol{q}}{4 pi epsilon_{o} a}right) )
( ^{mathrm{A}} cdot V(x)=V_{o}left(frac{1}{left|frac{x}{a}-1right|}-frac{1}{left|frac{x}{a}+1right|}right) )
B. ( V(x)=V_{o}left(frac{1}{left|frac{x}{a}+1right|}-frac{1}{left|frac{x}{a}-1right|}right) )
c. ( V(x)=left(frac{1}{left|frac{x}{a}-1right|}-frac{1}{left|frac{x}{a}+1right|}right) )
D. ( V(x)=left(frac{1}{left|frac{x}{a}+1right|}-frac{1}{left|frac{x}{a}-1right|}right) )
12
831Two identical conductors of copper and
aluminium are placed in an identical electric field. What is the magnetic of induced charge in the aluminium?
A. Less than in copper
B. Equal to that in copper
c. Greater than in copper
D. zero
12
832If 3 charges are placed at the vertices of
equilateral triangle of charge ( ^{prime} boldsymbol{q}^{prime} ) each
What is the net potential energy, if the side of equilateral triangle is ( 1 c m )
A. ( frac{1}{4 pi epsilon_{0}} frac{q^{2}}{l} )
B. ( frac{1}{4 pi epsilon_{0}} frac{2 q^{2}}{l} )
c. ( frac{1}{4 pi epsilon_{0}} frac{3 q^{2}}{l} )
D. ( frac{1}{4 pi epsilon_{0}} frac{4 q^{2}}{l} )
12
833What is the name of ( varepsilon_{0} ) ? what is the
value
12
834The equivalent capacitance between points ( A ) and ( B ) for the given figure is
( A cdot 1 F )
В. ( 2 F )
( c .3 F )
2.4
12
835A parallel plate capacitor is connected
to a cell. It’s positive plate ( A ) and the
negative plate B have charges ( +boldsymbol{Q} ) and
( -Q ) respectively. A third plate ( C )
identical to ( A ) and ( B ) with charge ( +Q ) is
now introduced midway between the plates ( A ) and ( B ) parallel to them What is the charge on the inner surface of ( A ) ?
A ( cdot Q )
в. ( frac{mathrm{Q}}{2} )
c. ( frac{3 Q}{2} )
D. ( frac{mathrm{Q}}{4} )
12
836In a uniform electric field, equipotential
surfaces must:
This question has multiple correct options
A. be plane surfaces
B. be normal to the direction of the field
C. be spaced such that surfaces having equal differences in potential are separated by equal distances
D. have decreasing potentials in the direction of the field
12
837A hollow metal ball carrying an electric charge produces no electric field at points.
A. outside the sphere
B. on its surface
c. Inside the sphere
D. At a distance more than twice
12
838Which of the following factors do not influence the capacity of a capacitor?
A. distance between the plates
B. material of the plates
c. area of the plates
D. curvature of the plates
12
839Area of each of the conducting plates 1
2,3,4,5 and 6 is ( A . ) The system is kept
in air. Find the the capacitance between
( A ) and ( B(1 & 4,2 & 5 text { and } 3 & 6 ) are pairs
of parallel plates)
A. ( frac{3 varepsilon_{0} A}{d} )
B. ( frac{2}{3} frac{varepsilon_{0} A}{d} )
c. ( frac{3}{2} frac{varepsilon_{0} A}{d} )
D. ( frac{varepsilon_{0} A}{3 d} )
12
840A ( 60 p F ) capacitor is fully charged by a
( 20 V ) supply. It is then disconnected
from the supply and is connected to another uncharged ( 60 p F ) capacitor in
parallel. The electrostatic energy that is
lost in this process by the time the charge is redistributed between them is ( (operatorname{in} n J) )
12
841Find the potential energy of an electric dipole (length ( 4 mathrm{cm} ) ) each experiences a torque of ( 4 sqrt{3} mathrm{Nm} ) placed in a from
electric field angle ( 60^{circ} q=1+n c )
12
842When a steady current passes through a cylindrical conductor, is there an electric
field inside the conductor?
12
843A charge of ( +4 mu C ) is kept at a distance
of ( 50 mathrm{cm} ) from a charge of ( -6 mu C ). Find the two points where the potential is
zero
A. Internal point lies at a distance of ( 20 mathrm{cm} ) from ( 4 mu mathrm{C} ) charge and external point lies at a distance of ( 100 mathrm{cm} ) from ( 4 mu C ) charge
B. Internal point lies at a distance of ( 30 mathrm{cm} ) from ( 4 mu C C ) charge and external point lies at a distance of ( 100 mathrm{cm} ) from ( 4 mu C ) charge
c. Potential is zero only at ( 20 mathrm{cm} ) from ( 4 mu mathrm{C} ) charge between the two charges
D. Potential is zero only at ( 20 mathrm{cm} ) from ( -6 mu mathrm{C} ) charge between the two charges
12
844Three charges, each ( +q, ) are placed at
the corners of an isosceles triangle ( A B C )
of sides ( mathrm{BC}, mathrm{AC} ) and ( mathrm{AB} ). D and ( mathrm{E} ) are the
midpoints of BC and CA. The work done in taking a charge ( Q ) from ( D ) to ( E ) is:
(Given ( B C=A C) )
A ( cdot frac{e q Q}{8 epsilon q} )
B. ( frac{q Q}{4 epsilon_{6} a} )
C. zero
D. ( frac{3 q Q}{4 epsilon_{6} a} )
12
845An extremely long wire is uniformly charged. An electron is revolving around the wire and making ( 10^{8} ) revolutions per
second in an orbit of radius ( 2 mathrm{cm} ). Linear
charge density of the wire is nearly?
A. ( 50 n C / m )
B. ( 25 n C / m )
c. ( 40 n C / m )
D. ( 12.5 n C / m )
12
846( N ) conducting plares are placed face to face as shown in figure. Distance
between any two plates is ( d ). Area of the plates is ( A, frac{A}{2}, frac{A}{4}, frac{A}{8} dots frac{A}{2(n-1)} . ) The
equivalent capacitance of the system is
12
847The work done in carrying a charge a circle of radius with a charge ‘Q’ at the
center is:
A. ( frac{1}{4 pi epsilon_{0}} cdot frac{q Q}{r} )
в. ( frac{1}{4 pi epsilon_{0}} cdot frac{q Q}{pi r} )
c. ( frac{1}{4 pi epsilon_{0}} cdot frac{q Q}{2 pi r} )
D. zero
12
848Deduce an expression for the capacitance of a parallel plate
capacitor.
12
849Two point charges ( Q ) and ( -Q / 4 ) are
separated by a distance ( x . ) Then:
This question has multiple correct options
A. potential is zero at a point on the axis which is ( x / 3 ) on the right side of the charge ( -Q / 4 )
B. potential is zero at a point on the axis which is ( x / 5 ) on the left side of the charge ( -Q / 4 )
C. electric field is zero at a point on the axis which is at a distance ( x ) on the right side of the charge ( -Q / 4 )
D. there exist two points on the axis where electric field is zero
12
850What is the unit of electric potential difference?
A. volt
B. Coulamb
c. Joul
D. watt
12
851toppr
close to each other. Is the magnitude of
electrostatic force between them
exactly given by ( Q_{1} Q_{2} / 4 pi epsilon_{0} r^{2}, ) where ( r )
is the distance between their centres?
(b) If Coulomb’s law involved ( 1 / r^{3} )
dependence (instead of ( 1 / r^{2} ) ),would Gauss’ law be still true?
(c) A small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point?
(d) What is the work done by the field of
a nucleus in a complete circular orbit of the electron? What if the orbit is
elliptical?
(e) We know that electric field is
discontinuous across the surface of a
charged conductor. Is electric potential also discontinuous there?
(f) What meaning would you give to the capacitance of a single conductor?
(g) Guess a possible reason why water has a much greater dielectric constant ( (=80) ) than say, mica ( (=6) )
12
852A capacitor is charged by a cell of emf ( boldsymbol{E} )
and the charging battery is then removed. If an identical capacitor is now inserted in the circuit in parallel with the previous capacitor, the potential difference across the new capacitor is :
( A cdot 2 E )
в. ( E )
c. ( E / 2 )
D. zero
12
853In given Figure, a charge ( Q ) is fixed.
Another charge ( q ) is moved along a circular arc MN of radius r around it,
from the point ( mathrm{M} ) to the point ( mathrm{N} ) such
that the length of the arc ( M N=l . ) The
work done in this process is :
A. Zero
В. ( frac{1}{4 pi epsilon_{0}} cdot frac{Q q}{r^{2}} l )
c. ( frac{Q q}{2 epsilon_{0} r^{2}} l )
D. ( frac{Q q}{2 pi epsilon_{0} r^{2}} )
12
854Calculate the electric potential
difference between the outside and the
inside cylinders in ( V )
12
855The vertical displacement traveled by
the proton as it exits the region between
the plates is (mass of proton is ( 1.67 times )
( left.10^{-27} k g .right) )
A ( cdot 1.6 times 10^{-8} mathrm{m} )
B . ( 3.25 times 10^{-8} mathrm{m} )
( c cdot 5.25 times 10^{-6} m )
D. ( 2.73 times 10^{-6} mathrm{m} )
12
856Assertion
Net charge given to a conductor resides on its outer surface under electrostatic
conditions.
Reason
Electric field lines do not enter a
conductor under electrostatic
conditions.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
12
857A spherical capacitor consists of two
concentric spherical conductors, held in
position by suitable insulating
supports (Fig.). Show that the
capacitance of a spherical capacitor is
given by ( c=frac{4 pi epsilon_{0} r_{1} r_{2}}{r_{1}-r_{2}} )
where ( r_{1} ) and ( r_{2} ) are the radii of outer
and inner spheres, respectively.
12
858The surface density on the copper
sphere is ( sigma . ) The electric field strength
on the surface of the sphere is:
( A )
B . ( sigma / 2 )
c. ( sigma / 2 varepsilon_{0} )
D. ( sigma / varepsilon_{0} )
12
charge of ( +5 q . ) Which diagram best
represents the charge distribution on
the sphere?
( mathbf{A} )
Solid Conducting Sphere
Stand
B. Solid Conducting Sphere
Stand
( c )
Solid Conducting Sphere
Stand
D. Solid Conducting Sphere
Stand
12
860Charge ( +q ) placed at point ( A ) is a distance ( 2 L ) apart from ( B ) and ( C ) is the
midpoint between A and B. The work
done in moving charge ( +mathrm{Q} ) along the
semicircle CRD is
( mathbf{A} cdot frac{mathrm{q} Q}{2 pi varepsilon_{mathrm{U}}} )
B. ( frac{9 Q}{6 pi varepsilon_{0}} )
( mathbf{c} cdot-frac{q Q}{6 pi varepsilon L} )
D. ( frac{q Q}{4 frac{q Q}{4 varepsilon_{0} L}} )
12
861apacitor ( (1) so as to fill the gap eeping the battery remainc charge on each capacit
( frac{2 m}{1+(1 / 1 / k)} )
( frac{omega(10)}{1} )
( frac{2 omega}{(1+k)} )
( frac{2 w}{10-k} )
12
862What is electrostatic shielding? Mention one application of it.12
863Two plates are placed at a separation of ( 2 mathrm{cm} . ) An electron placed at the perryferry of one plate reaches the second plate in 2 microsecond. Calculate the inner charge density of the surface assuming the case of infinite plate.
A . ( 0.505 times 10^{-12} mathrm{Cm}^{-2} )
В. ( 0.15 times 10^{-12} mathrm{Cm}^{-2} )
c. ( 1.01 times 10^{-12} mathrm{Cm}^{-2} )
D. ( 0.505 times 10^{-11} mathrm{Cm}^{-2} )
12
864The dielectric to be used in a parallelplate capacitor has a dielectric constant of 3.60 and a dielectric
strength of ( 1.60 times 10^{7} V / ) m. The
capacilnr is to have a capacitance of ( 1.25 times 10^{-9} F ) and must be able to ( u )
withstand a maximum potential difference of 5500 V. The minimum area
the plates of the capacitor may have is
equal to ( 135 times 10^{-x} m^{2} . ) The value of ( x )
is:
12
865Nature of equipotential surface for a
point charge is:
A. Ellipsoid with charge at foci
B. Sphere with charge at the center of the sphere
C. Sphere with charge on the surface of the sphere
D. Plane with charge on the surface
12
866A capacitor of capacitance ( C ) is charged to a potential difference ( V ) from a cell and then disconnected from it. A charge
( +mathrm{Q} ) is now given to its positive plate. The potential difference across the capacitor is now:
A.
в. ( v+frac{Q}{C} )
c. ( v+frac{Q}{2 C} )
D. ( V-frac{Q}{C} ), if ( Q<C V )
12
867Calculate the amount of work done in
moving a charged particle of charge ( q )
through a potential difference of ( V )
A ( cdot frac{q}{V} )
в. ( frac{V}{q} )
c. ( frac{1}{q V} )
D. ( q V )
12
868An ideal dipole of dipole moment ( vec{p} ) is placed in front of an uncharged conducting sphere of radius ( R ) as shown
A ( cdot ) The potential at point ( A ) is ( frac{K P}{(r-R)^{2}} )
B. The potential at point A is ( frac{K P}{r^{2}} )
C the potential due to dipole at point B is ( frac{K P}{(r+R)^{2}} )
D. The potential due to dipole at point B is ( frac{K}{r^{2}} )
12
869The capacitance between adjacent plates shown in Fig ( 20.95(a) ) is 50 nF. ( A 1 mu C ) charge is placed on the middle
plate. Find the charge on the outer surface of upper plate and the potential difference between upper and middle plates:
A. ( 0.5 mu C, 10 V )
B. ( 1 mu C, 20 V )
c. ( 0.5 mu C, 20 V )
D. ( 1.0 mu, 40 V )
12
870Work done in carrying an electric
charge ( Q_{1} ) once round a circle of radius
( R ) with a charge ( Q_{2} ) at the centre of the circle:
A. ( frac{Q_{1} Q_{2}}{4 pi varepsilon_{Omega} R} )
B. ( infty )
c. ( frac{Q_{1} Q_{2}}{4 pi varepsilon_{0} R^{2}} )
D.
12
871One Volt is equal to:
A . 1 Joule
B. 1 Newton/Coulomb
c. 1 Joule/Coulomb
D. 1 Coulomb/Newton
12
872The charge ( Q ) and ( -2 Q ) are placed at some distance. What is the locus of
point in the plane of the charges where the potential is zero?
1. Parabola
2. Circle
3. Ellipse
only.
12
873The equivalent capacitance between
points a and b in given arrangement of plates will be:(each plate has the area
‘A’ ( & ) separation between two adjacent plates is ‘d’)
A ( cdot frac{2}{3} frac{varepsilon_{o} A}{d} )
B ( cdot frac{3}{2} frac{varepsilon_{o} A}{d} )
c. ( frac{2 varepsilon_{o} A}{d} )
D. ( frac{varepsilon_{o} A}{3 d} )
12
874Equipotential surface associated with an electric field which is increasing in
magnitude along the y-direction, are
A. parallel to ( X Y ) plane
B. parallel to ( X Z ) plane
C. parallel to ( Y Z ) plane
D. coaxial cylinders of increasing radii around the the ( x ) axis
12
875A small uncharged metallic sphere is positioned exactly at a point midway between two equal and opposite point charges separated by very small distance. If the spheres is slightly displaced towards the positive charge and released, then
This question has multiple correct options
A. It will oscillate about it’s original position.
B. It will move further towards the positive charge.
c. Its potential energy will decrease and kinetic energy will increase
D. The total energy remains constant but is non-zero
12
876A capacitor is formed by two square
metal-plates of edge ( alpha_{1} ) separated by a
distance ( d ). Dielectrics of dielectric
constants ( K_{1} ) and ( K_{2} ) are filled in the
gap as shown figure. Find the
capacitance.
12
877A capacitor has a capacitance of ( boldsymbol{C} )
when a potential difference of ( V ) is
across it.
The potential difference is increased to ( 2 V, ) what is the new capacitance?
A. ( C )
B. ( 2 C )
( c .3 C )
D. ( 5 C )
12
878A parallel plate condenser with a dielectric of dielectric constant ( boldsymbol{K} )
between the plates has a capacity ( C ) and is charged to a potential ( V ) volt. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is :
A . zero
в. ( frac{1}{2}left[(K-1) C V^{2}right. )
c. ( frac{C V^{2}(K-1)}{K} )
D. ( (K-1) C V^{2} )
12
879A condenser is charged to a potential difference of ( 120 mathrm{V} ). It’s energy is ( 1 times )
( 10^{-5} J . ) If battery is there and the space
between plates is filled up with a
dielectric medium ( left(varepsilon_{r}=5right) . ) Its new energy
is
( mathbf{A} cdot 10^{-5} J )
В. ( 2 times 10^{-5} J )
c. ( 3 times 10^{-5} J )
D . ( 5 times 10^{-5} J )
12
880The equipotential surfaces corresponding to a single positive charge are concentric
spherical shells with the charge at its origin. The spacing between the surfaces for the same change in potential:
A. is uniform throughout the field
B. is getting closer as ( r rightarrow infty )
c. is getting closer as ( r rightarrow 0 )
D. can be varied as one wishes to
12
881What are polar and non polar molecules12
882In an uniform electric field ( boldsymbol{E}=mathbf{1 0} boldsymbol{N} / boldsymbol{C} )
as shown in figure, find ( boldsymbol{V}_{boldsymbol{A}}-boldsymbol{V}_{boldsymbol{B}} )
( mathbf{A} cdot 10 V )
B. ( -10 V )
( mathbf{c} cdot 20 V )
D ( .-20 V )
12
883Three point charges ( 3 n C, 6 n C ) and ( 9 n C )
are placed at the corners of an
equilateral triangle of side 0.1 m. The
potential energy of the system is :
A ( .8910 n J )
в. ( 89100 mathrm{mJ} )
c. ( 9910 J )
D. ( 99100 K J )
12
884Assertion
Each of the plates of a parallel-plate
capacitor is given equal positive charge
Q. The charges on the facing surfaces
will be same.
Reason
A negative charge ( (-Q) ) will be induced
on each of the facing surfaces.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
12
885The capacitive time constant of the RC
circuit shown in the figure is:
A. zero
B. infinity
( c cdot 2 s )
D. 2 ( mu ) s
12
886Potential difference between two points
is equal to
A. electric charge / time
B. work done/time
c. work done/charge
D. work done ( times ) charge
12
887The electric potential at the surface of an atomic nucleus ( (z=50) ) of radius
( 9.0 times 10^{-13} mathrm{cm} ) is:
A ( cdot 9 times 10^{5} ) volt
B. ( 8 times 10^{6} ) volt
c. 80 volt
D. 9 volt
12
888A charge ( +q ) is placed at the origin 0 of ( x-y ) axes as shown in the figure. The work done in taking a charge ( Q ) from ( A ) to B along the straight line ( A B ) is:
A ( cdot frac{q Q}{4 pi varepsilon_{0}}left(frac{a-b}{a b}right) )
в. ( frac{q Q}{4 pi varepsilon_{0}}left(frac{b-a}{a b}right) )
c. ( frac{q Q}{4 pi varepsilon_{0}}left(frac{b}{a^{2}}-frac{1}{b}right) )
D. ( frac{q Q}{4 pi varepsilon_{0}}left(frac{a}{b^{2}}-frac{1}{b}right) )
12
889For the configuration of media of
permitivities ( varepsilon_{o}, varepsilon ) and ( varepsilon_{o} ) between
parallel plates each of area ( A ), as show
in figure, the equivalent capacitance is
( mathbf{A} cdot varepsilon_{0} A / d )
В ( cdot varepsilon_{0} varepsilon A / d )
C. ( frac{varepsilon_{0} varepsilon A}{dleft(varepsilon+varepsilon_{0}right)} )
D. ( frac{varepsilon_{0} varepsilon A}{left(2 varepsilon+varepsilon_{0}right)} )
12
890Four identical charges each of charge
are placed at the corners of a square.
Then at the centre of the square the
resultant electric intensity E and the net electric potential V are
A. ( E neq 0, V=0 )
B. ( E=0, V=0 )
c. ( E=0, V neq 0 )
D. ( E neq 0, V neq 0 )
12
891What is the angle between electric field and equipotential surfaces?
A. 90 always
B. O always
( c cdot 0 ) to 90
D. 0 to 180
12
892I ne IIgure snows lour palrs ol unılormıy
charged spheres. The red spheres are positively charged while the blue spheres are negatively charged. Each sphere has the same amount of charge. Assume each pair is isolated. For which pair there is a point between
them on the dotted line where the
magnitude of electric field is zero as well as the electric potential is also
zero?
A.
B. 2
( c cdot 3 )
D. 4
E. None of the pairs has points that meet these conditions
12
893The charge supplied to a good
conductor always resides:
A. at the supplied position itself
B. on its outer surface
C. inside the body
D. all of the above
12
894Which among the following statement is true about the work done in bringing
a unit positive charge from point ( P ) to ( Q )
in an electrostatic field?
A. Minimum work is done in case of path II
B. Maximum work is done in case of path1
c. Work done is same in all the three paths
D. Work done is zero in case of path
12
895The capacity of a parallel plate condenser is inversely proportional to
A. Area of each plate
B. Dielectric constant
c. Permittivity of medium
D. Distance between two plates
12
896A conducting sphere of radius r has a
charge. Then:
A. The charge is uniformly distributed over its surface, if there is an external electric field.
B. Distribution of charge over its surface will be non uniform if no external electric field exist in space.
C. Electric field strength inside the sphere will be equal to zero only when no external electric field exists.
D. Potential at every point of the sphere must be same.
12
897Two charges of equal magnitude ‘ ( q ) ‘ are
placed in air at a distance ( ^{prime} 2 a^{prime} ) apart
and third charge ( -2 q^{prime} ) is placed at midpoint. The potential energy of the system is ( left(epsilon_{0}= ) permittivity of free right. space) :
( ^{mathrm{A}} cdot-frac{q^{2}}{8 pi epsilon_{0} a} )
в. ( -frac{3 q^{2}}{8 pi epsilon_{6} a} )
c. ( -frac{5 q^{2}}{8 pi epsilon_{0} a} )
D. ( -frac{7 q^{2}}{8 pi epsilon_{6} a} )
12
898Why is electrostatic potential constant throughout the volume of the conductor and has the same value (as inside) on
its surface?
12
899Identify the dimension of electric potential,
A ( cdot L^{2} M T^{-3} I^{-1} )
B . ( L^{1} M T^{-2} I^{-1} )
( mathbf{c} cdot L^{-2} M T^{-2} I^{-1} )
D. none of the above
12
900The ratio of charge densities on the surface of two conducting spheres is 3:
2. lithe radii of t: the spheres are ( 4 mathrm{cm} ) and ( 8 mathrm{cm} ) the ratio of the electric potential on the surfaces of the sphere 2
is
( A cdot 3: 4 )
B. 3:1
( c cdot 1: 3 )
D. 4: 9
12
901Four charges ( 1 mathrm{mc}, 2 mathrm{mc}, 3 mathrm{mc}, ldots 6 mathrm{mc} )
are placed on at corner of a square of
side ( 1 mathrm{m} . ) The square lies in ( mathrm{XY} ) plane with its centre at origin
A. The electric potential at origin at origin
B. The electric potential is zero every where along ( x ) axis
c. The electric potential is not zero along z-axis
D. The electric potential is zero along Z- axis for any orientation of square in ( mathrm{XY} ) plane
12
902Two concentric shells have radii ( mathbf{R} ) and
2R, charges ( q_{A} ) and ( q_{B} ) and potentials ( 2 V )
and ( (3 / 2) vee ) respectively. Now shell ( B ) is
earthed and let charges on them
become ( boldsymbol{q}_{boldsymbol{A}}^{prime} ) and ( boldsymbol{q}_{boldsymbol{B}}^{prime} . ) Then:
This question has multiple correct options
( mathbf{A} cdot q_{A} / q_{B}=1 / 2 )
( mathbf{B} cdotleft|q_{A}^{prime}right| /left|q_{B}^{prime}right|=1 )
C. Potential of A after earthing becomes (3/2)V
D. Potential difference between A and B after earthing becomes V/2
12
903The surface of the sphere
A. is an equi-potential surface
B. is a zero-potential surface
C. is an uncharged surface
D. None of these
12
904The capacity between the adjacent plates of a parallel plate capacitor is ( 10 mu F . ) If we want a capacity of ( 50 mu F ) the number of plates to be used is
A. 5
B. 50
( c cdot 6 )
( D )
12
905When the separation between the two charges is increased the electric
potential energy of the charges
A. Increases
B. Decreases
c. Remains unchanged
D. May increase or decrease
12
906Why must electrostatic field at the surface of a charged conductor be
normal to the surface at every point? Give reason.
12
907If the value charge density of a dielectric sphere with a cavity (a shown
in the figure) is ( rho . ) Find the electrostatic
self energy.
12
908There are two concentric metal shells of
radii ( r_{1} ) and ( r_{2}left(>r_{1}right) . ) If the outer shell
has a charge ( q ) and the inner shell is grounded, the charge on the inner shell is
A. zero
B. ( -left(r_{1} / r_{2}right) ) q
c. ( r_{1} r_{2} ) q
D. None of thee
12
909Three capacitors, ( 3 mu F, 6 mu F ) and ( 6 mu F ) are connected in series to a source of
120V. The potential difference, in
volts, across the ( 3 mu F ) capacitor will be
A . 24
B. 30
( c cdot 40 )
( D cdot 60 )
12
910A cube of side ‘a’ has a charge ( q ) placed
at each of its eight corneres. The potential at the centre of the cube due
to all the charges is :
A ( cdot frac{16 q}{4 pi varepsilon_{0} a sqrt{3}} )
в. ( frac{16 q}{4 pi varepsilon_{0} a} )
c. ( frac{q}{4 pi varepsilon_{0} a} )
D. ( frac{q}{4 pi varepsilon_{0} a sqrt{3}} )
12
911Plot ( A & B ) represent variation of charge
with potential difference across the
combination (series and parallel) of two
capacitors. Then find the value of
capacitance of capacitors.
A ( .20 mu F, 30 mu F )
B. ( 10 mu F, 40 mu F )
с. ( 10 mu F, 15 mu F )
D. ( 25 mu F, 25 mu F )
12
912Five conducting plates are placed parallel to each other Separation
between them is ( d ) and area of each
plate is ( A ). Plate number 1,2 and 3 are
connected with each other and at the
same time through a cell of emf ( boldsymbol{E} ). The
charge on plate number 1 is
( mathbf{A} cdot E varepsilon_{0} A / d )
B . ( E varepsilon_{0} A / 2 d )
( mathbf{c} cdot 2 E varepsilon_{0} A / d )
D. zero
12
913Two equal charges of magnitude ( Q ) each
are placed at a distance d apart. Their electrostatic energy is E. A third charge
( -Q / 2 ) is brought midway betway these two charges. The electrostatic energy of the system is now.
A . ( -2 E )
B . ( -E )
( c .0 )
D. E
12
914Electric potential can be calculated in a
A. static electric field
B. dynamic electric field
c. both static and dynamic electric field
D. neither static nor dynamic electric field
12
915How many ( 6 mathrm{mF}, 200 mathrm{V} ) condensers are
needed to make a condenser of ( 18 mathrm{mF} )
( 600 vee ? )
( A cdot 9 )
B. 18
( c cdot 3 )
D. 27
12
916Two condensers of capacitance ( 4 mu F ) and ( 5 mu F ) are joined in series. If the potential difference across ( 5 mu F ) is ( 10 V ), then the
potential difference across ( 4 mu F )
condenser is :
( mathbf{A} cdot 22.5 V )
B. ( 10 V )
c. ( 12.5 V )
D. ( 25 V )
12
917Breakdown voltage is
A. voltage at which dielectric behaves as conductor
B. voltage at which molecules starts flowing inside the dielectric freely Which of the following is correct regarding above case,
A. Both ( B, A ) are correct
B. ( B ) is correct
c. ( A ) is correct
D. None of the above is correct
12
918The dielectric strength of air is ( 3.0 times )
( 10^{6} N C^{-1} . ) The largest charge that a
( 0.30 mathrm{cm} ) radius metal sphere can hold without sparking is:
A. 9 nc
B. 8.2 nc
( c cdot 6 n c )
D. 3 nc
12
919Five identical conducting plates 1, 2, 3, 4 and 5 are fixed parallel to and equidistant from each other (see figure). Plates ( 2 & 5 ) are connected by a conductor while ( 1 & 3 ) are joined by another conductor. The junction of ( 1 & 3 )
and the plate 4 are connected to a
source of constant e.m.f. ( V_{0} . ) Find:
(i) The effective capacity of the system between the terminals of the source.
(ii) the charges on plates ( 3 & 5 )
Given ( boldsymbol{d}= ) distance between any
successive plates ( & boldsymbol{A}= ) area of either face of each plate
12
920Determine the electric potential at point P due to two point charges each of charge ( +Q, ) with one point charge being at a distance ( mathrm{R} ) and the other being at a distance ( 2 R )
( A )
[
frac{3 Q}{8 pi_{6} R}
]
в.
[
frac{2 Q}{12 pi epsilon_{0} R}
]
( c )
[
frac{3 Q}{12 pi epsilon_{0} R}
]
D.
[
frac{2 Q}{8 pi epsilon_{0} R}
]
12
921The value of the static dielectric
constant of any material is always
A. greater than 1
B. equal to 1
c. lesser than 1
D. None
12
922Three condensers are connected as
shown in series. If the insulated plate of
( C_{1} ) is at ( 45 V ) one plate of ( C_{3} ) is earthed
find the p.d between the plate of ( C_{2} )
A . ( 10 V )
B . ( 20 V )
( c .30 V )
D. ( 45 V )
12
923Three point charges ( Q_{1}=25 mu C, Q_{2}= )
( 50 mu C ) and ( Q_{3}=100 mu C, ) are kept at the
corners ( A, B ) and ( C ) respectively of an
equilateral triangle ABC having each side equal to ( 7.5 mathrm{m} ). Calculate the total electrostatic potential energy of the
system
12
924The plates of a parallel plate capacitor are charged to ( 200 mathrm{V} ) and then, the charging battery is disconnected. Now, a dielectric
slab of dielectric constant 5 and
thickness ( 4 mathrm{mm} ) is inserted between the
capacitor plates. To maintain the original
capacity, the increase in the separation between the plates of the capacitor is:
A. ( 1.6 mathrm{mm} )
B. ( 3.2 mathrm{mm} )
( mathrm{c} .0 .8 mathrm{mm} )
D. ( 4.8 mathrm{mm} )
12
925(a) Three point charges ( q,-4 q ) and ( 2 q ) are placed at the vertices of an
equilateral triangle ( A B C ) of side ( ^{prime} l^{prime} ) as
shown in the figure. Obtain the expression for the magnitude of the resultant electric force acting on the
charge ( boldsymbol{q} )
(b) Find out the amount of the work done to separate the charges at infinite
distance.
12
926Two concentric spheres of radius ( R ) and
( 2 R ) have charges ( Q ) and ( 2 Q . ) The potential at a point ( mathrm{P} ) situated at a point 3R/2 distance from common centre is
( V, ) Now if outer sphere is earthed, the
potential at point ( P ) is :
A. ( V / 5 )
в. ( V / 10 )
c. ( V / 3 )
D. ( V )
12
927Two small equal point charges of magnitude ( q ) are suspended from a
common point o the ceiling by insulating massless strings of equal lengths. They come to equilibrium with
each string making angle ( theta ) from the
vertical. If the mass of each charge is ( m )
( mathrm{m}, ) then the electrostatic potential at
the center of line joining them will be ( left(frac{1}{4 pi epsilon_{0}}=Kright) )
A ( .2 sqrt{k / m g tan theta} )
B . ( sqrt{k m g tan theta} )
c. ( 4 sqrt{k / m g tan / theta} )
D. ( 4 sqrt{k m g tan theta} )
12
928An isolated conductor of any shape has a net charge of ( +15 mu C ). Inside the conductor is a cavity within which is a point-charge of ( +3.0 mu C . ) What is the charge on the cavity wall and on the outer surface of the conductor?12
929The electric potential at a point in free space due to a charge ( Q ) coulomb is ( Q times 10^{11} V . ) The electric field at that
point is
A ( cdot 4 pi varepsilon_{0} Q times 10^{22} V / m )
B . ( 127 pi varepsilon_{0} Q times 10^{20} V / m )
C. ( 4 pi varepsilon_{0} Q times 10^{20} V / m )
D . ( 12 pi varepsilon_{0} Q times 10^{22} mathrm{V} / mathrm{m} )
12
930A potential difference of ( 5 V ) is applied
across a conductor of length ( 10 mathrm{cm} . ) If
drift velocity of electrons is ( 2.5 times )
( 10^{-4} m / s, ) then electron mobility will be
A ( .5 times 10^{-4} mathrm{m}^{2} mathrm{V}^{-1} mathrm{s}^{1} )
B. ( 5 times 10^{-6} mathrm{m}^{2} mathrm{V}^{-1} mathrm{s}^{1} )
c. ( 5 times 10^{-2} mathrm{m}^{2} mathrm{V}^{-1} mathrm{s}^{1} )
D. zero
12
931If a piece of copper having internal cavity weighs 264 gms.in air and 221 gms. in water, then volume of the cavity is ( ldots . . . . . . . . . . . . . . . . . ) Density of copper ( =8.8 ) ( left.g / c m^{3}right) )
( mathbf{A} cdot 10 mathrm{cm}^{3} )
В. ( 11 mathrm{cm}^{3} )
( mathbf{c} cdot 13 c m^{3} )
D. ( 15 mathrm{cm}^{3} )
12
932If a charge is placed on a conductor having a pointed end, then
A. the charge gets accumulated at the points
B. the charge gets distributed around the conductor
c. the charge collects inside the conductor
D. the charge gets dissipated to the surrounding
12
933The earth has Volume ‘V’ and surface
area ‘A’ then its capacitance would be
12
934Two condensers each of capacitance ( 2 mu F ) are connected in parallel and this
combination is connected in series with
a ( 12 mu F ) capacitor. The resultant
capacity of the system will be:
A. ( 16 mu f )
в. ( 13 mu f )
c. ( 6 mu f )
D. ( 3 mu f )
12
935Two point charges ( 4 mu C ) and ( -6 mu C ) are
seperated by a distance of ( 10 mathrm{cm} ) in air.
At what point between the charges on the line joining the charges is the potential zero.
12
936The equivalent capacitance of three
capacitors of capacitance ( C_{1}, C_{2} ) and ( C_{3} )
connected in parallel is 12 units and the
product ( C_{1} C_{2} C_{3}=48 . ) When the
capacitors ( C_{1} ) and ( C_{2} ) are connected in
parallel the equivalent capacitance is 6
units. Then the capacitance are:
( mathbf{A} cdot 1.5,2.5,8 )
B. 2,3,7
( mathbf{c} cdot 4,2,6 )
D. 1,5,6
12
937A point charge of magnitude ( +1 mu c ) is
fixed at ( (0,0,0) . ) An isolated uncharged spherical conductor is fixed its centre
at ( (4 m, 0,0) . ) The potential and the induced electric field at the centre of
the sphere is
A . ( 1.8 times 10^{5} V ) and ( -5.625 times 10^{6} V / m )
B. ( 0 mathrm{V} ) and ( 0 mathrm{V} / mathrm{m} )
C . ( 2.25 times 10^{5} V ) and ( -5.625 times 10^{6} V / m )
D. ( 2.25 times 10^{5} V ) and ( 0 V / m )
12
938A current of ( 10 A ) is maintained in a
conductor of cross-section ( 1 mathrm{cm}^{2} ). If the
number density of free electrons be ( 9 times 10^{28} m^{-3}, ) the drift velocity of free
electrons is
A. ( 6.94 times 10^{-6} mathrm{m} / mathrm{s} )
B. ( 5.94 times 10^{-2} mathrm{m} / mathrm{s} )
c. ( 1.94 times 10^{-3} mathrm{m} / mathrm{s} )
D. ( 2.94 times 10^{-4} mathrm{m} / mathrm{s} )
12
939The potential difference between points
( A ) and ( D ) in the given circuit is:-
( A cdot frac{2}{V} )
( B cdot frac{8}{0} V )
( c cdot frac{4}{3} v )
D. ( 2 V )
12
940If a unit charge is taken from one point to another over an equipotential surface, then :
A. Work is done on the charge
B. Work is done by the charge
c. work done on the charge is constant
D. No work is done
12
941Explain series combination of Capacitors. Derive the formula for equivalent capacitance.12
942The effective capacitance between ( boldsymbol{A} )
and ( B ) will be
A. ( 0.5 F )
В. ( 1.5 F )
( c .2 F )
D. 2.5
12
943Capacitance of a capacitor made by a
thin metal foil is ( 2 mu F ). If the foil is folded with paper of thickness ( 0.15 mathrm{mm} ) dielectric constant of paper is 2.5 and width of paper is ( 400 mathrm{mm} ), the length of foil will be
A. ( 0.34 mathrm{m} )
B. 1.33 ( m )
c. ( 13.4 mathrm{m} )
D. 33.9 m
12
944Equipotential surfaces are shown in fig,
then the electric field strength will be
A . ( 100 mathrm{Vm}-1 ) along ( mathrm{X} ) -axis
B. ( 100 mathrm{Vm}-1 ) along ( mathrm{Y} ) -axis
c. ( 200 mathrm{Vm}-1 ) at an angle ( 120^{circ} ) wirh ( mathrm{x} ) -axis
D. 50 Vm-1 at an angle ( 180^{circ} ) wirh ( x ) -axis
12
945Water is not used as a dielectric
between the plates of a capacitor because its.
A. Dielectric constant is very low
B. Dielectric strength is very low
c. Dielectric constant is very highh
D. Dielectric strength is very large
12
946A ( 10.0 mu F ) parallel-plate capacitor with
circular plates is connected to a ( 12.0 V )
battery. How much charge ( (text { in } mu C) ) would be on the plates if the capacitor were connected to the ( 12.0 V ) battery
after the radius of each plate was
doubled without changing their separation?
12
947The diagram shows equipotential lines from an unknown charge configuration.
Determine the direction of the field at ( A )
( A cdot U p )
B. Down
c. Left
D. Right
12
948The surface of a planet is found to be uniformly charged. When a particle of
mass ( m ) and no charge is thrown at an angle from the surface of the planet, it has a parabolic trajectory as in projectile motion with horizontal range ( L ). A particle
of mass ( m ) and charge ( q ) with the same initial conditions has a range ( frac{L}{2} ). The range of particle of mass ( m ) and charge ( 2 q )
with the same initial conditions is :
A. ( L )
в. ( frac{L}{2} )
c. ( frac{L}{3} )
D. ( frac{L}{4} )
12
949Inside a uniformly charged spherical
conductor, the electric:
This question has multiple correct options
A. Potential is zero everywhere
B. Potential is non-zero and same everywhere
C. Field is zero everywhere
D. Field has the same magnitude everywhere but it is not
zero
12
95027 identical drops of mercury are charged simultaneously with the same potential of ( 10 V . ) Assuming the drop to
the spherical, if all the charged drops are made to combine to form one large
drop, then its potential will be
( boldsymbol{V} )
A . 40
B. 90
( c .160 )
D. 10
12
951A charge ( Q ) is placed inside the sphere of radius ( a ) then what will be the value of
charge that will be accumulated on the surface of the sphere,
( mathbf{A} cdot mathbf{0} )
в. ( Q )
c. ( -Q )
D. – 2Q
12
952If the inductance and capacitance are both doubled in L-C-R circuit, the resonant frequency of the circuit will:
A. Decrease to one-half of the original value
B. Decrease to one-fourth of the original value
c. Increase to twice the original value
D. Decrease to twice the original value
12
953Parallel plate condenser having a plate separation d is charged to a potential ( V ) It is then isolated. The intensity of the separation of the plates is then doubled The new electric field intensity is :
A . 2 E
B. E
( c cdot E / 4 )
D. E/2
12
954Name the unit of electrical potential:
A. Coulomb
B. Watt
c. Joule
D. volt
12
955A charge of ( 10^{-9} C ) moves from ( X ) to ( Z )
Find the work done by the electric field due to the charge ( Q=2 C ) in moving the
charge from ( X ) to ( Z ). The value of
coulomb’s constant is ( 9 times 10^{9} N m^{2} C^{-2} )
A . ( 0 . J )
В. ( 150 J )
( c .300 J )
D. ( 560 J )
E. ( 1,000 J )
12
956Assertion
There is no current in the metals in the
absence of electric field.
Reason
Motion of free electrons are random.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
12
957An infinite number of charges each equal to ( ^{prime} q^{prime} ) are placed along the ( X ) -axis at ( x=1 )
( x=2, x=4, x=8 ) The potential at the
point ( x=0 ) due to this set of charges is :
( ^{A} cdot frac{Q}{4 pi epsilon_{0}} )
в. ( frac{2 Q}{4 pi epsilon_{0}} )
с. ( frac{3 Q}{4 pi epsilon_{0}} )
D. ( frac{Q}{pi epsilon_{0}} )
12
958f a unit charge is taken from one point to another over an equipotential surface, then work done on the charge is
A. Positive
B. Negative
c. zero
D. constant
12
959If ( 4 times 10^{20} e V ) of energy is required to
move a charge of 0.25 coulomb between
two points, the p.d between them is:
A . 256 ( v )
B. 512 ( v )
( c cdot 123 v )
D. 215 V
12
960A pendulum ( positively charged and hinged at some length above the plate) is swinging above a parallel plate (infinitely large and having negative charge),now consider the following statements, (consider gravity)
A. angular momentum about the hinge point of the ball will be max at lowest point
B. electric potential energy will be max at highest point
c. gravitational potential energy will be lowest at highest point
D. none of the above
12
961There is 10 units of charge at the centre of a circle of radius 10m. The work done in
moving 1 unit of charge around the circle
once is:
A . zero
B. 10 units
c. 100 units
D. 1 unit
12
962A charge of ( 20 mu C ) is placed on the
positive plate of an isolated parallelplate capacitor of capacitance ( 10 mu F ) Calculate the potential difference developed between the plates.
12
963Find the equivalent capacitance across A and B for the arrangement shown in figure. All the capacitors are of
capacitance ( mathbf{C}: )
A ( cdot frac{3 C}{14} )
в. ( frac{C}{8} )
c. ( frac{3 C}{16} )
D. none of these
12
964Two charges of ( +10 mu mathrm{C} ) and ( +20 mu mathrm{C} ) are separated by a distance of 2 cm. The net potential (electric) due to the pair at the middle point of the line joining the two charges, is :
A . 27 MV
B. 18 MV
c. 20 MV
D. 23 MV
12
965The equivalent capacitance between
points ( mathrm{M} ) and ( mathrm{N} ) is :
A . Infinity
в. ( c_{1}+frac{C_{2}}{C_{1}} )
( c_{C_{2}+frac{C_{2}}{C_{1}}} )
D. ( frac{C_{1} C_{2}}{C_{1}+C_{2}} )
12
966The potential and electric field in the
above set up if the consecutive charges
have opposite sign is :
A ( cdot frac{q}{6 pi epsilon_{0}} ) and ( frac{q}{5 pi epsilon_{0}} )
B. ( frac{q}{6 pi epsilon_{0}} ) and ( frac{q}{6 pi epsilon_{0}} )
c. ( frac{q}{5 pi epsilon_{0}} ) and ( frac{q}{6 pi epsilon_{0}} )
D. ( frac{q}{4 pi epsilon_{0}} ) and ( frac{q}{6 pi epsilon_{0}} )
12
967Why should electrostatic field be zero
inside a conductor?
12
968Find the correct relation from the
following:
A. Work done=charge ( times ) power
B. Work done=charge ( times ) potential difference
C. Work done=current ( times ) voltage
D. All
12
969in a certain region of free space a non-
uniform electric field which depends on
X-coordinates is given by ( overrightarrow{boldsymbol{E}}=boldsymbol{E}_{0} boldsymbol{x} hat{boldsymbol{i}} )
What is the total amount of electric
potential energy contained within the
cube of sides of length L as shown
below?
A ( cdot frac{1}{5} varepsilon_{0} E_{0}^{2} L^{5} )
B ( cdot frac{1}{5} varepsilon_{0} E_{0}^{2} L^{6} )
C ( cdot frac{1}{6} varepsilon_{0} E_{0}^{2} L^{6} )
D ( cdot frac{1}{2} varepsilon_{0} E_{0}^{2} L^{5} )
12
970Three charges ( -q, Q ) and ( -q ) are placed at equal distances on a straight line. If the total potential energy of the system of three charges is zero, then the ratio ( mathrm{Q} ) ( : q ) is
A .1: 2
B . 2: 1
c. 1: 1
D. 1: 4
12
971An infinite number of equal charges ( (q ) each) are placed at distance ( x= )
( 1,2,4,8, dots dots ). ( 0 . ) Then the electric potential at the origin ( (x=0) ) will be :
A. zero
B. infinite
c. ( frac{q}{4 pi varepsilon_{0}} )
D. ( frac{2 q}{4 pi varepsilon_{0}} )
12
972Seven capacitors, each of capacitance ( 2 mu F ) are to be connected to obtain a
capacitance of ( 10 / 11 mu F ).Which of the following combinations is possible?
A. 5 in parallel 2 in series
B. 4 in parallel 3 in series
c. 3 in parallel 4 in series
D. 2 in parallel 5 in series
12
973A parallel-plate air capacitor of
capacitance ( 245 p F ) has a charge of
magnitude ( 0.148 mu C ) on each plate. The
plates are ( 0.328 m m ) apart. What is the
potential difference between the plates ( (text { in } V) ? )
12
974The amount of energy that a unitary point electric charge would have, if located at any point in space, is defined
its:
A. electric potential energy
B. electric potential
c. electric potential difference
D. electric field
12
975Which of the following can be used as dielectric?
A. Plastics
в. Mica
c. Porcelain
D. All of the above
12
976Electric field as a function of distance
from the centre of a uniformly charged solid sphere is mathematically:
A . a discontinuos function
B. inversely related to distance from the centre
c. proportional to distance from the centre
D. none of the above
12
977A condenser of capacity ( 0.2 mu F ) is
charged to a potential of 600 V. The battery is now disconnected and the
condenser of capacity ( 1 mu F ) is connected across it. The potential of the condenser will reduce to
( mathbf{A} cdot 600 V )
B. ( 300 V )
c. ( 100 V )
D. ( 120 V )
12
978The Sl units of potential is12
979Four metallic plates each with a surface area of one side ( A ) are placed at a
distance ( d ) from each other as shown in
figure. Then the capacitance of the
system between ( X ) and ( Y ) is
A.
B. ( frac{2 epsilon_{0} A}{3 d} )
c. ( frac{3 epsilon_{0} A}{d} )
D.
12
980The capacitance of a parallel-plate
capacitor is ( C_{0} ) when the region
between the plates has air. This region
is now filled with a dielectric slab of
dielectric constant K. The capacitor is
connected to a cell emf ( varepsilon_{1} ) and the slab
is taken out.
This question has multiple correct options
A. Charge ( varepsilon C_{0}(K-1) ) flows through the cell
B. Energy ( varepsilon^{2} C_{0}(K-1) ) is absorbed by the cell.
C. The energy stored in the capacitor is reduced by ( varepsilon^{2} C_{0}(K-1) )
D. The external agent has to do ( frac{1}{2} varepsilon^{2} C_{0}(K-1) ) amount of work to take the slab out.
12
981A hollow metal sphere of radius ( 10 mathrm{cm} ) is
charged such that the potential on its surface becomes ( 80 mathrm{V} ). The potential at the centre of the sphere is?
A . ( 80 v )
в. 800 V
c. ( 8 v )
D. zero
12
982The force of attraction between the
plates of a charged condenser is :
A ( cdot q^{2}left(2 varepsilon_{0} Aright) )
B ( cdot q^{2}left(2 varepsilon_{0} A^{2}right) )
( mathbf{c} cdot q^{2} /left(2 varepsilon_{0} Aright) )
D. none of these
12
983Two spheres of radii ( 3 mathrm{cm} ) and ( 5 mathrm{cm} ) are charged to potentials 3000 V and 4500 V respectively. They are then connected by
a thin metallic wires. The loss of electric
energy in this process is?
( mathbf{A} cdot 2 times 10^{-8} mathbf{J} )
B ( cdot 4 times 10^{-8} mathrm{J} )
D . ( 2.36 times 10^{-7} ) J
12
984A capacitor of capacitance ( boldsymbol{C}=mathbf{1 5 p} boldsymbol{F} )
is charged with voltage ( V=500 V . ) The
electric field inside the capacitor with
dielectric is ( 10^{6} V / m ) and the area of the plate is ( 10^{-4} m^{2}, ) then the dielectric
constant of the medium is : ( left(varepsilon_{0}=right. )
( 8.85 times 10^{-12} ) in S.l.units
A. 12.47
B. 8.47
c. 10.85
D. 14.85
12
985A charge of 10 e.s.u is placed at the distance of ( 2 mathrm{cm} ) from a charge of 40
e.s.u and ( 4 mathrm{cm} ) from another charge of
20 e.s.u.The potential energy of charged
10 e.s.u is?
A. 87.5
B. 112.5
c. 150
D. 250
12
986Two large, parallel conducting plates ( x ) and ( Y, ) kept close to each other, are given charges ( Q_{1} ) and ( Q_{2}left(Q_{1}>Q_{2}right) ). The
four surfaces of the plates are ( A, B, C ) and ( D, ) as shown in figure. Then :
This question has multiple correct options
A ‘ the charge on A is ( frac{1}{2}left(Q_{1}+Q_{2}right) )
B ‘ the charge on B is ( frac{1}{2}left(Q_{1}-Q_{2}right) )
c. The charge on ( c ) is ( -frac{1}{2}left(Q_{1}-Q_{2}right) )
D ‘ the charge on D is ( frac{1}{2}left(Q_{1}+Q_{2}right) )
12
987A dielectric slab fills the lower half of a
parallel plate capacitor as shown in
figure :
(Take plate are as ( boldsymbol{A} ) )
This question has multiple correct options
A . equivalent capacity of the system is ( left(left(varepsilon_{0} A / 2 dright)(1+right. )
( K) )
B. the net charge of the lower half of the left hand plate is ( 1 / K ) times the charge on the upper half of the plate
C. net charges on the lower and upper halves of the left hand plate are different
D. net charge on the lower hand of the left hand plate is ( frac{K varepsilon_{0} A}{2 d} times V )
12
988The equivalent capacitance between
point ( a ) and ( b ) in the combination of
capacity figure is
( A cdot 15 mu F )
B. ( 10 mu F )
с. ( 11.2 mu F )
D. ( 7.4 mu F )
12
989A parallel plate capacitor having
capacitance ( C ) has two plates of same
area ( A ) and thickness t. The figure shows the charges available on the four
surfaces of the plates. The potential
difference V between the two plates is
given by:
A ( cdot frac{q_{2}-q_{3}}{2 C} )
в. ( frac{q_{2}-q_{3}}{C} )
c. ( frac{q_{1}-q_{4}}{2 C} )
D. ( frac{q_{1}-q_{4}}{C} )
12
990Angle between an equipotential surface and electric lines of force is :
A . ( 0^{circ} )
B. ( 90^{circ} )
( c cdot 180^{circ} )
D. ( 270^{circ} )
12
991An uncharged parallel plate capacitor filled with a dielectric of dielectric
constant ( K ) is connected to an air filled
identical parallel capacitor charged to
potential ( V_{1} . ) If the common potential is
( V_{2}, ) the value of ( K ) is
A. ( frac{V_{1}-V_{2}}{V_{1}} )
B. ( frac{V_{1}}{V_{1}-V_{2}} )
c. ( frac{V_{2}}{V_{1}-V_{2}} )
D. ( frac{V_{1}-V_{2}}{V_{2}} )
E ( cdot frac{V_{1}-V_{2}}{V_{1}+V_{2}} )
12
992Two small identical metal balls ( A ) and
( B ) of radius ‘ ( r^{prime} ) are placed apart. The
distance between centre of balls is ‘a ( _{0} ).
The net potential of ball ( A ) is ( V_{1} ) and that
of ( B ) is ( V_{2} . ) Let ( q_{1} ) and ( q_{2} ) are the charges
on balls ( A ) and ( B ) respectively. Then the
charges on ( A ) and ( B ) are ( left(operatorname{given} r<<a_{0}right) )
A ( cdot q_{1}=4 pi varepsilon_{0} frac{a_{0} rleft(V_{1} a_{0}-V_{2} rright)}{a_{0}^{2}-r^{2}} )
B. ( quad q_{1}=4 pi varepsilon_{0} frac{a_{0} rleft(V_{1} a_{0}+V_{2} rright)}{a_{0}^{2}+r^{2}} )
( ^{mathbf{C}} cdot_{q_{2}}=4 pi varepsilon_{0} frac{a_{0} rleft(V_{1} a_{0}+V_{2} rright)}{a_{0}^{2}+r^{2}} )
D. ( _{q_{2}}=4 pi varepsilon_{0} frac{a_{0} rleft(V_{1} a_{0}-V_{2} rright)}{a_{0}^{2}-r^{2}} )
12
993Two charges ( +Q ) and ( -2 Q ) are placed at ( (- )
a,0) ( &(+a, 0) ). The locus of points in the plane of the charges where the potential is zero will be :
A. straight line
B. circle
c. parabola
D. ellipse
12
994The waves which are produced by accelerated electrons in electronic
circuits are
A . ‘-‘-waves
B. ‘+’waves
D. Infrared rays
12
995A parallel plate capacitor has area
( 20 c m^{2} ) and separation between the plates is 0.1 m ( m . ) The dielectric break
down strength is ( 3 times 10^{6} v / m )

The maximum r.m.s voltage which can be safely applied is :
( mathbf{A} cdot 210 V )
в. ( 300 V )
c. ( 100 V )
D. 200

12
996Calculate the electric potential at the
center of the square:
( A )
в. ( k frac{29}{x^{2}} )
( c cdot_{k} frac{4 q}{c^{2}} )
D. ( k frac{49}{6} )
( E )
[
k frac{(4 sqrt{2})}{s}
]
12
997Assertion
A capacitor blocks direct current in the
Reason
The capacitive reactance of the capacitor is inversely proportional to
frequency f of the source of e.m.f…
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
12
998All the capacitance in the figure are of capacitance ( C . ) The effective capacitance between ( P ) and ( Q ) is :
4.20
3. ( 3 C )
( c cdot 4 C )
D. ( 1.5 C )
12
999Four equipotential curves in an electric
field are shown in the figure. A,B,C are
three points in the field. If electric
intensity at ( A, B, C ) are ( E_{A}, E_{B}, ) and ( E_{C} )
then:
( mathbf{A} cdot E_{A}=E_{B}=E_{C} )
в. ( E_{A}>E_{B}>E_{C} )
c. ( E_{A}<E_{B}E_{B}<E_{C} )
12
1000A proton is moved ( 15 mathrm{cm} ) on path parallel to the field lines of a uniform electric
field of ( 2.0 times 10^{5} mathrm{V} / mathrm{m} )
What are the possible change in potential ?consider both cases of a
moving the proton.
12
1001At what point on the line joining the two charge is the electric potential zero.12
1002From a supply of identical capacitors rated ( 8 m F, 250 V ), the minimum
number of capacitors required to form a composite ( 16 m F, 1000 V ) is :
A . 2
B. 4
c. 16
D. 32
12
1003Consider a capacitor-charging circuit.
Let ( Q_{1} ) be the charge given to the capacitor in a time interval of ( 10 m s )
and ( Q_{2} ) be the charge given in the next time interval of 10 ms. Let ( 10 mu C ) charge be deposited in a time interval ( t_{1} ) and
the next ( 10 mu C ) charge is deposited in
the next time interval ( t_{2} )
A. ( Q_{1}>Q_{2}, t_{1}>t_{2} )
в. ( Q_{1}>Q_{2}, t_{1}<t_{2} )
c. ( Q_{1}t_{2} )
D. ( Q_{1}<Q_{2}, t_{1}<t_{2} )
12
1004A particle of mass ( 1 g m ) and charge ( 1 mu C )
is held at rest on a frictional horizontal
surface at distance ( 1 mathrm{m} ) from a fixed
charge ( 2 m C . ) If the particle is released, it will be repelled. The speed of the particle when it is at a distance of ( 10 m )
from the fixed charge will be:
A ( cdot 60 m s^{-1} )
B. ( 100 mathrm{ms}^{-1} )
( mathrm{c} .90 mathrm{ms}^{-1} )
D. ( 180 m s^{-1} )
12
1005Two equal positive charges are kept at points ( A ) and ( B . ) The electric potential at the points between ( A ) and ( B ) (excluding these points) is studied while moving
from ( A ) to ( B ). The potential
A. continuously increases
B. continuously decreases
c. increases then decreases
D. decreases then increases
12
1006In the circuit shown in the figure, there are two parallel plate capacitors each of
the capacitance ( C ) The switch ( S_{1} ) is
pressed first to fully charge the
capacitor ( C_{1} ) and then released. The
switch ( S_{2} ) is then pressed to charge the
capacitor ( C_{1} ) 2. After some time, ( S_{2} ) is
released and then ( S_{3} ) is pressed. After
some time,
A. the charge on the upper plate of ( C_{1} ) is ( 2 C V_{o} )
B. The charges on the upper plate of ( C_{1} ) is ( C V_{o} )
c. The charge on the upper plate of ( C_{2} ) is 0
D. The charge on the upper plate of ( C_{2} ) is ( -C V_{o} )
12
1007A cube of side ( x ) has a charge ( q ) at each of its vertices. The potential due to this charge array at the centre of the cube is
A ( cdot frac{4 q}{3 pi varepsilon_{0} x} )
В. ( frac{4 q}{sqrt{3} pi varepsilon_{0} x} )
c. ( frac{3 q}{4 pi varepsilon_{0} x} )
D. ( frac{2 q}{sqrt{3} pi varepsilon_{0} x} )
12
1008Assertion
A capacitor can be given only a limited
quantity of charge
Reason
A capacitor is an arrangement which can store sufficient quantity of charge
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
12
1009When two capacitors of capacities ( 3 mu F )
and ( 6 mu F ) are connected in series and
connected to ( 120 V, ) the potential
difference across ( 3 mu F ) is:
A . ( 40 V )
B. ( 60 V )
c. ( 80 V )
D. ( 180 V )
12
1010Five identical plates are connected
across a battery as in figure. If the
charge on plate 1 be ( +q ), then the
charges on the plates 2,3,4 and 5 are:
( mathbf{A} .-q,+q,-q,+q )
в. ( -2 q,+2 q,-2 q,+q )
c. ( -q,+2 q,-2 q,+q )
D. none of the above.
12
1011Find the change in the potential energy of the proton in the displacement.
A. ( -6.4 times 10^{-15} J )
В. ( 6.4 times 10^{-15} mathrm{J} )
c. ( -6.4 times 10^{-19} J )
D. ( 6.4 times 10^{-19} mathrm{J} )
12
1012A thunder cloud and the earth’s surface
may be regarded as a pair of charged
parallel plates separated by a distance
( h ) and the capacitance of the system is
C. When a flash of mean current ‘ ( i ) ‘
occurs for a time duration ‘t’, the
electric field strength between the cloud and earth is:
( mathbf{A} cdot frac{i t}{C} )
B. Cit
c. ( frac{i t}{C h} )
D. ( frac{text { Cit }}{h} )
12
1013Two parallel-plate vacuum capacitors
have areas ( A_{1} ) and ( A_{2} ) and equal plate spacing d. Show that when the capacitors are connected in parallel, the equivalent capacitance is the same as for a single capacitor with plate area
( A_{1}+A_{2} ) and spacing d.
12
1014A parallel plate capacitor with air as dielectric is charged to a potential ‘V using a battery. Removing the battery, the charged capacitor is then connected across an identical
uncharged parallel plate capacitor filled with wax of dielectric constant ‘K’ the
common potential of both the
capacitor is
A. V volts
B. kV volts
( c cdot(k+1) v v o l t s )
D. ( frac{V}{k+1} ) volts
12
1015A parallel plates capacitor is located horizontally such that one of the plates is submerged in a liquid while the other is above the liquid surface. When plates are charged the level of liquid
A . rises
B. falls
c. remains unchanged
D. may rise or fall depending on the amount of charge
12
1016What is the electronic potential at the centre of square of side 1 m? The
charges ( 1 times 10^{-8} C,-2 times 10^{-8} C, 3 times )
( 10^{-8} ) Cand ( 2 times 10^{-8} C ) are placed at the
corners of the square.
12
1017How accurate is one-dimensional
model?
A. Less accurate
B. Quite accurate
c. cannot say
D. None
12
1018A capacitor of capacitance ( C_{0} ) is
charged to a potential ( V_{0} ) and then
isolated. A small capacitor ( C ) is then
charged from ( C_{0}, ) discharged and charged again. This process is being
repeated ( n ) times. Due to this, the
potential of the larger capacitor is
decreased to ( V ). The value of ( C ) is :
( ^{mathbf{A}} cdot_{C_{0}}left(frac{V_{0}}{V}right)^{1 / n} )
( ^{mathrm{B}} C_{0}left[left(frac{V_{0}}{V}right)^{1 / n}-1right] )
( ^{mathbf{c}} cdot_{C_{0}}left[left(frac{V}{V_{0}}right)-1right]^{n} )
( ^{mathrm{D}} C_{0}left[left(frac{V_{0}}{V}right)^{n}+1right] )
12
1019Five identical capacitor plates, each of
area ( A, ) are arranged such that the
adjacent plates are at a distance ( boldsymbol{d} )
a part. The plates are connected to a
source of emf ( V ) as shown in figure.
Match the following?
12
1020Two neutral conducting spheres are next to each other and touching each
other, They are also each separated from the table with an insulating stand.
Then, a negatively charged rod is brought near, but not touching, sphere
A. The two spheres are then separated
by touching only their insulating base Finally, the charged rod is removed. What are the charges of sphere ( A ) and
sphere B?
A. Sphere A is positive while sphere B is negative
B. Sphere A is negative while sphere B is positive
c. Both spheres are positively charged.
D. Both spheres are negatively charged
12
1021Two charges are placed at a distance apart. If a glass slab is placed between them, force between them will
A. be zero
B. increase.
c. decrease.
D. remains the same
12
1022If
100 joule of work must be done to move electric charge equal to ( 4 C ) from
a place, where potential is -10 volt to another place, where potential is ( V ) volt, find the value of ( V )
12
1023topp
Q трерош (и)
onstant EMF is connected to the system such that B is connected to the positive terminal and A and c are nected to the negative terminal Vhich of the following diagrams orrectly depicts the isolines of electric otential (shown as dotted lines) in the egion between the plates?
12
1024A parallel plate capacitor has capacitance ( C . ) If it is equally filled the parallel of materials of dielectric
constant ( K_{1} ) and ( K_{2} ) its capacity
becomes ( C_{1} . ) The ratio of ( C_{1} ) and ( C ) is
A. ( K_{1}+K_{2} )
в. ( frac{K_{1} K_{2}}{K_{1}+K_{2}} )
c. ( frac{K_{1}+K_{2}}{K_{1} K_{2}} )
D. ( frac{2 K_{1} K_{2}}{K_{1}+K_{2}} )
12
1025A uniform electric field of magnitude ( 290 V / m ) is directed in the positive ( x ) direction. ( A+13.0 mu C ) charge moves from the origin to the point ( (x, y)= ) ( (20.0 c m, 50.0 c m) )
What is the change in the potential
energy of the charge field system?
A . ( -754 J )
в. ( -754 m J )
c. ( -754 k J )
D. ( -754 mu J )
12
1026An electron is taken from point ( A ) to
point ( B ) along the path ( A B ) in a uniform
electric field of intensity ( boldsymbol{E}=mathbf{1 0} boldsymbol{V m}^{-1} )
Side ( A B=5 m, ) and side ( B C=3 m )
Then, the amount of work done on the
electron by us is :
A. 50 ev
B. 40 ev
c. – -50 ev
D. -40 eV
12
1027Effective capacitance of parallel
combination of two capacitors ( C_{1} ) and
( C_{2} ) is ( 10 mu F ). when these capacitors are individually connected to a voltage
source of ( 1 V ), the energy stored in the capacitor ( C_{2} ) is 4 times that of ( C_{1} ). If
these capacitors are connected in series, their effective capacitance will be:
( mathbf{A} cdot 8.4 mu F )
в. ( 3.2 mu F )
c ( .1 .6 mu F )
D. ( 4.2 mu F )
12
1028How many electrons should be removed
from a conductor so that it acquires a positive charge of 3.5 nC?
12
1029A charge ‘ ( Q ) ‘ is placed at each corner of a cube of side ‘a’. The potential at the
centre of the cube is :
A ( cdot frac{8 Q}{pi varepsilon_{0} a} )
в. ( frac{4 Q}{4 pi varepsilon_{0} a} )
c. ( frac{4 Q}{sqrt{3} pi varepsilon_{0} a} )
D. ( frac{2 Q}{pi varepsilon_{0} a} )
12
1030Two conducting spheres of radii ( r_{1} ) and
( r_{2} ) are charged to the same surface
charge density. The ratio of electric
fields near their surface is :
A ( cdot r_{1}^{2} / r_{2}^{2} )
B . ( r_{2}^{2} / r_{1}^{2} )
( mathbf{c} cdot r_{1} / r_{2} )
D. 1: 1
12
1031Two point charges ( +q ) and ( -q ) are
located at points ( (0,0,-a) ) and ( (0,0, a) ) respectively. The potential at a point ( (0,0, z) ) where ( z>a ) is
A ( cdot frac{2 q a}{4 pi epsilon_{0}left(z^{2}+a^{2}right)} )
в. ( frac{q}{4 pi epsilon_{0} a} )
c. ( frac{q a}{4 pi epsilon_{0} z^{2}} )
D. ( frac{2 q a}{4 pi epsilon_{0}left(z^{2}-a^{2}right)} )
12
1032An equipotential surface is a surface with constant value of potential at all points on the surface. What is the amount of work done in
moving a ( 2 mu c ) charge between two
points at ( 3 c m ) apart on an equipotential
surface?
12
1033A capacitor of capacitance ( 10 mu F ) is
charged a potential ( 50 V ) with a battery. The battery is now disconnected and an additional charge ( 200 mu C ) is given to the positive plate of the capacitor. The potential difference across the
capacitor will be :
A . ( 50 V )
B. ( 80 V )
( mathbf{c} cdot 100 V )
D. ( 60 V )
12
1034Consider a finite insulated, uncharged conductor placed near a finite positively charged conductor. The uncharged body must have a potential:
A. less than the charged conductor and more than at infinity.
B. more than the charged conductor and less than at infinity.
c. more than the charged conductor and more than at infinity.
D. less than the charged conductor and less than at infinity.
12
1035If the susceptibility of dia, para and ferro magnetic materials are Xd. ( X p . X f ) respectively, then
A. ( X d<X p<X f )
в. ( X f<X p<X d )
c. ( X f<X d<X p )
D. ( X d<X f<X p )
12
1036The surface of a conductor is an
equipotential surface:
12
1037Two point charges ( +boldsymbol{q} ) and ( -boldsymbol{q} ) are held fixed at ( (-d, 0) ) and ( (d, 0) ) respectively of a ( (x, y) ) coordinate system, then
A. the electric field ( vec{E} ) at all points on the ( x ) -axis has the same direction
B. ( vec{E} ) at all points on the ( y ) -axis is along ( hat{i} )
C. positive work is done in bringing a test charge from infinity to the origin
D. all of the above
12
1038What is the work required to set up the four-charge configuration of the figure, assuming the charges are initially infinitely far apart?
A ( cdot frac{q^{2}}{4 pi epsilon_{0} a}(4+sqrt{2}) )
В ( cdot frac{q^{2}}{4 pi epsilon_{0} a}(4-sqrt{2}) )
c. ( frac{q^{2}}{4 pi epsilon_{0} a}(-4+sqrt{2}) )
D. ( frac{q^{2}}{4 pi epsilon_{0} a}(-4-sqrt{2}) )
12
1039Derive the formula for equivalent capacitance when the capacitors are connected in series.12
10405
00
10
12
1041The potential difference between points ( A ) and ( B, ) in a section of a circuit shown,
is
A. 5 volt
B. 1 Volt
c. 10 volt
D. -16volt
12
1042Suppose ( n ) conducting plates are
placed face to face, and the distance
between two successive plates is ( d )
Each plate is half of the area of the
previous one. If area of first plate is ( A ). If
the area of the first plate is ( A ), the
equivalent capacitance of the system is ( operatorname{given} operatorname{as} frac{varepsilon_{0} A}{dleft(x^{n}-2right)} . ) Find ( x )
12
1043Find the dimensions of capacitance :
( mathbf{A} cdot=left[M^{-1} L^{2} T^{4} A^{-2}right] )
B . ( =left[M^{-1} L^{-2} T^{-4} A^{2}right] )
( mathbf{c} cdot=left[M^{-1} L^{-1} T^{4} A^{2}right] )
D. ( =left[M^{-1} L^{-2} T^{4} A^{2}right. )
12
1044The work done in carrying a charge ( q ) once round a circle of radius a with a
charge ( Q ) at its centre is:
A ( cdot frac{q Q}{4 pi varepsilon_{0} a} )
в. ( frac{q Q}{4 pi varepsilon_{0} a^{2}} )
c. ( frac{q}{4 pi varepsilon_{0} a} )
D. zero
12
1045f some charge is given to a solid metallic sphere, the field inside remains zero and by Gauss’s law all the charge resides on the surface. Suppose now that Coulomb’s force between two
charges varies as ( 1 / r^{3} . ) Then, for a charged solid metallic sphere
A . field inside will be zero and charge density inside will be zero
B. field inside will not be zero and charge density inside will not be zero
c. field inside will not be zero and charge density inside will be zero
D. field inside will be zero and charge density inside will not be zero
12
1046Figure shows a capacitor made of two
circular plates each of radius ( 12 mathrm{cm} )
and separated by ( 5.0 mathrm{cm} . ) The capacitor
is being charged by an external source (not shown in the figure). The charging
current is constant and equal to 0.15 A.
(a) Calculate the capacitance and the
rate of change of potential difference
between the plates.
( (b) )
Obtain the displacement current across
the plates.
( (c) )
Is
Kirchhoffs first rule (junction rule) valid
at each plate of
the capacitor Explain.
12
1047Five equal point charges with ( Q= )
( 10 n C ) are located at ( x=2,4,5,10 ) and
( 20 m . ) If ( varepsilon_{0}=frac{10^{-9}}{36 pi} F / m, ) then the
potential at the origin ( (x=0) ) is?
A . ( 9.9 v )
B. ( 11.1 mathrm{v} )
c. ( 90 v )
D. ( 99 v )
E. 111
12
1048Four metallic plates each with a surface
area of one side ( A, ) are placed at a
distance ( d ) from each other. The two
outer plates are connected to one point
( A ) and the two other inner plates to
another point ( B ) as shown in the figure.
Then the capacitance of the system is :
( A cdot frac{epsilon_{0} A}{d} )
в. ( frac{2 epsilon_{0} A}{d} )
c. ( frac{3 epsilon_{0} A}{d} )
D. ( frac{4 epsilon_{6} A}{d} )
12
1049When air is replaced by a dielectric
medium of constant ( K ), the capacity of
the condenser:
A. increases ( K ) times
B. increases ( K^{2} ) times
C . remains unchanged
D. decreases ( K ) times
12
1050Two parallel plate air capacitors have the same separation. The plates of the first are squares of side ( 10 mathrm{cm} . ) The
plates of the second are squares of side ( 20 mathrm{cm} . ) The ratio of their capacitance is :
( A cdot 2: )
B. 1: 2
( c cdot 4: 1 )
D. 1: 4
12
1051Two point charges ( +9 q ) and ( +q ) are kept ( 16 mathrm{cm} ) apart. Where should a third charge ( Q ) be placed between them so that the system remains in equilibrium
( ? )
A. ( 24 mathrm{cm} ) from ( +9 q )
в. ( 12 mathrm{cm} ) from ( +9 q )
c. 24 cm from ( +q )
D. ( 12 mathrm{cm} ) from ( +q )
12
1052A voltmeter reads ( 4 V ) when connected
to a parallel plate capacitor with air as a dielectric. When a dielectric slab is
introduced between plates for the same configuration, voltmeter reads ( 2 V ) What is the dielectric constant of the
material?
A . 0.5
B. 2
c. 8
D. 10
12
1053The potential difference between the
plates of a capacitor separated by ( 3 mathrm{mm} ) is ( 12.0 mathrm{V} ). Calculate the magnitude of ( mathrm{E} ) between the plates?
12
1054(A) Estimate the speed with which electrons emitted from a heated emitter
of an evacuated tube impinge on the collector maintained at a potential difference of ( 500 mathrm{V} ) with respect to the emitter. Ignore the small initial speeds of the electrons. The specific charge of the electron, i.e., its e/m is given to be ( 1.76 times 10^{11} C k g^{-1} )
(B) Use the same formula you employ in
(a) to obtain electron speed for a collector potential of ( 10 mathrm{MV} ). Do you see what is wrong? In what way is the formula to be modified?
12
1055The potential difference between two
parallel plates is ( 10^{4} V . ) If the plates are
separated by ( 0.5 mathrm{cm}, ) the force on an electron between the plates is :
A . ( 32 times 10^{-13} N )
В. ( 0.32 times 10^{-13} N )
D. ( 3.2 times 10^{-13} ) ( N )
12
1056Two identical metal plates, separated by a distance d form a parallel plate
capacitor. A metal sheet of thickness ( frac{a}{2} ) of the same area as that of either plate, is
inserted between the plates. The ratio of the capacitance’s after the insertion of the sheet to that before insertion is:
2
( mathbf{A} cdot sqrt{2}: 1 )
B. 2:
c. 1:
D. ( 1: sqrt{2} )
12
1057Two identical plates of different metals are joined to form a single plate whose thickness is double the thickness of
each plate. If the coefficients of conductivity of each plate are 2 and 3 respectively, then the conductivity of the composite plate will be
A. 5
B. 2.4
c. 1.5
D. 1.2
12
1058An electron that accelerates from a
point near a collection of positive source charges toward a point near a collection of negative source charges
experiences
A. A decrease in electrical potential energy as it moves toward a region at a lower electric potential
B. A decrease in electrical potential energy as it moves toward a region at a higher electric potential
C. An increase in electrical potential energy as it moves toward a region at a lower electric potential
D. An increase in electrical potential energy as it moves toward a region at a higher electric potential
E. No change in electrical potential energy
12
1059Equipotential surfaces
A. are closer in regions of large electric fields compared to regions of lower electric fields
B. will be more crowded near sharp edges of a conductor
C . will always be equally spaced
D. both
(a) and
(b) are correct
12
1060Which of the material can be used as a
dielectric?
This question has multiple correct options
A. Ceramics
B. Woodd
c. copper
D. Aluminium
12
1061In the electric field of charge ( Q ), another
charge is carried from ( boldsymbol{A} ) to ( boldsymbol{B} . boldsymbol{A} ) to ( boldsymbol{C}, boldsymbol{A} )
to ( D ) and ( A ) to ( E ), then work done will be
A. Minimum along path ( A B ).
B. Minimum along path ( A D ).
C. Minimum along path ( A E ).
D. zero along all the paths
12
1062Derive the expression for the capacitance of a parallel plate
capacitore having plate area ( A ) and plate separation d.
12
1063Two metallic spheres of radii ( 2 mathrm{cm} ) and
( 6 mathrm{cm} ) are given charge ( 3 times 10^{-2} mathrm{C} ) and
( 7 times 10^{-2} C, ) respectively. If these are
connected by a conducting wire, the final charge on the bigger sphere is
12
1064Work done in moving an electric charge
( q ) in an electric field does not depend
upon:
A. Magnitude of the charge
B. Potential difference between two points
c. Mass of the particle
D. All of these
12
1065Which of the following units is not equivalent to Farad?
A ( . C V^{2} )
в. ( J / V^{2} )
c. ( Q^{2} / J )
D. ( Q / V )
12
1066In scattering experiment, find the distance of closest approach, if a ( 6 M e V alpha- ) particle is used
A ( .3 .2 times 10^{-16} m )
В. ( 2 times 10^{-14} mathrm{m} )
c. ( 4.6 times 10^{-15} mathrm{m} )
D. 3.2 ( times 10^{-15} mathrm{m} )
12
1067A highly conducting sheet of aluminium foil of negligible thickness is placed between the plates of a parallel plate capacitor. The foil is parallel to the plates at distance ( frac{d}{2} ) from positive plate where ( d ) is distance between plates. If the capacitance before the insertion of
foil was ( 10 mu F ), its value after the insertion of foil will be:
( mathbf{A} cdot 20 mu F )
в. ( 10 mu F )
( mathrm{c} .5 mu F )
D. zero
12
1068Define the capacity of a condenser
Derive an expression for the capacity of a parallel plate condenser. How can its capacity be increased?
12
1069Three charges of ( +5 mu C ) are located at
the comes of an equilateral triangle whose sides are ( 6 mathrm{cm} ) long. Find the potential at the midpoint of the base of the of the triangle.
12
1070To bring a unit positive charge from infinity to a point in an electric field, some work has to done, which is called:
A. potential energy
B. electric potential
c. electric field
D. electric induction
12
1071Assertion
Coaxial cables make use of a dielectric
between the two conducting lines.
Reason
dielectrics are good insulators.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
12
1072Four plates of same area of cross-
section are joined as shown in figure. The distance between each plate is d.
The equivalent capacity between ( A ) and
B will be
A ( cdot frac{2 epsilon_{0} A}{d} )
B. ( frac{epsilon_{0} A}{d} )
с. ( frac{3 epsilon_{0} A}{d} )
D. ( frac{3 epsilon_{0} A}{2 d} )
12
1073An isolated hollow metal sphere is electrically neutral (no excess charge)
and supported on an insulating stand. A small amount of negative charge is suddenly placed at one point ( P ) on this
metal sphere. If we check on this excess negative charge a few seconds later we will find one of the following
possibilities:
A. All of the excess charge remains right around P.
B. The excess charge has distributed it self evenly over the outside surface of the sphere.
C. The excess charge is evenly distributed over the inside and outside surface
D. Most of the charge is still at point ( P ), but some will have spread over the sphere.
12
1074A hollow metal sphere of radius ( 5 mathrm{cm} ) is charged such that the potential on its
surface is ( 10 V . ) The potential at a
distance of ( 2 mathrm{cm} ) from the centre of the
sphere is:
A. zero
B. ( 10 V )
( c .4 V )
D. ( 10 / 3 V )
12
1075If the plates of a parallel plate capacitor are not equal in area, then quantity of charge
A. On the plates will be same but nature of charge will differ
B. On the plates as well as nature of charge will be different
c. on the plates will be different but nature of charge will be same
D. As well as nature of charge will be same
12
1076Which of the following statement(s)
is/are correct?
This question has multiple correct options
A. Conductors are materials that allow the flow of electric current, whereas dielectric (insulators) do not
B. The main difference between conductor and dielectric
behavior is the amount of available free electrons
C. Not all conductors have the same level of conductivity, just as not all insulators are resistant to electric
current.
D. Both A and B only
12
1077Determine the electrostatic potential energy of a system consisting of two
charges ( 7 mu C ) and ( -2 mu C ) separated by distance of ( 20 mathrm{cm} )
12
1078We increase the charge on the plate of a capacitor, it means
A. increasing the capacitance
B. increasing P.D. between plates
c. decreasing P.D. between plates
D. no change in field between plates
12
1079Obtain an expression for equivalent capacitance when three capacitors ( C_{1}, C_{2} ) and ( C_{3} ) are connected in series.12
the center (point ( C ) ) of the equilateral
triangle with charges at the corners?
( A )
B.
( c )
( D )
12
1081Two thin wire rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are ( +q ) and ( -q ) The potential difference between the centres of the two rings is –
A ( . Q R / 4 pi varepsilon 0 d^{2} )
B. ( frac{Q}{2 pi_{c theta}}left[frac{1}{R}-frac{1}{sqrt{R^{2}+alpha^{2}}}right. )
c. zero
D. ( frac{Q}{4 pi varepsilon_{0}}left[frac{1}{R}-frac{1}{sqrt{R^{2}+bar{d}^{2}}}right] )
12
1082Three charges ( -q, Q ) and ( -q ) are
placed at equal distances on a straight line. If the total potential energy of the system of three charges is zero, then the ratio ( Q: q ) is :
A . 1: 2
B . 2: 1
( c cdot 1: 1 )
D. 1: 4
12
1083Capacity of a parallel plate condenser is ( 10 mu F ) when the distance between the plates is ( 8 mathrm{cm} . ) If the distance between the plates is reduced to ( 4 mathrm{cm}, ) its capacity will be:
A. ( 10 mu F )
B. ( 15 mu F )
c. ( 20 mu F )
D. ( 40 mu F )
12
1084The distance between the plates of a
parallel plate capacitor is ( d ). A metal
plate of thickness ( d / 2 ) is placed between the plates. The capacitance would be then be
A. Unchanged
B. Initial
c. zero
D. Doubled
12
1085Charge(Q) on capacitor( of capacitance
C) and potential difference(V) across it are related as:
A. ( Q=C times V )
в. ( Q=C / V )
c. ( Q=V / C )
D. Cannot be related
12
1086At the moment ( t=0, ) an electron leaves
one plate of a parallel-plate condenser
with a negligible velocity. An accelerating voltage varying as ( boldsymbol{V}=boldsymbol{a} boldsymbol{t} )
where ( a ) is a constant is applied between the plates. The separation
between the plates is ( l ). The velocity of
the electron at the moment it reaches
the opposite plate will be :
( ^{mathrm{A}}left(frac{2 e a l}{9 m}right)^{frac{1}{3}} )
( ^{mathrm{B}}left(frac{3 e a l}{4 m}right)^{frac{1}{3}} )
( ^{mathrm{c}}left(frac{4 e a l}{m}right)^{frac{1}{3}} )
( left(frac{9 e a l}{2 m}right)^{frac{1}{3}} )
12
1087It is required to construct a ( 10 mu F )
capacitor which can be connected
( operatorname{across} ) a ( 200 V ) battery. Capacitors of
capacitance ( 10 mu F ) are available but
they can withstand only ( 50 V ) Design a
combination which can yield the
desired result
12
1088When two capacitors are connected in parallel the resulting combination has capacitance ( 10 u F . ) The same
capacitors when connected in series results in a capacitance ( 0.5 u F . ) The respective values of individual
capacitors are
A . ( 1.9 u F ) and ( 0.2 u F )
B . ( (8+2 sqrt{5}) u F ) and ( (2-2 sqrt{5}) u F )
c. ( (5+2 sqrt{5}) u F ) and ( (5-2 sqrt{5}) u F )
D. ( 12 u F ) and ( 17 u F )
E . ( 5 u F ) and ( 2 u F )
12
1089The parallel combination of two air filled parallel plate capacitors of capacitance ( mathrm{C} ) and ( mathrm{NC} ) is connected to a battery of
voltage, ( V ). When the capacitors are fully charged, the battery is removed and after that a dielectric material of
dielectric constant ( mathrm{K} ) is placed between the two plates of the first capacitor. The new potential difference of the combined system is?
A ( cdot frac{V}{K+n} )
в. ( V )
c. ( frac{(n+1) V}{(K+n)} )
D. ( frac{n V}{K+n} )
12
1090What is the field in the cavity if a
conductor having a cavity is charged? Does the result depend on the shape and size of cavity or conductor?
12
109164 identical spheres of charge ( q ) and capacitance ( C ) each are combined to form a large sphere. The charge and capacitance of the large sphere is:
( A cdot 64 q, c )
B. 169, 4C
( c cdot 649,4 c )
D. ( 169,64 mathrm{c} )
12
1092Two conducting plates ( x ) and ( y ) each of area ( A ) are placed parallel to each other at a small separation ( boldsymbol{d} . boldsymbol{X} ) is given a charge ( 3 q ) and ( Y ) is given a charge ( q ) The potential difference between the plates is
A ( cdot frac{q d}{2 varepsilon_{0} A} )
в. ( frac{q d}{varepsilon_{0} A} )
c. ( frac{3 q d}{2 varepsilon_{0} A} )
D. ( frac{2 q d}{varepsilon_{0} A} )
12
1093Two capacitors connected in parallel
having the capacities ( C_{1} ) and ( C_{2} ) are
given ‘ ( q^{prime} ) charge, which is distributed among them. The ratio of the charge on
( C_{1} ) and ( C_{2} ) will be :
A ( cdot frac{C_{1}}{C_{2}} )
в. ( frac{C_{2}}{C_{1}} )
( mathbf{c} cdot C_{1} C_{2} )
D. ( frac{1}{C_{1} C_{2}} )
12
1094toppr ०६
In tigure. I nen the Key ( mathbf{K} ) Is pressed to
complete the circuit. Finally the net
charge on upper plate and net charge the circuit. Finally the net charge on
upper plate and net charge on lower
plate of capacitor ( C ) is positive.

Reason : In a parallel plate capacitor
both plates always carry equal and
opposite charge.
A. If both Assertion arid Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
C. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct.

12
1095The capacity of parallel plate capacitor depends on:
A. metal used to make plates
B. thickness of plate
c. potential applied across the plate
D. area of plate
12
1096In a series combination of two
capacitances ( C^{prime} ) and ( C(C>C) ) (as
shown in the circuit)
A. C’ stores more energy than ( C )
B. ( C ) stores more energy than ( C^{prime} )
c. potential difference across ( C ) is more than that across
( C )
D. potential difference across ( C^{prime} ) is less than that across ( C )
12
1097An infinite cylinder of radius ( r_{0} ) carrying
linear charge density ( lambda ). The equation of the equipotential surface for this
cylinder is
( mathbf{A} cdot r=r_{0} e^{pi varepsilon_{0}left[V(r)+Vleft(r_{0}right)right] lambda} )
B . ( r=r_{0} e^{2 pi varepsilon_{0}}left[V(r)-Vleft(r_{0}right)right] lambda^{2} )
C . ( r=r_{0} e^{-2 pi varepsilon_{0}}left[V(r)-Vleft(r_{0}right)right] / lambda )
D. ( r=r_{0} e^{-2 pi varepsilon_{0}leftlfloor V(r)-Vleft(r_{0}right) backslash lambdaright.} )
12
1098If the distance between the place of a parallel plate capacity ( 10 mu F ) is doubled, then new capacity will be:
A ( .5 mu F )
в. ( 20 mu F )
c. ( 10 mu F )
D. ( 15 mu F )
12
1099Electric potential due to a point charge ( q ) at a distance ( r ) from is given by
A ( cdot V=frac{q}{4 pi epsilon_{0}} )
B. ( V=frac{q}{4 pi epsilon_{0} r^{2}} )
( mathbf{c} cdot v=frac{q}{4 pi epsilon_{0} r} )
D. ( v=frac{q^{2}}{4 pi epsilon_{6} r} )
12
1100A solid copper sphere has a charge of ( +mathrm{Q} )
on it. Where on the sphere does the
charge reside?
A. ( +Q ) at the center of the sphere
B. ( mathrm{Q} / 2 ) at the center of the sphere and ( mathrm{Q} / 2 ) on the outer surface
c. ( mathrm{Q} ) at the center of the sphere and ( +2 mathrm{Q} ) on the outer surface
D. ( + ) Q on the outer surface
E. The charge is spread evenly throughout the sphere
12
1101A regular hexagon of side ( 10 mathrm{cm} ) has a charge ( 5 mu C ) at each of its vertices.
Calculate the potential at the centre of the hexagon.
( mathbf{A} cdot 5.8 times 10^{6} V )
В. ( 3.2 times 10^{6} V )
c. ( 9.3 times 10^{6} V )
D. ( 2.7 times 10^{6} V )
12
1102The electric potential ( V ) at any point ( P(x, y, z) ) in space is given by ( V= )
( 4 x^{2} V . ) The electric field at the point
( (1 m, 2 m) ) is:
A . ( -8 i )
B. ( 8 hat{i} )
( mathrm{c} cdot-16 hat{i} )
D. ( 16 hat{i} )
12
1103Two large vertical and parallel metal plates having a separation of ( 1 mathrm{cm} ) are
connected to a DC voltage source of potential difference ( X . ) A proton is released at rest midway between the two plates. It remains at rest in the air then ( X ) is:
A ( cdot 1 times 10^{-5} V )
В. ( 1 times 10^{-7} V )
c. ( 1 times 10^{-9} V )
D. ( 1 times 10^{-10} V )
12
1104Assertion
A charged metallic sphere when brought nearer to an uncharged metallic sphere, it may exert an attractive force, but once they touch
each other, they exert repulsive force.
Reason
The net electric field Inside a conductor
is zero.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
12
1105A uniform vertical field ( E ) is established
between two parallel plates. In this field, a small conducting sphere of mass ( boldsymbol{M} )
is suspended from a string of length ( l ). If the sphere is given a charge ( +q ) (statcoulomb) and if lower plate is charged
positively, the period of the simple pendulum is:
A ( .2 pi sqrt{l / g} )
( ^{mathrm{B}} cdot 2 pi sqrt{frac{l}{left(g+frac{q E}{m}right)}} )
c.
[
sqrt[2 pi]{frac{l}{left(g-frac{q E}{m}right)}}
]
( D )
[
sqrt{frac{l}{left(frac{q E}{m}-gright)}}
]
12
1106Four charges, all of same magnitude are placed at the four corners of a
square. At the centre of the square, the
potential is ( V ) and the field is ( E . B y ) suitable choices of the signs of the four charges, which of the following can be obtained?
This question has multiple correct options
A. ( V=0, E=0 )
B. ( V=0, E neq 0 )
c. ( V neq 0, E=0 )
D. ( V neq 0, E neq 0 )
12
1107f a proton is released from rest at point p in the diagram, what will it do?
A. Move to the right
B. Move to the left
c. Move toward the top of the screen
D. Move toward the bottom of the screer
12
1108Two fixed, equal, positive charges, each of magnitude ( 5 times 10^{-5} C ) are located at
point ( A ) and ( B ) separated by a distance
( 6 m . ) An equal and opposite charge moves towards them along the line
COD, the perpendicular bisector of the
line ( A B . ) The moving charge, when it reaches the point ( C ) at a distance of ( 4 m ) from ( O, ) has a kinetic energy of 4
joules. Calculate the distance of the
farthest point ( D ) which the negative
charge will reach before returning
towards ( C )
12
1109In the uniform electric field shown in
figure, ( boldsymbol{V}_{boldsymbol{A}}-boldsymbol{V}_{boldsymbol{D}} ) is :
( A cdot 5 V )
B. ( 10 V )
( c .20 V )
D. ( 0 V )
12
1110In the figure ( Q-26 ) the potential at ( A ) is
when the potential at B is zero.
12
1111Two point charges ( Q ) and ( -Q / 4 ) are separated by12
1112If we introduce a large thin metal plate
between two points charges, what will
happen to the force between the charges?
12
1113The equivalent capacity between the
points ‘A’ and ‘B’ in the following figure
will be:
( A cdot 9 mu F )
в. ( 1 mu F )
c. ( 4.5 mu F )
D. ( 6 mu F )
12
1114Two capacitors are connected as shown
in figure below. If the equivalent
capacitance of the combination is ( 4 mu F )
(i) Calculate the value of ( C )
(ii) Calculate the charge on each
capacitor.
(iii) What will be the potential drop
across each capacitor?
12
1115Two insulated charged spheres of radii
( R_{1} ) and ( R_{2} ) having charges ( Q_{1} ) and ( Q_{2} )
respectively are connected to each other, then there is:
B. an increase in the energy of the system
C. always a decrease in the energy of the system
D. a decrease in energy of the system unless ( q_{1} R_{2}=q_{2} R_{1} )
12
1116Two spherical conductors ( A ) and ( B ) of
radii ( 1 mathrm{mm} ) and ( 2 mathrm{mm} ) separated by a distance of ( 5 mathrm{cm} ) and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of
the electric fields at the surfaces of
spheres ( A ) and ( B ) is:
A . 4: 1
B. 1: 2
c. 2: 1
D. 1: 4
12
1117Five charges of magnitudes
( 24 mu C,-25 mu C, 3 mu C,-7 mu C ) and ( 28 mu C )
are situated along the circumference of
a circle of radius ( 3 mathrm{cm} ). Then the
potential at the centre of the circle is
A ( .54 times 10^{7} V )
В. ( 45 times 10^{6} V )
( mathbf{c} cdot 72 times 10^{6} V )
( mathbf{D} cdot 69 times 10^{5} V )
12
1118Two points ( mathbf{P} ) and ( mathbf{Q} ) are maintained at
the potentials of ( 10 mathrm{V} ) and ( -4 mathrm{V} ) respectively. The work done in moving
100 electrons from ( mathbf{P} ) to ( mathbf{Q} ) is :
В ( cdot 9.60 times 10^{-17} mathrm{J} )
c. ( -2.24 times 10^{-16} mathrm{J} )
D ( .2 .24 times 10^{-16} mathrm{J} )
12
1119Dielectric constant, property of an electrical insulating material (a dielectric) equal to
A. the ratio of the capacitance of a capacitor filled with the given material to the capacitance of an identical capacitor in a vacuum without the dielectric material.
B. the ratio of the capacitance of a capacitor filled with the given material to the capacitance of an identical capacitor in a vacuum with the dielectric material
c. the capacitance of a capacitor filled with the given material
D. none of the above
12
1120An equipotential line and a line of force
are:
A. perpendicular to each other
B. parallel to each other
c. in any direction
D. at an angle of ( 45^{circ} )
12
1121The charges of ( 2 mu c, 4 mu c ) and ( 6 mu c ) are
placed at the corner ( A, B quad ) and
respectively of a square ( A B C D ) of side
( 0.2 m ) calculate the work done to
transfer a charge of ( 2 mu c ) from ( D ) to the
center of the square.
12
1122what is the potential difference between two points, if 2 J of work must be done to move a ( 4 mathrm{mC} ) charge from one point to
another is:
A. ( 50 v )
B. 500
( c cdot 5 v )
D. 5000
12
1123What is the geometrical shape of equipotential surface due to a single isolated charge?12
1124In the situation shown in figure, what
should be the relation between ( Q ) and ( q )
so that electric potential at centre of the
square is zero:
A. ( Q=q )
в. ( Q=3 q )
c. ( Q=2 q )
D. ( Q=-3 q )
12
1125Define equipotential surface.12
1126Equipotential surfaces associated with an electric field which is increasing in magnitude along the x-direction are:
A. Planes parallel to yz-plane
B. Planes parallel to xy-plane
c. Planes parallel to xz-plane
D. coaxial cylinders of increasing radii around
the x-axis
12
1127Which of the following statement is true about the relation between electric field
and potential?
A. Electric field in the direction in which the potential decreases steepest
B. Magnitude of electric field is given by the change in the magnitude of potential per unit displacement normal to the equipotential surface at that point.
C. In the region of strong electric field, equipotentia
D. Both the statements
(a) and
(b) are correct.
12
1128The Sl unit of electric potential is
A. ( V m^{-1} )
в. ( C )
c. ( N C^{-1} )
D. ( V )
12
1129Two charges ( 5 times 10^{-8} C ) and ( -3 x )
( 10^{-8} C ) are located ( 16 mathrm{cm} ) apart. At what
point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
12
1130The plates of parallel-plate condenser are being moved away with velocity v. If the plate separation at any instant of time is ( d ) then the rate of change of capacitance with time is proportional to
A ( cdot d^{2} )
B. ( d )
( c cdot d^{-2} )
D. ( d^{-1} )
12
1131Within a spherical charge distribution of charge density ( rho(r), ) N equipotential
surfaces of potential ( V_{0}, V_{0}+ )
( boldsymbol{Delta} boldsymbol{V}, boldsymbol{V}_{0}+boldsymbol{2} boldsymbol{Delta} boldsymbol{V}, ldots . ., boldsymbol{V}_{0}+ )
( N Delta V(Delta V>0), ) are drawn and have
increasing radii ( r_{0}, r_{1}, r_{2}, dots . . r_{N} )
respectively. If the difference in the radii of the surfaces is constant for all values
of ( V_{0} ) and ( Delta V ) then :
A ( cdot rho(r)= ) constant
B. ( rho(r) propto frac{1}{r^{2}} )
c. ( rho(r) propto frac{1}{r} )
D. ( rho(r) propto 1 )
12
1132Two circular coils ( P ) and ( Q ) are kept
close to each other, of which coil ( boldsymbol{P} )
carries a current. If coil ( boldsymbol{P} ) is moved
towards ( Q, ) will some current be
induced in coil ( Q ) ? Give the reason for
12
1133Illustrate a condition in which :
Electric field is not zero but potential is
zero
12
1134An electron initially at rest is accelerated through a potential difference of one volt. The energy gained by the electron is:
A. 15
B . ( 1.6 times 10^{-19} mathrm{J} )
( mathbf{c} cdot 10^{-19} J )
D. None of these
12
1135Where do charges reside in the case of a charged conductor?
A. Inside the conductor
B. on the outer surface of the conductor
c. on the inner surface of the conductor
D. Anywhere outside the conductor
12
1136The distance between the plates of a
condenser is reduced to ( frac{1}{4} t h ) and the
space between the plates is filled up by a medium of dielectric constant ( mathrm{K}(2.8) ). The
capacity is increased by :
A. 5.6times
B. 11.2times
c. 22.4 times
D. 44.8 times
12
1137Evaluate potential energy per ion for NaCl crystal. Use inter atomic spacing ( 2.82 times 10^{10} m )
В. ( 2.67 times 10^{-19} mathrm{J} )
( mathbf{c} cdot 5.67 times 10^{-19} J )
D. none
12
1138Find the dimensions and units of ( varepsilon_{0} ? )12
1139A parallel plane capacitor ( C ) with plates
of unit area and separation ( d ) is filled
with a liquid of dielectric constant ( k= )
2. The level of liquid is ( frac{u}{3} ) initially.
Suppose the liquid level decreases at a
constant speed ( v ), the time constant as
a function of time ( t ) is
A ( frac{6 varepsilon_{0} R}{5 d+3 v} )
B. ( frac{(15 d+9 v t) varepsilon_{0} R}{2 d^{2}-3 d u t-9 v^{2} t^{2}} )
c. ( frac{6 pi varepsilon_{0} R}{5 d-3 v} )
D. ( frac{(15 d-9 v t) varepsilon_{0} R}{2 d^{2}+3 d v t-9 v_{2 t^{2}}} )
12
1140Four equal charges q each are placed at four corners of a square of side a each. Work done in carrying a charge q from its centre to infinity is:
A. zero
В. ( frac{2 q^{2}}{pi varepsilon_{0} a} )
c. ( frac{sqrt{2} q^{2}}{pi varepsilon_{0} a} )
D. ( frac{q^{2}}{2 pi varepsilon_{0} a} )
12
1141Four identical charges are placed at the points (1,0,0),(0,1,0),(-1,0,0) and
( (0 .-1,0) )
A. The potential at the origin is zero
B. The field at the origin is zero
c. The potential at all points on the z-axis, other than the origin, is zero
D. The potential at all points on the z-axis, other than the origin acts along the z-axis
12
1142A parallel plate capacitor is charged
and then the battery is disconnected, When the plates of the capacitor are brought closer, then This question has multiple correct options
A. energy stored in the capacitor decreases
B. the potential difference between the plates decreases
c. the capacitance increases
D. the electric field between the plates decreases
12
1143Two charges ( 5 times 10^{-8} C ) and ( -3 x )
( 10^{-8} C ) are located ( 0.16 m ) apart. At what
point(s) on the line joining the two charges in the electric potential zero? Take the potential at infinity to be zero.
12
1144Define dielectric constant of a medium.
What is its ( S . I . ) unit?
12
1145A particle A has charge +q and a particle B has a charge +9q with each of them having the same mass m.If both the particles are allowed to all from rest through the same potential difference, then the ratio of their speed is
A .1: 2
B. ( 1: sqrt{3} )
c. ( 1: 2 sqrt{2} )
D. none of these
12
1146If a positive charge is shifted from a low potential region to a high potential region, the electric potential energy:
A. Increases
B. Decreases
c. Remains unchanged
D. May increase or decrease
12
1147Electrical potential at the centre of a charged conductor is:
A . zero
B. twice as that on the surface
c. half of that on the surface
D. same as that on the surface
12
1148Charges are placed on the vertices of a square as shown. Let ( vec{E} ) be the electric
field and V the potential at the centre. If the charges on ( A ) and ( B ) are interchanged with those on D and
respectively, then
A. ( bar{E} ) changes, v remains unchanged
B. ( bar{E} ) remains unchanged, v changed
c. both ( vec{E} ) and ( v ) change
D. ( vec{E} ) and v remain unchange
12
1149Assertion
The dielectric constant is a number
without dimensions.
Reason
Dielectric constant is a ratio.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
12
1150In a regular polygon of ( n ) sides, each corner is at a distance ( r ) from the centre. Identical charges are placed at ( (n-1) ) corners. At the centre, the magnitude of intensity is ( mathrm{E} ) and the potential is V.The ratio V/E is
( A cdot r n )
B. ( r(n-1) )
( c cdot(n-1) / r )
( D cdot r(n-1) / n )
12
1151Positive charge flow from a body at to a body at Fill
in the blanks.
A. higher potential, lower potential
B. lower potential, higher potential
c. higher charge, , lower charge
D. higher force, lower force
12
115214
field intensity at the center of a square having fixed point charges at their
vertices as shown in figure are zero.
Reason

If electric potential at a point is zero
then the magnitude of electric field at that point must be zero.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct

12
1153The insertion of a dielectric between the
plates of a parallel-plate capacitor always
A. increases its capacitance
B. decreases its capacitance
c. remains same its capacitance
D. none of the above
12
1154Find the relation between potential
difference V and separation between the
plates z:
( ^{mathrm{A}} cdot_{V^{2}}=frac{K_{z}left(z_{0}-zright)^{2}}{A varepsilon_{0}} )
B. ( V^{2}=frac{2 K_{z}left(z_{0}-zright)^{2}}{A varepsilon_{0}} )
c. ( V^{2}=frac{4 K_{z}left(z_{0}-zright)^{2}}{A varepsilon_{0}} )
D. ( V^{2}=frac{K_{z}left(z_{0}-zright)^{2}}{4 A varepsilon_{0}} )
12
1155Four identical parallel conductors,
carrying charges ( Q,-2 Q, 3 Q ) and ( 4 Q )
are placed as shown in the figure. The
plates carrying charges ( Q ) and ( 4 Q ), are
connected through a switch, as shown.
The amount of charge flowing through the switch, after closing it is found to be
( n Q . ) Find ( n )
12
1156A dielectric slab of thickness dis
inserted in a parallel plate capacitor
where negative plate is at ( x=0 ) and
positive plate is at ( x=3 d . ) The slab is
equidistant from the plates. The capacitor is given some charge. As ( x )
goes from 0 to ( 3 d )
This question has multiple correct options
A. The magnitude of electric field remains the same
B. The direction of electric field remain the same
c. The electric potential increases continuously.
D. The electric potential increase at first then decrease and again increase.
12
1157Two identical particles of mass ( m ) carry
charge ( Q ) each. Initially one is at rest on a smooth horizontal plane and the other is projected along the plane directly towards first particle from a large
distance with speed ( v ). The closest
distance of approach will be
A ( cdot frac{1}{4 pi varepsilon_{0}} frac{Q^{2}}{m v} )
B. ( frac{1}{4 pi varepsilon_{0}} frac{4 Q^{2}}{m v} )
( ^{mathbf{C}} frac{1}{4 pi varepsilon_{0}} frac{4 Q^{2}}{m v^{2}} )
( ^{mathrm{D}} frac{1}{4 pi varepsilon_{0}} frac{2 Q^{2}}{m v^{2}} )
12
1158If a unit charge is taken from one point to another over an equipotential surface,
then
A. work is done on the charge
B. work is done by the charge
c. work on the charge is constant
D. no work is done
12
1159(a) Distinguish with the help of a suitable diagram, the difference in the
behaviour of a conductor and a
dielectric placed in an external electric field. How does polarised dielectric modify the original external field?
(b) A capacitor of capacitance ( C ) is charged fully by connecting it to a battery of emf E. It is then disconnected from the battery. If the separation between the plates of the capacitor is now doubled, how will the following change?
(i) Charge stored by the capacitor.
(ii) Field strength between the plates.
(iii) Energy stored by the capacitor. Justify your answer in each case.
12
1160Figure shows equipotential surfaces
concentric at ‘O’ the magnitude of electric fields at distance r(in meter)
measured from
A ( cdot frac{9}{r^{2}}left(V m^{-1}right) )
в. ( frac{6}{r^{2}}left(V m^{-1}right) )
c. ( frac{2}{r^{2}}left(V m^{-1}right) )
D. ( frac{16}{r^{2}}left(V m^{-1}right) )
12
1161Two points charges ( 4 mu C ) and ( -2 mu C ) are separated by a distance of ( 1 mathrm{m} ) in air. ( mathrm{At} ) what point in between the charges and on the line joining the charges, is the electric potential zero?
A. In the middle of the two charges
B. ( 1 / 3 m ) from ( 4 mu C )
c. ( 1 / 3 m ) from ( -2 mu C )
D. Nowhere the potential is zero
12
1162A parallel plate capacitor consists of
two circular plates each of radius ( 12 mathrm{cm} )
and separated by ( 5.0 m m . ) The capacitor is being charged by an external source. The charging current is constant and is
equal to ( 0.15 A ). The rate of change of potential difference between the plates will be :
A. ( 8.173 times 10^{7} V / s )
В . ( 7.817 times 10^{8} V / s )
C ( .1 .873 times 10^{9} mathrm{V} / mathrm{s} )
D. ( 3.781 times 10^{10} V / s )
12
1163The ratio of momentum of an electron
and an alpha particle which are accelerated from rest by potential difference of ( 100 mathrm{V} ) is:
A ( cdot sqrt{frac{m_{alpha}}{m_{e}}} )
В. ( sqrt{frac{m_{e}}{m_{alpha}}} )
c. ( frac{2 m_{e}}{m_{alpha}} )
D. ( sqrt{frac{m_{e}}{2 m_{alpha}}} )
12
1164Two charges ( 2 mu C ) and ( -2 mu C ) are placed
at points ( A ) and ( B 6 mathrm{cm} ) apart.
(a) Identify an equipotential surface of the system.
(b) What is the direction of the electric field at every point on this surface?
12
1165Charges ( -boldsymbol{q}, boldsymbol{Q} ) and ( -boldsymbol{q} ) are placed at an equal distance on a straight line. If the
total potential energy of the system of three charges is zero, then find the ratio ( boldsymbol{Q} / boldsymbol{q}: )
A. ( 1 / 2 )
в. ( 1 / 4 )
( c cdot 2 / 3 )
D. ( 3 / 4 )
12
1166Consider a parallelogram ( A B C D, ) with
angle ( angle B=120^{circ} . ) A charge ( +Q ) placed
at the corner ( A ) produces field ( E ) and
potential ( V ) at corner ( D ). If we now add
charges ( -2 Q ) and ( +Q ) at corners ( B ) and
( C ) respectively, the magnitude of field
and potential at ( D ) will become
respectively
( ^{A} cdot frac{sqrt{3}}{2} E, V )
в. ( frac{sqrt{3}}{2} E, ) о
( c . E, 0 )
D. ( frac{E}{sqrt{2}}, frac{V}{sqrt{2}} )
12
1167Two electrons separated by a distance ( r )
experiences a force ( F ) between them.
The force between a proton and a single joined helium atom separated by a
distance ( 2 r ) is
A ( .4 F )
в. ( 2 F )
c. ( F / 2 )
D. ( F / 4 )
12
1168Net Capacitance of three identical in
series is ( 1 mu F ). What will be their net
capacitance, if connected in parallel?
Find the ratio of energy stored in the two configurations, if they are both connected to the same source.
12
1169What should be the charge on a sphere of radius ( 2 mathrm{cm} ) so that when it is
brought in contact with another sphere of radius ( 5 mathrm{cm} ) carrying a charge of ( 10 mu C, ) there is no transfer of charge
between the spheres?
12
1170From a supply of identical capacitors rated ( 8 mu F, 250 V ) the minimum number of capacitors required to form a composite of ( 16 mu F, 1000 V ) is
( A cdot 2 )
B. 4
( c cdot 16 )
D. 32
12
1171In the circuit shown the current through
the ( 4 Omega ) resistor is 1 amp when the
points ( P ) and ( M ) are connected to a d.c voltage source. The potential difference
between the points ( M ) and ( N ) is:
A. 0.5 volt
B. 3.2 volt
c. 1.5 volt
D. 1.0 volt
12
1172Assertion
Dielectric materials can be solids,
liquids, or gases.
Reason
Usage of dielectric depends on the application i.e.Industrial coatings such as parylene provide a dielectric barrier between the substrate and its
environment.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
12
1173( frac{frac{pi}{4}}{frac{pi}{4}} )12
1174A solid sphere of radius ( boldsymbol{R} ) has a charge
( +2 Q . ) A hollow spherical shell of radius
( 3 R ) placed concentric with the first
sphere has net charge ( -Q . ) If the inner
sphere is earthed, what will be the
charge on it?
A ( cdot frac{2 Q}{3} )
B. ( frac{-6}{3} )
c. ( frac{Q}{3} )
D. ( frac{-2 Q}{3} )
12

Hope you will like above questions on electrostatic potential and capacitance and follow us on social network to get more knowledge with us. If you have any question or answer on above electrostatic potential and capacitance questions, comments us in comment box.