Electrostatics

MCQ FOR XII BOARDS, NEET & JEE MAINS

Vardan Patni’s Physics Classes

New Adarsh Nagar, Durg | 9584120300
Electrostatics Vardan Patni’s Physics Classes – 9584120300

Contents
Electric Charges ............................................................... 2
Coulomb’s Law................................................................. 3
Electric field ..................................................................... 9
Electric Flux .................................................................... 18
Electric dipole ................................................................ 21
Potential Due to point charge ....................................... 23
Potential due to charged sphere ................................... 25
Potential difference in electric field .............................. 29
Relation between electric field and potential ............... 31
Potential energy of system of charges .......................... 33
Capacitors ...................................................................... 36
Combination of Capacitors ............................................ 39
Capacitors with Dielectrics ............................................ 44
Electrostatics Vardan Patni’s Physics Classes – 9584120300

Electric Charges
1. Out of the following options which one can be 7. A negatively charged object 𝑋 is repelled by
used to produce a propagating electromagnetic another charged object 𝑌. However, an object 𝑍
wave is attracted to object 𝑌. Which of the following is
a. A charge moving at constant velocity the most possibility for the object 𝑍 ?
b. A stationary charge a. Positive charged only
c. A chargeless particle b. Negatively charged only
d. An accelerating charge c. Neutral or positively charged
e. None of these d. Neutral or negatively charged
2. Metallic sphere 𝐴 is given positive charge where e. None of these
as another identical metallic sphere 𝐵 of exactly 8. In an experiment three microscopic latex
same mass as of 𝐴, is given equal amount of spheres are, sprayed into a chamber and
negative charge. Then became charged with charges +3𝑒, +5𝑒 and 3𝑒,
a. Mass of 𝐴 and mass of 𝐵 still remain respectively. All the three spheres came in
equal contact simultaneously for a moment and got
b. Mass of 𝐴 increases separated. Which one of the following are
c. Mass of 𝐵 decreases possible values for the final charge on the
d. Mass of 𝐵 increases spheres?
e. None of these a. +5𝑒, −4𝑒, +5𝑒
3. Number of electrons in one coulomb of charge b. +6𝑒, +6𝑒, −7𝑒
will be c. +4𝑒, +3.5𝑒, +5.5𝑒
a. 5.46 × 1029 d. +5𝑒, −8𝑒, +7𝑒
e. None of these
b. 6.25 × 1018
c. 1.6 × 1019 9. Five balls numbered 1 to 5 are suspended using
d. 9 × 1011 threads. Pair (1,2)(2,4) and (4,1) shows
e. None of these electrostatic attraction, while pair (2,3) and
4. When 1019 electrons are removed from a (4,5) shows repulsion. Therefore ball 1 must be
neutral metal plate through some process, the a. Positively charged
charge on it becomes b. Negatively charged
a. −1.6 𝐶 c. Neutral
b. +1.6 𝐶 d. Can’t say
c. 1019 𝐶 e. None of these
d. 10−19 𝐶 10. The charge on alpha particle is
e. None of these a. −3.2 × 10−19 𝐶
5. If 1010 electrons are acquired by a body every b. 1.6 × 10−10 𝐶
second, the time required for the body to get a c. 3.2 × 10−19 𝐶
total charge of 1 𝐶 will be d. −1.6 × 10−10 𝐶
a. 20 hours e. None of these
b. 20 days 11. A conductor has given a charge −3 × 10−7 𝐶 by
c. 2 years transferring electron. Mass increase (in 𝑘𝑔) of
d. 20 years the conductor and the number of electrons
e. None of these added to the conductor are, respectively
6. A cup contains 250 𝑔 of water. Find the total a. 2 × 10−16 and 2 × 1031
positive charge present in the cup of water. b. 5 × 10−31 and 5 × 1019
a. 1.34 × 107 𝐶 c. 3 × 10−19 and 9 × 1016
b. 2.43 × 1019 𝐶 d. 2 × 10−18 and 2 × 1012
c. 2.43 × 107 𝐶 e. None of these
d. 1.34 × 1019 𝐶
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

Coulomb’s Law
1. Three equal positive charges ‘𝑞’ are placed at
the vertices of an equilateral triangle of side 𝑙. 6. Four equal positive charges are placed at the
Calculate total electric force acting on any vertices of a square. How to put the system of
charge because of the rest two charges in equilibrium.
𝑘𝑞2 −(2√2+1)
a. 𝑙2
a. 4
𝑞
√6𝑘𝑞2 (2√2+1)
b. b. 𝑞
𝑙2 4
√2𝑘𝑞2 −(2√2+1)
c. 𝑙2
c.
2
𝑞
√3𝑘𝑞2 (2√2+1)
d. 𝑙2
d. 2
𝑞
e. None of these e. None of these
2. Four equal positive charges ‘𝑞’ are placed at 7. Two pith balls carrying equal charges are
vertices of a square of side 𝑙. Calculate total suspended from a common point by strings of
electric force acting on any charge. equal length, at equilibrium separation between
𝑘𝑞2 them is 𝑟. Now strings are rigidly clamped at half
a. (2√2 + 1) 2𝑙 2
𝑘𝑞2
the height. The equilibrium separation 𝑟’ now
b. (2√2 − 1) becomes
2𝑙 2
𝑘𝑞2 𝑟
c. (2√2 + 1) a. 𝑟 ′ = 1
𝑙2 23
𝑘𝑞2 ′ 𝑟
d. (2√2 − 1) b. 𝑟 = 2
𝑙2 23
e. None of these c. 𝑟 ′ =
𝑟
1
3. A charge +𝑄 is placed at each of the opposite 32
𝑟
corners of a square. A charge 𝑞 is placed at each d. 𝑟 ′ = 1
33
of the other corners. If net electric force on 𝑄 is
𝑄
e. None of these
zero then 𝑞 equals 8. Two identical charged spheres are suspended by
a. −2√2 strings of equal lengths. The string makes an
b. 2√2 angle of 30° with each other. When suspended
𝑔𝑚
c. −√2 is a liquid of density 0.8 3 , angle remains
𝑐𝑚
𝑔𝑚
d. √2 same. If density of material of sphere is 1.6 𝑐𝑚3 .
e. None of these Find dielectric constant of liquid.
4. How to put system of two equal charges in a. 1
equilibrium b. 2
𝑞
a. − c. 3
4
b.
𝑞 d. 4
4
𝑞 e. None of these
c. − 2
9. Two charges, equal to 𝑞, are kept at 𝑥 = −𝑎 and
𝑞
d. 𝑥 = +𝑎 on the 𝑥-axis. A particle of mass 𝑚 and
2
𝑞
e. None of these charge 𝑞0 = − 2 is placed at origins. If charge 𝑞0
5. Three equal positive charges 𝑞 are placed at the is given a small displacement (𝑦 ≪ 𝑎) along 𝑦-
vertices of an equilateral triangle. How to put axis, the net force acting on particle is
the system of charges in equilibrium. proportional to
𝑞
a. − 3 a. 𝑦
√
𝑞 b. 2𝑦
b.
√3 c. 𝑦 2
𝑞
c. − 3 d. 𝑦 3
√3
𝑞
d. e. None of these
3√3
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

10. Two equal negative charges −𝑞 are fixed at 14. Two identical charged particles each having a
points (0, 𝑎) and (0, −𝑎) on 𝑦-axis. A positive mass 10 𝑔 and charge 2.0 × 10−7 𝐶 are placed
charge 𝑄 is released from rest at points (2𝑎, 0) on a horizontal table with a separation of 𝑙
on 𝑥-axix. The charge 𝑄 will between them such that they stay in limited
a. Execute SHM about origin equilibrium. If the coefficient of friction between
b. Move to origin and remains at rest each particle and the table is 0.25. Find the
c. Move to infinity 𝑚
value of 𝑙. (𝑔 = 10 2 )
𝑠
d. Execute oscillatory but not SHM
a. 10 𝑐𝑚
e. None of these
b. 12 𝑐𝑚
11. A 10 𝜇𝐶 charge is divided into two parts and c. 0.10 𝑐𝑚
placed at 1 𝑐𝑚 distance so that the repulsive d. 0.12 𝑐𝑚
force between them is maximum. The charges of e. None of these
two parts are 15. Two point charges +9𝑒 and −𝑒 are separated by
a. 5 𝜇𝐶, 5 𝜇𝐶 a distance of 20 𝑐𝑚 in air. Where should a third
b. 4 𝜇𝐶, 6 𝜇𝐶 charge be placed so that net electric force on it
c. 3 𝜇𝐶, 7 𝜇𝐶 is zero.
d. 2 𝜇𝐶, 8 𝜇𝐶
a. 10 𝑐𝑚
e. None of these
b. 5 𝑐𝑚
12. Two identical metallic spheres 𝐴 and 𝐵, when c. 7 𝑐𝑚
placed at certain distance in air repel each other d. 8 𝑐𝑚
with a force of 𝐹. Another identical uncharged e. None of these
sphere 𝐶 is first placed in contact with 𝐴 and 16. Two point charges +9𝑒 and +𝑒 are separated by
then in contact with 𝐵 and finally placed at mid- a distance of 20 𝑐𝑚 in air. Where should a third
point between sphere 𝐴 and 𝐵. The force charge be placed so that net electric force on it
experienced by sphere 𝐶 will be is zero.
3𝐹
a. a. 10 𝑐𝑚
4
3𝐹 b. 5 𝑐𝑚
b. 2
𝐹 c. 7 𝑐𝑚
c. d. 8 𝑐𝑚
4
𝐹
d. e. None of these
2
e. None of these 17. Two point charges repel each other with a force
13. Two identical conducting spheres 𝐴 and 𝐵 carry of 100 𝑁. One charge is increased by 10% and
equal charge. They are separated by a distance other is reduced by 10%. The force of repulsion
much larger than their diameter and the force at same distance would be
between them is 𝐹. A third identical uncharged a. 0.9 𝑁
conducting sphere 𝐶 is first touched to 𝐴 then to b. 9 𝑁
𝐵 and then removed. As a result, the force c. 99 𝑁
d. 9.9 𝑁
between 𝐴 and 𝐵 would be equal to
3𝐹 e. None of these
a.
8 18. Five balls numbered 1 to 5 are suspended using
𝐹
b. 8
threads, pair (1,2) (2,4) and (4,1) shows
c.
𝐹 electrostatic attraction, while pair (2,3) and
4 (4,5) show repulsion. Therefore ball 1 must be
3𝐹
d. 4 a. Positively charged
e. None of these b. Negatively charged
c. Neutral
d. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

19. The dimensional formula for permittivity of free 24. Under the influence of coulomb field of charge
1 𝑞 𝑞 +𝑄, a charge −𝑞 is moving in an elliptical orbit.
space (𝜀0 ) in the equation 𝐹 = 4𝜋𝜀0
⋅ 𝑟1 2 2
Find out correct statement.
where, symbols have their usual meaning is
a. Angular momentum of charge −𝑞 is
a. [𝑀1 𝐿3 𝐴−2 𝑇 −4 ]
constant
b. [𝑀−1 𝐿−3 𝐴2 𝑇 4 ]
b. Linear momentum of charge −𝑞 is
c. [𝑀−1 𝐿−3 𝐴−2 𝑇 −4 ]
constant
d. [𝑀1 𝐿3 𝐴2 𝑇 −4 ]
c. Angular velocity of charge −𝑞 is
e. None of these
constant
20. Three equal charges are placed on the three
d. Linear speed of charge −𝑞 is constant
corners of a square. If the force between 𝑞1 and
25. In the given figure, net force on charge 𝑞0 is
𝑞2 is 𝐹12 and that between 𝑞1 and 𝑞3 is 𝐹13 , then 𝑘𝑄𝑞0
𝐹 a.
the ratio of their magnitudes (𝐹12 ) is 𝑎2
13 3√3𝑘𝑄𝑞0
a.
1 b.
𝑎2
2 𝑘𝑄𝑞0
b. 2 c. 3𝑎 2
1
c. d. 𝑧𝑒𝑟𝑜
√2
e. None of these
d. √2
26. In the given figure, net force on 𝑞0 charge is
e. None of these
a. 4𝑘𝑄𝑞0
21. Five point charges, each of value +𝑞, are placed
b. 5𝑘𝑄𝑞0
on five vertices of a regular hexagon of side 𝐿.
c. 12𝑘𝑄𝑞0
The magnitude of the force on a point charge of
d. 13𝑘𝑄𝑞0
value −𝑞 Coulomb placed at the centre of the e. None of these
hexagon is 27. Force between two identical unlike charges is 𝐹.
1 𝑞 2
a. ( ) Now 25% of one charge is transferred to
𝜋𝜀0 𝐿
2 𝑞 2
another then new force between the charges at
b. 𝜋𝜀0 𝐿
( ) same distance will be
1 𝑞 2 16
c. ( ) a. 9
𝐹
2𝜋𝜀0 𝐿 9
1 𝑞 2 b. 𝐹
d. ( ) 16
4𝜋𝜀0 𝐿 15
c. 𝐹
e. None of these 16
16
22. A charge +𝑄 is placed at each of the opposite d. 15
𝐹
corner of a square. A charge 𝑞 is placed at each 28. There are two fixed charged spheres 𝑃 and 𝑄
of the other corners. If net electric force on 𝑄 is repelling each other with force of 16 𝑁. A third
𝑄
zero, then 𝑞 equals to neutral sphere is placed between the charged
spheres. The new force between spheres is
a. −2√2
(assuming all three spheres are insulating
b. −1
spheres)
c. 1
1 a. 8 𝑁
d. − 2
√ b. 32 𝑁
e. None of these c. 16 𝑁
23. Three charges are placed at the vertices of an d. 4 𝑁
equilateral triangle of side ‘𝑎’ as shown in the 29. On rotating a point charge having a charge 𝑞
figure. The force experienced by charge placed around a charge 𝑄 in a circle of radius 𝑟. The
at vertex 𝐴 in a direction work done will be
normal to 𝐵𝐶 is a. 𝑞 × 2𝜋𝑟
𝑄2 𝑞×2𝜋𝑄
a. 4𝜋𝜀0
b. 𝑟
b. −𝑄 2 (4𝜋𝜀0 𝑎2 ) c. Zero
𝑄
c. Zero d.
2𝜀0 𝑟
𝑄2
d. 2𝜋𝜀0 𝑎 2
Electrostatics Vardan Patni’s Physics Classes – 9584120300

30. Two point charges placed at a certain distance 𝑟 34. A particle ‘𝑎’ having a charge of 2 × 10−6 𝐶 and
in air exert a force 𝐹 on each other. Then the mass 100 𝑔𝑚 is fixed at bottom of a smooth
distance 𝑟 ′ at which these charges will exert the inclined plane of inclination 30° where should
same force in a medium of dielectric constant 𝑘 another particle having same charge and mass
is given by be placed so that 𝐵 may remain in equilibrium
a. 𝑟 a. 8 𝑐𝑚 from bottom
b. 𝑟⁄𝑘 b. 13 𝑐𝑚 from bottom
c. 𝑟⁄√𝑘 c. 21 𝑐𝑚 from bottom
d. 𝑟√𝑘 d. 27 𝑐𝑚 from bottom
e. None of these e. None of these
31. Electric charges of 1 𝜇𝐶, −1 𝜇𝐶 and 2 𝜇𝐶 are 35. An electron is moving around the nucleus of a
placed in air at the corners 𝐴, 𝐵 and 𝐶 hydrogen atom in a circular orbit of radius 𝑟. The
respectively, of an equilateral triangle 𝐴𝐵𝐶 1
Coulomb force between the two is (𝐾 = )
4𝜋𝜀0
having length of each side 10 𝑐𝑚. The resultant 𝐾𝑒 2
force on the charge at 𝐶 is a. − 𝑟3
𝑟̂
a. 0.9 𝑁 𝐾𝑒 2
b. 𝑟3
𝑟⃗
b. 1.8 𝑁 𝐾𝑒 2
c. 2.7 𝑁 c. − 𝑟3 𝑟⃗
d. 3.6 𝑁 𝐾𝑒 2
d. 𝑟̂
𝑟3
e. None of these
1
e. None of these
32. The Coulomb force (𝐹) versus (𝑟2 ) graphs for 36. Two charges are at a distance ‘𝑑’ apart. If a
two pairs of point charges (𝑞1 and 𝑞2 ) and (𝑞2 𝑑
copper plate (conducting medium) of thickness 2
and 𝑞3 ) are shown in figure. The charge 𝑞2 is
is placed between them, the effective force will
positive and has least magnitude, then
be
a. 2𝐹
𝐹
b. 2
c. 0
d. √2𝐹
e. None of these
37. A particle of mass 𝑀 and charge 𝑞 is at rest, at
the midpoint between two other fixed similar
a. 𝑞1 > 𝑞2 > 𝑞3
charges each of magnitude 𝑄 placed a distance
b. 𝑞1 > 𝑞3 > 𝑞2 2𝑑 apart. The system is collinear as shown in the
c. 𝑞3 > 𝑞2 > 𝑞1 figure. The particle is now displaced by a small
amount 𝑥(𝑥 ≪ 𝑑) along the line joining the two
d. 𝑞3 > 𝑞1 > 𝑞2
charges and is left to itself. It will now oscillate
e. None of these about the mean position with a time period
33. Two equal point charges each of 3 𝜇𝐶 are (𝜀0 = permittivity of free space)
separated by a certain distance in meter. If they
are located at (𝑖̂ + 𝑗̂ + 𝑘̂ ) and (2𝑖̂ + 3𝑗̂ + 3𝑘̂ ),
then magnitude of electric force between them
us given by
a. 9 × 103 𝑁
𝜋3 𝑀𝜀0 𝑑
b. 9 × 10−3 𝑁 a. 2√ 𝑄𝑞
c. 1.0 × 10−3 𝑁 𝜋2 𝑀𝜀0 𝑑 3
d. 3 × 103 𝑁 b. 2√ 𝑄𝑞
e. 1.0 × 103 𝑁 𝜋3 𝑀𝜀0 𝑑 3
c. 2√ 𝑄𝑞
𝜋3 𝑀𝜀0
d. 2√
𝑄𝑞𝑑 3
Electrostatics Vardan Patni’s Physics Classes – 9584120300

38. Two identical conducting balls 𝐴 and 𝐵 have 43. Two small spheres each having the charge +𝑄
positive charges 𝑞1 and 𝑞2 , respectively. But are suspended by insulating threads of length 𝐿
𝑞1 ≠ 𝑞2 . The balls are brought together so that from a hook. This arrangement is taken in space
they touch each other and then kept in their where there is no gravitational effect, then the
original positions. The force between them is angle between the two suspensions and the
a. Less than that before the balls touched tension in each will be
b. Greater than that before the balls 1 𝑄2
a. 180°,
touched 4𝜋𝜀0 (2𝐿)2
1 𝑄2
c. Same as that before the balls touched b. 90°,
4𝜋𝜀0 (𝐿)2
d. Zero 1 𝑄2
39. Two identical particles of mass ‘𝑚’ and charge 𝑞 c. 180°,
4𝜋𝜀0 2(𝐿)2
are shot at each other from a very great distance 1 𝑄2
d. 180°,
with an initial speed 𝑣. The distance of closest 4𝜋𝜀0 (𝐿)2
approach of these charges is 44. An infinite number of charges, each of charge
𝑞2 1 𝜇𝐶, are placed on the 𝑥-axis with co-ordinates
a.
8𝜋𝜀0 𝑚𝑣 2 𝑥 = 1, 2, 4, 8, … … … ∞. If a charge of 1 𝐶 is kept
𝑞2
b. 4𝜋𝜀0 𝑚𝑣 2
at the origin, then what is the net force acting in
𝑞2 1 𝐶 charge
c. 2𝜋𝜀0 𝑚𝑣 2 a. 9000 𝑁
d. 0 b. 12000 𝑁
40. Two small spherical balls each carrying a charge c. 24000 𝑁
𝑄 = 10 𝜇𝐶 are suspended by two insulating d. 36000 𝑁
threads of equal lengths 1 𝑚 each, from a point 45. The acceleration of an electron due to the
fixed in the ceiling. It is found that in equilibrium mutual attraction between the electron and a
threads are separated by an angle 60° between proton when they are 1.6 Å apart is,
them. What is the tension in the threads (𝑚𝑒 ≅ 9 × 10−31 𝑘𝑔), (𝑒 = 1.6 × 10−19 𝐶)
1 𝑁𝑚2 1
Take (𝐾 = 4𝜋𝜀 = 9 × 109
𝑁𝑚2
)
(𝐾 = = 9 × 109 2 ) 𝐶2
4𝜋𝜀0 𝐶 𝑚
0

a. 18 𝑁 a. 1024 𝑠2
𝑚
b. 1.8 𝑁 b. 1023 𝑠2
c. 0.18 𝑁 c.
𝑚
1022 𝑠2
d. None of the above 𝑚
41. Three charges +𝑄1 , +𝑄2 and 𝑞 are placed on a d. 1025 𝑠2
straight line such that 𝑞 is somewhere in 46. Two identical conducting spheres carry identical
between +𝑄1 and +𝑄2 . If this system of charges charges. If the spheres are set at a certain
is in equilibrium, what should be the magnitude distance apart, they repel each other with a
and sign of charge 𝑞 ? force 𝐹. A third conducting sphere, identical to
𝑄1 𝑄2 the other two, but initially uncharged, is then
a. 2 , positive
(√𝑄1 +√𝑄2 ) touched to one sphere, and then into the other
𝑄1 +𝑄2
b. , positive before being removed. The force between the
2
𝑄1 𝑄2 original two spheres is now
c. 2 , negative 𝐹
(√𝑄1 +√𝑄2 ) a.
𝑄1 +𝑄2 2
d. 2
, negative b.
𝐹
4
42. Point charges +4𝑞, −𝑞 and +4𝑞 are kept on the 3𝐹
c.
𝑥-axis at points 𝑥 = 0, 𝑥 = 𝑎 and 𝑥 = 2𝑎, 4
3𝐹
respectively. Then d. 8
a. Only −𝑞 is in stable equilibrium
b. None of the charges is in equilibrium
c. All the charges are in unstable
equilibrium
d. All the charges are in stable equilibrium
Electrostatics Vardan Patni’s Physics Classes – 9584120300

47. Two positive ions, each carrying a charge 𝑞, are

separated by a distance 𝑑. If 𝐹 is the force of
repulsion between the ions, the number of
electrons missing from each ion will be (𝑒 being
the charge on an electron)
4𝜋𝜀0 𝐹𝑑 2
a. 𝑞2
4𝜋𝜀0 𝐹𝑑 2
b. 𝑒2
4𝜋𝜀0 𝐹𝑒 2
c. √ 𝑑2
4𝜋𝜀0 𝐹𝑑 2
d. √ 𝑒2
e. None of these
48. Three charges 𝑞, −𝑞 and 𝑞0 are placed as shown
in the figure. The magnitude of the net force on
the charge 𝑞0 at point
1
𝑂 is take, 𝐾 = 4𝜋𝜀
0
a. 0
2𝐾𝑞𝑞0
b. 2 𝑎
√2𝐾𝑞𝑞0
c. 𝑎2
𝐾𝑞𝑞0
d.
√2𝑎2
e. None of these
49. According to Coulomb’s law, which is the correct
relation for the following figure?
a. 𝑞1 𝑞2 > 0
b. 𝑞1 𝑞2 < 0
c. 𝑞1 𝑞2 = 0
d. 1 > 𝑞1 𝑞2 > 0
e. None of these
50. Charges 5.0 × 10−7 𝐶, −2.5 × 10−7 𝐶 and
1.0 × 10−7 𝐶 are held fixed at the three corners
𝐴, 𝐵, 𝐶 of an equilateral triangle od side 5.0 𝑐𝑚.
Find the electric force on the charge at 𝐶 due to
the rest two.
a. 0.16 𝑁
b. 1.16 𝑁
c. 2.16 𝑁
d. 3.16 𝑁
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

Electric field
1. Three equal positive charges are placed at the 6. Two charges 16𝑒 and −𝑒 are separated by a
vertices of an equilateral triangle. Find the net distance of 10 𝑐𝑚 in air. Find the location where
electric field at its centroid. net electric field is zero.
a. 0 10
a. 𝑐𝑚 from −𝑒 charge
b. 1 3
10
c. 2 b. 3
𝑐𝑚 from 16𝑒 charge
d. 3 c. 10 𝑐𝑚 from −𝑒 charge
e. None of these d. 10 𝑐𝑚 from 16𝑒 charge
2. Four charges are arranged at corners of a square 7. An electron projected with velocity 𝑣⃗ = 𝑣0 𝑖̂ in
as shown in figure. The magnitude and direction electric field 𝐸⃗⃗ = 𝐸0 𝑗̂. Trace the path followed
of electric field at centre. by the electron
√2𝑞 𝑁
a. along OD a. Parabola
𝜋𝜀0 𝑙 2 𝐶
√2𝑞 𝑁 b. Circle
b. 𝜋𝜀0 𝑙 2 𝐶
along OC c. Straight line in positive 𝑦 direction
c.
√2𝑞 𝑁
along OA d. Straight line in negative 𝑦 direction
𝜋𝜀0 𝑙 2 𝐶
8. The figure shows the path of a positively
√2𝑞 𝑁
d. 𝜋𝜀0 𝑙 2 𝐶
along OB charged particle through a rectangular region of
e. None of these uniform electric field as shown in figure. What is
3. Figure shows six unequal charges placed at the direction of electric field and direction of
vertices of a regular hexagon. Find net electric particles 2, 3 and 4
field at its centre
3𝑞 𝑁
a. 2𝜋𝜀0 𝑙 2 𝐶
𝑖̂
√3𝑞 𝑁
b. 2𝜋𝜀0 𝑙 2 𝐶
𝑖̂
3𝑞 𝑁 a. Top, down, top, down
c. 𝑖̂
𝜋𝜀0 𝑙 2 𝐶
b. Top, down, down, top
√3𝑞 𝑁
d. 𝑖̂
𝜋𝜀0 𝑙 2 𝐶
c. Down, top, top, down
e. None of these d. Down, top, down, down
9. A pendulum bob of mass 𝑚 carrying a charge 𝑞
4. Find net electric field at is at rest with its string making an angle of 𝜃
point 𝑂 with vertical in a uniform electric field 𝐸. Find
√3𝑞 𝑁 tension in string
a. 𝜋𝜀0 𝑑 2 𝐶
𝑚𝑔
a. 𝑠𝑖𝑛𝜃
4√3𝑞 𝑁
b. 𝜋𝜀0 𝑑 2 𝐶
b. 𝑚𝑔
𝑞𝐸
√3𝑞 𝑁 c. 𝑠𝑖𝑛𝜃
c.
4𝜋𝜀0 𝑑 2 𝐶 𝑞𝐸
d. None of these d. 𝑐𝑜𝑠𝜃
5. Four particles each having a charge 𝑞, are placed e. None of these
on four vertices of a regular pentagon. The 10. A charged particle of mass 𝑚 and charge 𝑞 is
distance of each corner from centre is 𝑎. Find released from rest in a uniform electric field 𝐸.
electric field at centre of pentagon. Neglecting the effect of gravity, kinetic energy of
a.
𝑘𝑞 charged particle after 𝑡 second is
𝑎2 𝐸𝑞2 𝑚
4𝑘𝑞 a.
b. 2𝑡 2
𝑎2 𝐸 2 𝑞2 𝑡 2
c. 0 b. 2𝑚
𝑘𝑞 2𝐸 2 𝑡 2
d. 4𝑎 2 c. 𝑞𝑚
e. None of these 𝐸𝑞𝑚
d. 𝑡
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

11. An electron of mass 𝑚𝑒 , initially at rest, moves 14. A charged particle of mass 1 𝑘𝑔 and charge 2 𝜇𝐶
𝑚
through a certain distance in a uniform electric is thrown with a speed of 20 making an angle
𝑠
field in time 𝑡1 . A proton of mass 𝑚𝑝 , also of 45° to the horizontal. The space contains a
initially at rest, takes time 𝑡2 , to moves through 𝑉
horizontal electric field of 2 × 107 . Find its
an equal distance in this uniform electric field. 𝑚
𝑡 range
Neglecting the effect of gravity 𝑡2 will be
1 a. 20 𝑚
a. 1836 b. 200 𝑚
b. 1 c. 50 𝑚
c. √ 𝑚𝑝
𝑚 d. 100 𝑚
𝑒 e. None of these
𝑚𝑒 8𝑚 𝑉
d. √𝑚𝑝 15. A uniform electric field 𝐸 = ( )
𝑒 𝑚
is created

e. None of these between two parallel plates of length 1 𝑚 as

12. A block of mass ‘𝑚’ containing a charge of −𝑞 is shown in figure (Where, 𝑚 = mass of the
placed on a horizontal frictionless surface and is electron and 𝑒 = charge of the electron). An
connected to wall through an unstretched spring electron enters the field symmetrically between
𝑚
of stiffness 𝑘. If horizontal electric field 𝐸 the plates with a speed of 2 . The angle of
𝑠
parallel to spring is switched on. Find maximum deviation ′𝜃′ of the path of the electron as it
compression of spring comes out of the field will be. (Neglect gravity)

2𝑞𝐸
a. √ 𝑘
𝑞𝐸
b. 𝑘 a. tan−1 (3)
c. 0 b. tan−1 (2)
2𝑞𝐸
d. c. tan−1 (4)
𝑘
e. None of these 1
d. tan−1 (3)
13. A point charge 𝑞 moves from point 𝑃 to 𝑆 along e. None of these
the path 𝑃𝑄𝑅𝑆 in a uniform electric field 16. There is a uniform electric field of strength
directed parallel to 𝑥-axis. The co-ordinates of 𝑉
103 𝑚 along 𝑦-axis. A body of mass 1 𝑔𝑚 and
point 𝑃, 𝑄, 𝑅 and 𝑆 are (𝑎, 𝑏), (2𝑎, 0), (𝑎, −𝑏)
and (0,0). Find work done by electric force in charge 10−6 𝐶 is projected into the field from
𝑚
the process origin along positive 𝑥-axis with velocity 10 . Its
𝑠
𝑚
speed in 𝑠 after 10 seconds will be
𝑚
a. 10 𝑠
𝑚
b. 10√2 𝑠
𝑚
c. 100√2 𝑠
a. 𝑞𝐸𝑎 d. None of these
b. −𝑞𝐸𝑎
c. 𝑞𝐸𝑎√2
d. 𝑞𝐸√(2𝑎)2 + 𝑏 2
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

17. An inclined plane making an angle of 30° with 21. Two parallel line charges with linear charge
𝑐 𝑐
the horizontal is placed in a uniform horizontal densities +𝜆 and −𝜆 are placed at a
𝑁 𝑚 𝑚
electric field of 200 𝐶 , as shown in the figure. A distance 2𝑅 in free space. Find electric field
body of mass 1 𝑘𝑔 and charge 5 𝑚𝐶 is allowed between two plates
𝜆 𝑁
to slide down from rest at a height of 1 𝑚. If the a. 𝐸⃗⃗𝑛𝑒𝑡 = ( ) towards −𝜆 charge
𝜋𝜀0 𝑅 𝐶
coefficient of friction is 0.2, find the time taken
density wire
by the body to reach the bottom 𝜆 𝑁2
b. 𝐸⃗⃗𝑛𝑒𝑡 = (𝜋𝜀 𝑅) 𝐶 towards −𝜆 charge
0
density wire
𝜆 𝑁
c. 𝐸⃗⃗𝑛𝑒𝑡 = (𝜋𝜀 𝑅) 𝐶 towards +𝜆 charge
0
density wire
𝜆 𝑁2

a. 10.3 second d. 𝐸⃗⃗𝑛𝑒𝑡 = (𝜋𝜀 𝑅) 𝐶 towards +𝜆 charge

0
b. 2 seconds density wire
c. 1.3 seconds e. None of these
d. None of these 22. Find the electric field at point 𝑃 on the
18. A toy car with charge 𝑞 moves on a horizontal perpendicular bisector of a uniformly charged
frictionless horizontal plane surface under the thin wire of length 𝐿 carrying a charge 𝑄. The
influence of a uniform electric field 𝐸⃗⃗ . Due to distance of the point 𝑃 from the centre of the
the force 𝑞𝐸⃗⃗ , its velocity increases from 0 to √3
wire is 𝑎 = 2
𝐿.
𝑚
6 in one second. At that instant direction of
𝑠
the field is reversed. The car continues to move
for two more seconds under the influence of
this field. The average velocity and average
speed of toy car between 0 to 3 seconds,
respectively are
𝑚 𝑚
a. 2 𝑠 , 4 𝑠 𝑄
𝑚 𝑚 a. 𝐸⃗⃗ = 2
b. 1 ,3 √3𝜋𝜀0 𝐿2
𝑠 𝑠 𝑄
𝑚 𝑚 b. 𝐸⃗⃗ =
c. 1 𝑠
,5 𝑠
2𝜋𝜀0 𝐿2
𝑄
d. None of these c. 𝐸⃗⃗ =
√3𝜋𝜀0 𝐿2
𝑔
19. An oil drop of radius 2 𝑚𝑚 with a density 3 𝑐𝑚3
d. None of these
is held stationary under a constant electric field 23. A thin semi-circular ring of radius 𝑟 has a
3.55 × 105
𝑉
in the Millikan’s oil drop positive charge 𝑞 distributed uniformly over it.
𝑚
The net field 𝐸 at the centre 𝑂 is
experiment. What is the number of excess
electrons that the oil drop will possess?
𝑚
(𝑔 = 9.81 𝑠2
)
a. 𝑛 = 1.73 × 1010
b. 𝑛 = 1.73 × 108
c. 𝑛 = 1.73 × 1012 𝑞 𝑁
a. 𝐸⃗⃗ = 2𝜋2 𝜀 2 𝑗̂ 𝐶
d. None of these 0 𝑟
−𝑞 𝑁
20. A proton is released from rest, 10 𝑐𝑚 away from b. 𝐸⃗⃗ = 𝑗̂
2𝜋2 𝜀0 𝑟 2 𝐶
a charged sheet carrying charged density of −𝑞 𝑁
𝐶 c. 𝐸⃗⃗ = 𝑖̂
−2.21 × 10−9 𝑚2 . It will strike the sheet after 2𝜋2 𝜀0 𝑟 2 𝐶
𝑞 𝑁
the time (approximately) d. 𝐸⃗⃗ = 𝑖̂
2𝜋2 𝜀0 𝑟 2 𝐶
a. 2 𝜇𝑠 e. None of these
b. 4 𝜇𝑠
c. 6 𝜇𝑠
d. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

24. A wire of length 𝐿 = 20 𝑐𝑚 is bent into a 27. Two infinite identical sheets each having surface
semicircular arc. If the two equal halves of the charge density of +𝜎 are placed at an angle of
arc were each to be uniformly charged with 30° as shown in the figure. Find net electric field
charges ±𝑄, (where |𝑄| = 103 𝜀0 𝐶𝑜𝑢𝑙𝑜𝑚𝑏𝑠). in a region between the plates.
The net electric field at the centre 𝑂 of the
semicircular arc would be
a. 𝐸⃗⃗𝑛𝑒𝑡 = 25 × 103 𝑖̂
b. 𝐸⃗⃗𝑛𝑒𝑡 = 20 × 103 𝑖̂
c. 𝐸⃗⃗𝑛𝑒𝑡 = 25 × 106 𝑖̂ 𝜎 √3 𝑥̂
a. [(1 + 2 ) 𝑦̂ + 2]
d. 𝐸⃗⃗𝑛𝑒𝑡 = 20 × 106 𝑖̂ 𝜀0
𝜎 √3 𝑥̂
e. None of the above b. [(1 − 2 ) 𝑦̂ − 2]
2𝜀0
25. A long wire with uniform linear charge density 𝜆 𝜎 𝑥̂
c. [(1 + √3)𝑦̂ + 2]
is bent into two configurations as shown in 2𝜀0
𝜎 𝑥̂
figure. Determine intensity of electric field at d. [(1 + √3)𝑦̂ − 2]
2𝜀0
point 𝑂, respectively for figure (𝑎) and (𝑏) e. None of these
28. A hollow metal sphere of radius 𝑅 is uniformly
charged. The electric field due to sphere at a
distance 𝑟 from centre
a. Increases as 𝑟 increases for 𝑟 < 𝑅 and
𝑟>𝑅
b. Zero as 𝑟 increases for 𝑟 < 𝑅 and
decreases as 𝑟 increases for 𝑟 > 𝑅
𝜆 𝑁 c. Zero as 𝑟 increases for 𝑟 < 𝑅 and
a. 0, 2√2𝜋𝜀0 𝑟 𝐶 increases as 𝑟 increases for 𝑟 > 𝑅
𝜆 𝑁
b. ,0 d. Decreases as 𝑟 increases for both 𝑟 < 𝑅
2√2𝜋𝜀0 𝑟 𝐶
𝜆 𝑁 and 𝑟 > 𝑅
c. 0, 4𝜋𝜀 𝑟 𝐶
0 e. None of these
𝜆 𝑁 3𝑅
d. ,0 29. The electric field at a distance from the
4𝜋𝜀0 𝑟 𝐶 2
e. None of these centre of a charged conducting spherical shell of
26. Three infinite long charged sheets are placed as 𝑅
radius 𝑅 is 𝐸. The electric field at a distance 2
shown in figure. The electric field at point 𝑃 is from the centre of the sphere is
a. 0
b. 𝐸
𝐸
c. 2
𝐸
d. 3
e. None of these
30. Charges 𝑄, 2𝑄 and 4𝑄 are uniformly distributed
2𝜎 𝑁
a. 𝜀0
𝑘̂ 𝐶 in three dielectric solid spheres 1, 2 and 3 or
𝑅
b.
2𝜎
− 𝜀 𝑘̂
𝑁 radii 2 , 𝑅 and 2𝑅, respectively. If magnitude of
0 𝐶
4𝜎 electric field at point 𝑃 at a distance 𝑅 from
c. 𝑘̂ 𝑁
𝜀0 𝐶 centre of spheres 1, 2 and 3 are 𝐸1 , 𝐸2 and 𝐸3 ,
4𝜎 𝑁
d. − 𝜀 𝑘̂ 𝐶
respectively. Then
0
a. 𝐸1 > 𝐸2 > 𝐸3
e. None of these
b. 𝐸2 > 𝐸1 > 𝐸3
c. 𝐸3 > 𝐸2 > 𝐸1
d. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

31. Which of the field pattern given below is valid 35. A few electric field lines for a system of two
for electric field as well as magnetic field charges 𝑄1 and 𝑄2 fixed at two different point
on 𝑥-axis is shown in figure. These lines suggest
that

a. |𝑄1 | > |𝑄2 |

b. at a finite distance to the right of 𝑄2 , the
electric field is zero
c. at a finite distance to the left of 𝑄1 , the
electric field is zero
d. |𝑄1 | < |𝑄2 |
e. None of these
36. The three charges 𝑞⁄2, 𝑞 and 𝑞⁄2 are placed at
the corners A, B and C of a square of field 𝐸 at
32. A metallic solid sphere is placed in a uniform
the corner D of the square is side 𝑎 as shown in
electric field. The lines of force follow the
figure. The magnitude of electric
path(s) shown in figure as
𝑞 1 1
a. ( + 2)
4𝜋𝜀0 𝑎 2 √2
𝑞 1
b. (1 + )
4𝜋𝜀0 𝑎 2 √2
𝑞 1
c. (1 − )
4𝜋𝜀0 𝑎 2 √2
a. 1 𝑞 1 1
b. 2 d. ( − 2)
4𝜋𝜀0 𝑎 2 √2
c. 3 e. None of the above
d. 4 37. A negatively charged oil drop is prevented from
e. None of these falling under gravity by applying a vertical
33. For a uniformly charged ring of radius 𝑅, the electric field 100 𝑉⁄𝑚. If the mass of the drop is
electric field on its axis has the largest 1.6 x 10-3g, the number of electrons carried by
magnitude at a distance ℎ from its centre. Then the drop is (g=10ms-2)
value of ℎ is a. 1018
a. 𝑅⁄√5 b. 1015
b. 𝑅⁄√2 c. 106
c. 𝑅 d. 109
d. 𝑅√2 e. 1012
e. None of these 38. A point charge 2 × 10−2 𝐶 is moved from P to S
34. Infinite charges each of magnitude 𝑞 are lying at in a uniform electric field of 30 𝑁𝐶 −1 directed
𝑥 = 1,2,4,8 … on 𝑥-axis. The value of intensity of along positive 𝑥-axis. If coordinates of P and S
electric field at point 𝑥 = 0 due to these charges are (1, 2, 0) 𝑚 and (0, 0, 0) 𝑚, respectively. The
will be work done by electric field will be
a. (12 × 109 )𝑞 𝑁⁄𝐶 a. 600 𝑚𝐽
b. 0 b. −1200 𝑚𝐽
c. (6 × 109 )𝑞 𝑁⁄𝐶 c. 1200 𝑚𝐽
d. (4 × 109 )𝑞 𝑁⁄𝐶 d. −600 𝑚𝐽
e. None of these e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

39. In the figure, a very large plane sheet of positive 43. The Electric field due to a uniformly charged
charge is shown. 𝑃1 and 𝑃2 are two points at sphere of radius 𝑅 as a function of the distance
distance 𝑙 and 2𝑙 from the charge distribution. If from its centre is represented graphically by
𝜎 is the surface charge density, then the
magnitude of electric fields 𝐸1 and 𝐸2 at 𝑃1 and
𝑃2 , respectively are

44. A particle of mass 𝑚 and charge 𝑞 is placed at

rest in a uniform electric field 𝐸 and then
a. 𝐸1 = 𝜎⁄𝜀0 , 𝐸2 = 𝜎⁄2𝜀0 released. The kinetic energy attained by the
b. 𝐸1 = 2𝜎⁄𝜀0 , 𝐸2 = 𝜎⁄𝜀0 particle after moving a distance 𝑦 is
c. 𝐸1 = 𝐸2 = 𝜎⁄2𝜀0 a. 𝑞𝐸𝑦 2
d. 𝐸1 = 𝐸2 = 𝜎⁄𝜀0 b. 𝑞𝐸 2 𝑦
40. Two large metal plates are placed parallel to c. 𝑞𝐸𝑦
each other. The inner surfaces of plates are d. 𝑞 2 𝐸𝑦
charged by +𝜎 and −𝜎 (𝐶 ⁄𝑚2 ). The outer 45. Three charged particles 𝐴, 𝐵 and 𝐶 with charges
surfaces are neutral. The electric field in the −4𝑞, 2𝑞 and −2𝑞 are present on the
region between the plates and outside the circumference of a circle of radius 𝑑, the
plates, respectively are charged particles 𝐴, 𝐶 and centre 𝑂 of the circle
2𝜎 𝜎 formed an equilateral triangle as shown in
a. 𝜀0
,𝜀
0
𝜎 figure. Electric field at 𝑂 along 𝑥-direction is
b. ,0
𝜀0
2𝜎 2√3
c. 𝜀0
,0 a. 𝜋𝜀0 𝑑 2
2𝜎
d. 0, 𝜀 √3𝑞
0 b. 4𝜋𝜀0 𝑑 2
41. Figure below shows regular hexagon, with 3√3𝑞
different charges placed at the vertices. In which c. 4𝜋𝜀0 𝑑 2
of the following cases is the electric field at the √3𝑞
d. 𝜋𝜀0 𝑑 2
centre zero?
46. An electron and proton are in uniform electric
field, the ratio of their accelerations will be
a. Zero
b. Unity
c. The ratio of the masses of proton and
electron
d. The ratio of the masses of electron and
proton
47. An electron falls from rest through a vertical
distance ℎ in a uniform and vertically upward
42. Two point charges +10-7𝐶 and -10-7𝐶 are placed directed electric field 𝐸. The direction of
at 𝐴 and 𝐵, 20 𝑐𝑚 apart as shown in the figure. electrical field is now reversed, keeping its
Calculate the electric field at 𝐶, 20 𝑐𝑚 apart magnitude the same. A proton is allowed to fall
from both 𝐴 and 𝐵 from rest in through the same vertical distance
ℎ. The time fall of the electron, in comparison to
a. 1.5 x 10-5 𝑁⁄𝐶 the time fall of the proton is
b. 2.2 x 104 𝑁⁄𝐶 a. Smaller
c. 3.5 x 106 𝑁⁄𝐶 b. 5 times greater
d. 3.0 x 105 𝑁⁄𝐶 c. 10 times greater
d. Equal
Electrostatics Vardan Patni’s Physics Classes – 9584120300

48. A uniform electric field 𝐸 exists along positive 𝑥- 53. Electric field at centre of triangle in the given
axis. The work done in moving a charge 0.5 𝐶 figure is
through a distance 2 𝑚 along a direction making 6𝑘𝑄
a. 𝑎2
𝑖̂
an angle 60° with 𝑥-axis is 10 𝐽. Then the 6𝑘𝑄
b. 𝑗̂
magnitude of electric field is 𝑎2
𝑉 3𝑘𝑄
a. 5 c. (−𝑖̂)
𝑚 𝑎2
𝑉 3𝑘𝑄
b. 2𝑚 d. (−𝑗̂)
𝑎2
𝑉 e. None of these
c. √5 𝑚
𝑉
54. The bob of a simple pendulum has mass 2g and
d. 40 a charge of 5 𝜇𝐶. It is at rest in a uniform
𝑚
𝑉
e. 20 horizontal electric field of intensity 2000 𝑉⁄𝑚.
𝑚
49. If an insulated non-conducting sphere of radius At equilibrium, the angle that the pendulum
𝑅 has charge density 𝜌. The electric field at a makes with the vertical is (take g = 10 m/s2)
distance 𝑟 from centre of sphere will be (𝑟 < 𝑅) a. 𝑡𝑎𝑛−1(5.0)
𝜌𝑅 b. 𝑡𝑎𝑛−1(2.0)
a. 3𝜀0 c. 𝑡𝑎𝑛−1(0.5)
𝜌𝑟
b. 𝜀0
d. 𝑡𝑎𝑛−1(2.0)
c.
𝜌𝑟 e. None of these
3𝜀0 55. Let 𝜎 be the uniform surface charge density of
3𝜌𝑅
d. 𝜀0 two infinite thin plane sheets shown in figure.
50. An electron of mass ′𝑚′ and charge ‘𝑞′ is Then the electric fields in three different regions
accelerated from rest in a uniform electric field 𝐸𝐼 , 𝐸𝐼𝐼 and 𝐸𝐼𝐼𝐼 are
of strength ‘𝐸’. the velocity acquired by it as it
travels a distance ‘𝑙’ is
2𝐸𝑞𝑙 1⁄2
a. [ ]
𝑚
2𝐸𝑞 1⁄2
b. [ ]
𝑚𝑙
1
2𝐸𝑚 ⁄2
c. [ 𝑞𝑙
]
1
𝐸𝑞 ⁄2
d. [𝑚𝑙] 𝜎 𝜎
a. 𝐸𝐼 = 𝜀 𝑛̂, 𝐸𝐼𝐼 = 0, 𝐸𝐼𝐼𝐼 = 𝜀 𝑛̂
0 0
51. The number of electrons to be put on a spherical 𝜎 𝜎
conductor of radius 0.1 𝑚 to produce an electric b. 𝐸𝐼 = 2𝜀 𝑛̂, 𝐸𝐼𝐼 = 0, 𝐸𝐼𝐼𝐼 = 2𝜀 𝑛̂
0 0
𝑁 𝜎
field of 0.036 𝐶 just above its surface is c. 𝐸𝐼 = 0, 𝐸𝐼𝐼 = 𝜀 𝑛̂, 𝐸𝐼𝐼𝐼 = 0
0
2𝜎 2𝜎
a. 2.7 × 105 d. 𝐸𝐼 = 𝑛̂, 𝐸𝐼𝐼 = 0, 𝐸𝐼𝐼𝐼 = 𝑛̂
𝜀0 𝜀0
b. 2.6 × 105
e. None of these
c. 2.5 × 105
56. An infinite long straight wire having a charge
d. 2.4 × 105
density 𝜆 is kept along 𝑌𝑌 ′ − axis in 𝑋𝑌 − plane.
e. None of these
The Coulomb force on a point charge 𝑞 at a
52. Figure shows two charges 𝑞1 and −𝑞2 placed on
point 𝑃(𝑥, 0) will be
𝑥-axis as shown. If electric field at P is along 𝑥- 𝑞𝜆
direction, find 𝑞1 /𝑞2 . a. Attractive and 2𝜋𝜀
0𝑥
𝑞𝜆
b. Repulsive and 2𝜋𝜀 𝑥
4√5 0
a. 𝑞𝜆
25 c. Attractive and 𝜋𝜀 𝑥
8√5 0
b. 𝑞𝜆
25 d. Repulsive and 𝜋𝜀 𝑥
12 0
c. 25 e. None of these
16√5
d. 25
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

57. Charges +2𝑞, +𝑞 and +𝑞 are placed at the 61. An electron is released from the bottom plate 𝐴
corners 𝐴, 𝐵 and 𝐶 of an equilateral triangle 𝑁
as shown in the figure (𝐸 = 104 ). The velocity
𝐶
𝐴𝐵𝐶. If 𝐸 is the electric field at the circumcentre
of the electron when it reaches plate 𝐵 will be
𝑂 of the triangle, due to the charge +𝑞, then the
nearly equal to
magnitude and direction of the resultant electric
field at 𝑂 is
a. 𝐸 along 𝐴𝑂
b. 2𝐸 along 𝐴𝑂
c. 𝐸 along 𝐵𝑂
d. 𝐸 along 𝐶𝑂
𝑚
e. None of these a. 0.85 × 107 𝑠
𝑚
58. An electron moving with the speed 5 × 106 𝑠 is b.
𝑚
1.0 × 107 𝑠
shot parallel to the electric field of intensity 𝑚
𝑁
c. 1.25 × 107 𝑠
1 × 103 𝐶 . Field is responsible for the 𝑚
d. 1.65 × 107 𝑠
retardation of motion of electron. Now evaluate
62. Two equal negative charges −𝑞 are fixed at
the distance travelled by the electron before
point (0, 𝑎) and (0, −𝑎) on the y-axis. A positive
coming to rest for an instant
charge ‘𝑞’ is released from rest at the point
a. 7 𝑚
(𝑥 ≪ 𝑎) on the x-axis. What is the frequency of
b. 0.7 𝑚𝑚
motion
c. 7 𝑐𝑚
2𝑞2
d. 0.7 𝑚 a. √4𝜋𝜀 3
0 𝑚𝑎
e. None of these
𝑉 4𝑞2
59. There is a uniform electric field strength 103 𝑚 b. √
2𝜋𝜀 3
0 𝑚𝑎
along 𝑦-axis. A body of mass 1 𝑔 and charge 𝑞2
10−6 𝐶 is projected into the field from origin c. √2𝜋𝜀 3
0 𝑚𝑎
𝑚
along the positive 𝑥-axis with a velocity 10 𝑠 . Its 𝑞2
d. √𝜋𝜀 3
𝑚 0 𝑚𝑎
speed in 𝑠
after 10 𝑠 is (Neglect gravity)
e. None of these
a. 10 63. A point charge of 10 𝜇𝐶 is placed at the origin.
b. 5√2 At what location on the 𝑥-axis should a point
c. 10√2 charge of 40 𝜇𝐶 be placed so that the net
d. 20 electric field is zero at 𝑥 = 2 𝑐𝑚 on the 𝑥-axis?
e. None of these a. 𝑥 = 8 𝑐𝑚
60. A rod lies along the x-axis with one end at the b. 𝑥 = −4 𝑐𝑚
origin and the other at 𝑥 → ∞. It carries a c. 𝑥 = 4 𝑐𝑚
𝐶
uniform charge 𝜆 𝑚
. The electric field at the d. 𝑥 = 6 𝑐𝑚
point 𝑥 = −𝑎 on the axis will be e. None of these
𝜆 64. A positive charge particle of 100 𝑚𝑔 is thrown
a. 𝐸⃗⃗ = (−𝑖̂)
4𝜋𝜀0 𝑎 in opposite direction to a uniform electric field
𝜆
b. 𝐸⃗⃗ = 4𝜋𝜀0 𝑎
(𝑖̂) 𝑁
of strength 1 × 105 𝐶 . If the charge on the
𝜆
c. 𝐸⃗⃗ = 2𝜋𝜀0 𝑎
(−𝑖̂) particle is 40 𝜇𝐶 and the initial velocity is
𝑚
𝜆 200 𝑠 , how much distance it will travel before
d. 𝐸⃗⃗ = 2𝜋𝜀0 𝑎
(𝑖̂)
coming to the rest momentarily
e. None of these a. 1 𝑚
b. 5 𝑚
c. 10 𝑚
d. 0.5 𝑚
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

65. Two point charges 𝐴 and 𝐵 of magnitude 68. What will be the magnitude of electric field at
+8 × 10−6 𝐶 and −8 × 10−6 𝐶, respectively are point 𝑂 as shown in figure? Each side of the
placed at a distance 𝑑 apart. The electric field at figure is 𝑙 and perpendicular to each other
the middle point 𝑂 between the charges is
𝑁
6.4 × 104 𝐶 . The distance 𝑑 between the point
𝐴 and 𝐵 is
a. 2.0 𝑚
b. 3.0 𝑚
c. 1.0 𝑚
d. 4.0 𝑚
e. None of these 𝑞
a.
66. Consider a sphere of radius 𝑅 which carries a 4𝜋𝜀0 (2𝑙)2
1 𝑞
uniform charge density 𝜌. If a sphere of radius
𝑅 b. 4𝜋𝜀0 2𝑙 2
(2√2 − 1)
2
|𝐸 | 1 𝑞
is carved out of it, as shown, the ratio |𝐸𝐴 | of c. 4𝜋𝜀0 𝑙 2
𝐵
1 2𝑞
magnitude of electric field 𝐸𝐴 and 𝐸𝐵, d.
4𝜋𝜀0 2𝑙 2
(√2)
respectively, at points 𝐴 and 𝐵 due to the e. None of these
remaining portion is 1
21
69. The dimensions of (2) 𝜀0 𝐸2 are
a. 34 a. 𝑀𝐿𝑇 −1
18
b. 54
b. 𝑀𝐿2 𝑇 −2
c.
17 c. 𝑀𝐿−1 𝑇 −2
54
18 d. 𝑀𝐿2 𝑇 −1
d. 34 e. None of these
e. None of these 70. The line 𝐴𝐴′ is on a charged infinite conducting
67. Four point charges −𝑞, +𝑞, +𝑞 and −𝑞 are plane which is perpendicular to the plane of the
placed on 𝑦-axis at 𝑦 = −2𝑑, 𝑦 = 𝑑, 𝑦 = +𝑑 paper. The plane has a surface density of charge
and 𝑦 = ±2𝑑, respectively. The magnitude of 𝜎 and 𝐵 is a ball of mass 𝑚 with a like charge
the electric field 𝐸 at a point on the 𝑥-axis at magnitude 𝑞. 𝐵 is connected by a string from a
𝑥 = 𝐷, with 𝐷 >> 𝑑, will behave as point on the line 𝐴𝐴’. The tangent of the angle
1
a. 𝐸 ∝ 𝐷 (𝜃) formed between the line 𝐴𝐴’ and the string
1 is
b. 𝐸 ∝ 𝐷3 𝑞𝜎
1 a.
2𝜀0 𝑚𝑔
c. 𝐸 ∝ 𝐷2 𝑞𝜎
1 b. 4𝜋𝜀0 𝑚𝑔
d. 𝐸 ∝ 𝐷4 𝑞𝜎
c.
e. None of these 2𝜋𝜀0 𝑚𝑔
𝑞𝜎
d. 𝜀0 𝑚𝑔
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

Electric Flux
7. A square sheet of side 𝑎 is lying parallel to 𝑋𝑌 −
1. Calculate the electric flux through a cube when plane at 𝑧 = 𝑎. The electric field in the region is
charge is at
𝐸 = 𝑐𝑧 2 𝑘̂. The electric flux through the sheet is
a. Centre
a. 𝑎4 𝑐
b. At the centre of one of the sides 1
b. 3 𝑎3 𝑐
c. At the centre of one of the faces
1 4
d. At vertices c. 3
𝑎 𝑐
2. Calculate the electric flux through a face of a d. 0
cube when charge is at 8. A cylinder of radius 𝑅 and length 𝐿 is placed in a
a. Centre uniform electric field 𝐸 parallel to the cylinder
b. At vertices axis. The total flux for the surface of the
3. A charge 𝑞 is placed at the point of intersection cylinder is given by
of body diagonals of a cube. The electric flux a. 2𝜋𝑅 2 𝐸
passing through any one of its faces is b. 𝜋𝑅 2 ⁄𝐸
𝑞
a. c. (𝜋𝑅 2 − 𝜋𝑅)⁄𝐸
6𝜀0
3𝑞 d. Zero
b. 𝜀0 9. A charge Q is enclosed by a Gaussian spherical
6𝑞
c. surface of radius R. If the radius is doubled,
𝜀0
𝑞 then the outward electric flux will
d. 3𝜀0 a. increase four times
4. The electric flux through a closed Gaussian b. be reduced to half
surface depends upon c. remain the same
a. Net charge enclosed and permittivity of d. be doubled
the medium 10. A square plate of side 𝐿 is in the plane of paper.
b. Net charge enclosed, permittivity of the A uniform electric field 𝐸, also in the plane of
medium and the size of the Gaussian paper, is limited to lower half of square plate.
surface Find flux through
c. Net charge enclosed only square plate
d. Permittivity of the medium only a. Zero
5. In a region of space, the electric field is given by b. 𝐸𝐿2
𝐸⃗⃗ = 8𝑖̂ + 4𝑗̂ + 3𝑘̂ . The electric flux through a c.
𝐸𝐿2
surface of area of 100 units in the 𝑥𝑦 plane is 2
𝐸𝐿2
a. 800 units d. 2𝜀0
b. 300 units 11. Which statement is true for Gauss’ law?
c. 400 units a. All the charges whether inside or
d. 1500 units outside the Gaussian surface contribute
6. If ∮ 𝐸 · 𝑑𝑠 = 0 over a surface, then to the electric flux.
a. The magnitude of electric field on the b. Electric flux depends upon the
surface is constant. geometry of the Gaussian surface.
b. All the charges must necessarily be c. Gauss theorem can be applied to non-
inside the surface. uniform electric field.
c. The electric field inside the surface is d. The electric field over the Gaussian
necessarily uniform. surface remains continuous and
d. The number of flux lines entering the uniform at every point.
surface must be equal to the number of
flux lines leaving it.
Electrostatics Vardan Patni’s Physics Classes – 9584120300

12. A cube of side 𝑎 is placed at a distance 𝑎 from 16. In figure +𝑄 charge is located at one of the
the origin, in a uniform electric field 𝐸 = 𝐶𝑥, edges of the cube, then electric flux through
directed towards 𝑥-axis. Find out the net charge cube due to +𝑄 charge is
inside the cube
+𝑄
a. 𝜀0
+𝑄
b. 2𝜀0
+𝑄
c.
4𝜀0
+𝑄
d. 8𝜀0
17. In a cuboid of dimension 2𝐿 × 2𝐿 × 𝐿, a charge
a. 𝐶𝑎3 𝜀0
𝑞 is placed at the centre of the surface 𝑆 having
b. − 𝐶𝑎3 𝜀0
area of 4𝐿2 . The flux through the opposite
c. 𝐶𝑎2 𝜀0
surface to 𝑆 is given by
d. −𝐶𝑎2 𝜀0 𝑞
13. Consider the charge configuration and spherical a. 2𝜀
0
𝑞
Gaussian surface as shown in the figure. When b. 12𝜀0
calculating the flux of the electric field over the 𝑞
c.
spherical surface the electric field will be due to 6𝜀0
𝑞
d.
3𝜀0
18. If a charge 𝑞 is placed at the centre of a closed
hemispherical non-conducting surface, the total
flux passing through the flat surface would be
𝑞
a. 𝜀
0
𝑞
a. 𝑞2 b.
2𝜀0
b. Only the positive charges 𝑞
c. 4𝜀0
c. All the charges 𝑞
d. +𝑞1 and −𝑞1 d.
2𝜋𝜀0
14. A square surface of side 𝐿 𝑚𝑒𝑡𝑒𝑟𝑠, in the plane 19. As shown in the figure, a point charge 𝑄 is
of paper, is placed in a uniform electric field placed at the centre of conducting spherical
𝐸 (𝑉/𝑚) acting along the same plane at an shell of inner radius 𝑎 and outer radius 𝑏. The
angle 𝜃 with the horizontal side of the square as electric field due to charge 𝑄 in three different
shown in figure. The electric flux linked to the regions 𝐼, 𝐼𝐼 and 𝐼𝐼𝐼 is given by
surface, in units of
𝑉𝑚 is

a. Zero
b. 𝐸𝐿2
c. 𝐸𝐿2 cos 𝜃
d. 𝐸𝐿2 𝑠𝑖𝑛 𝜃
15. A charge 𝑞 is placed at a height of 𝑎⁄2 from (𝐼: 𝑟 < 𝑎, 𝐼𝐼: 𝑎 < 𝑟 < 𝑏, 𝐼𝐼𝐼: 𝑟 > 𝑏)
centre of a square plate of side 𝑎. Find electric a. 𝐸𝐼 ≠ 0, 𝐸𝐼𝐼 = 0, 𝐸𝐼𝐼𝐼 = 0
flux through the plate b. 𝐸𝐼 = 0, 𝐸𝐼𝐼 = 0, 𝐸𝐼𝐼𝐼 ≠ 0
𝑞 c. 𝐸𝐼 ≠ 0, 𝐸𝐼𝐼 = 0, 𝐸𝐼𝐼𝐼 ≠ 0
a. 𝜀
0 d. 𝐸𝐼 = 0, 𝐸𝐼𝐼 = 0, 𝐸𝐼𝐼𝐼 = 0
𝑞
b. 6𝜀0
e. None of these
𝑞
c. 4𝜀0
d. 0
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300
𝑎
20. A disk of radius 4 having a uniformly distributed
charge 6𝐶 is placed in the 𝑥-𝑦 plane with its
𝑎
centre at (− , 0, 0). A rod of length ‘𝑎’ carrying
2
a uniformly distributed charge 8𝐶 is placed on
𝑎 5𝑎
the 𝑥-axix from 𝑥 = to 𝑥 = . Two point
4 4
𝑎 𝑎
charges −7𝐶 and 3𝐶 are placed at ( , − , 0)
4 4
3𝑎 3𝑎
and (− , , 0),
4 4
respectively. Consider a
cubical surface formed by six surfaces
𝑎 𝑎 𝑎
𝑥 = ± 2 , 𝑦 = ± 2 , 𝑧 = ± 2 . The electric flux
through this cubical surface is

2𝐶
a. − 𝜀
0
2𝐶
b. 𝜀0
10𝐶
c.
𝜀0
12𝐶
d. 𝜀0
21. If the electric flux entering and leaving an
enclosed surface respectively is 𝜑1 and 𝜑2 the
electric charge inside the surface will be
a. (𝜑1 + 𝜑2 )𝜀0
b. (𝜑2 − 𝜑1 )𝜀0
(𝜑1 +𝜑2 )
c. 𝜀0
(𝜑2 −𝜑1 )
d. 𝜀0
Electrostatics Vardan Patni’s Physics Classes – 9584120300

Electric dipole
6. An electric dipole of moment 𝑝⃗ is placed normal
1. Three point charges +𝑞, −2𝑞 and +𝑞 are placed
to the lines of force of electric intensity 𝐸⃗⃗ , then
at points (𝑥 = 0, 𝑦 = 𝑎, 𝑧 = 0),
the work done in deflecting it through an angle
(𝑥 = 0, 𝑦 = 0, 𝑧 = 0) and (𝑥 = 𝑎, 𝑦 = 0, 𝑧 = 0),
of 180° is
respectively. The magnitude and direction of the
a. 𝑝𝐸
electric dipole moment vector of this charge
b. +2𝑝𝐸
assembly are c. −2𝑝𝐸
a. √2𝑞𝑎 along +𝑦 direction d. 0
b. √2𝑞𝑎 along the line joining points 7. Work done in rotating a dipole from stable
(𝑥 = 0, 𝑦 = 0, 𝑧 = 0) and equilibrium to unstable equilibrium is
(𝑥 = 𝑎, 𝑦 = 𝑎, 𝑧 = 0) a. 𝑃𝐸
c. 𝑞𝑎 along the line joining points b. 2𝑃𝐸
(𝑥 = 0, 𝑦 = 0, 𝑧 = 0) and c. −2𝑃𝐸
(𝑥 = 𝑎, 𝑦 = 𝑎, 𝑧 = 0) d. 0
d. √2𝑞𝑎 along +𝑥 direction 8. Positive and negative charges of equal
𝑎 𝑎
2. An electric dipole has a fixed dipole moment 𝑝⃗, magnitude are placed at (0, 0, 2 ) and (0, 0, − 2 ).
which makes angle 𝜃 with respect to 𝑥-axis. Work done in moving a positive charge of same
When subjected to an electric field 𝐸⃗⃗1 = 𝐸𝑖̂, it magnitude from (−𝑎, 0, 0) and (0, 𝑎, 0) is
experiences a torque 𝑇 ⃗⃗1 = 𝜏𝑘̂ . When subjected a. Positive
to another electric field 𝐸⃗⃗2 = √3𝐸1 𝑗̂, it b. Negative
experiences a torque 𝑇 ⃗⃗2 = −𝑇 ⃗⃗1 . The angle 𝜃 c. Zero
a. 90° d. Data insufficient
b. 30° 9. An electric dipole is situated in an electric field
c. 45° of uniform intensity 𝐸 whose dipole moment is
d. 60° 𝑃 and moment of inertia is 𝐼. If dipole is
3. An electric dipole is placed at an angle of 30° displaced slightly from the equilibrium position,
𝑁 then angular frequency of its oscillation is
with an electric field intensity 2 × 105 𝐶 . It
1
experiences a torque equal to 4 𝑁𝑚. The charge 𝑃𝐸 2
a. ( )
𝐼
on the dipole, if the dipole length is 2 𝑐𝑚, is 3
𝑃𝐸 2
a. 7 𝜇𝐶 b. (𝐼)
b. 8 𝑚𝐶 1
𝐼 2
c. 2 𝑚𝐶 c. (𝑃𝐸 )
d. 5 𝑚𝐶 1
𝑃 2
4. An electric dipole is kept in non-uniform electric d. (𝐼𝐸 )
field. It experiences 10. Two point charges −𝑞 and +𝑞 are placed at a
a. A force and a torque distance of 𝐿. The magnitude of electric field
b. A force but not a torque intensity at a distance 𝑅(𝑅 ≫ 𝐿) varies as
c. A torque but not a force a.
1
d. Neither a force nor a torque 𝑅3
1
5. An electric dipole consisting of two opposite b. 𝑅4
1
charges of 2 × 105 𝐶 each separated by a c. 𝑅6
distance of 3 𝑐𝑚 is placed in an electric field of 1
d.
𝑁 𝑅2
2 × 105 . The maximum torque on the dipole
𝐶
will be
a. 12 × 10−1 𝑁𝑚
b. 12 × 10−3 𝑁𝑚
c. 24 × 10−1 𝑁𝑚
d. 24 × 10−3 𝑁𝑚
Electrostatics Vardan Patni’s Physics Classes – 9584120300

11. A dipole is placed in an electric field as shown. In

which direction will it move?

a. Towards the left as its potential energy

will increase
b. Towards the right as its potential energy
will decrease
c. Towards the left as its potential energy
will increase
d. Towards the right as its potential energy
will increase
12. Polar molecules are the molecules
a. having zero dipole moment
b. acquire a dipole moment only in the
presence of electric field due to
displacement of charge.
c. acquire a dipole moment only when
magnetic field is absent
d. having a permanent electric dipole
moment
13. Determine the electric dipole moment of the
system of three charges placed on the vertices
of an equilateral triangle as shown in the figure.

𝑗̂ −𝑖̂
a. √3𝑞𝑙
√2
b. 2𝑞𝑙𝑗̂
c. −√3𝑞𝑙𝑗̂
𝑖̂+𝑗̂
d. 𝑞𝑙
√2
Electrostatics Vardan Patni’s Physics Classes – 9584120300

Potential Due to point charge

1. Eight point charges 𝑞 are placed at the vertices 6. At a certain distance from a point charge, the
𝑉
of a cube of side 𝑙. Find electric potential and field intensity is 500 and the potential is
𝑚
electric field at the centre. 3000 𝑉. The distance to charge and magnitude
4𝑞
a. ,0 of charge, respectively are
3𝜋𝜀0 𝑙
16𝑞 a. 𝑟 = 6 𝑐𝑚, 𝑞 = 2 𝜇𝑚
b. ,0
√3𝜋𝜀0 𝑙 b. 𝑟 = 6 𝑐𝑚, 𝑞 = 4 𝜇𝑚
𝑞
c. ,0 c. 𝑟 = 6 𝑚, 𝑞 = 2 𝜇𝑚
√3𝜋𝜀0 𝑙
4𝑞 d. 𝑟 = 6 𝑚, 𝑞 = 4 𝜇𝑚
d. ,0
√3𝜋𝜀0 𝑙 e. None of these
e. None of these 7. Two charges +6 𝜇𝑚 and −4 𝜇𝑚 are placed
2. Four point charges −𝑄, −𝑞, 2𝑞 and 2𝑄 are 15 𝑐𝑚 apart as shown in the figure. At what
placed at each corner of a square. The relation distance in 𝑐𝑚, from 𝐴 to its right, total
between 𝑄 and 𝑞 for which potential at centre is electrostatic potential is zero.
zero will be
a. 𝑄 = 2𝑞
b. 𝑄 = 𝑞
c. 𝑄 = −𝑞
d. 𝑄 = −2𝑞 a. 4, 9, 60
e. None of these b. 9, 15, 45
3. Find total electric potential at ′𝐴′ for charge c. 20, 30, 40
configuration shown in the figure d. 9, 45, ∞
e. None of the above
8. A point charge 𝑞1 = +6𝑒 is fixed at origin of a
co-ordinate system. Another point charge
𝑞2 = −10𝑒 is fixed at 𝑥 = 8 𝑛𝑚 and 𝑦 = 0. The
locus of all points in 𝑥-𝑦 plane for which
potential 𝑉 = 0 is a circle, centred on 𝑥-axis, as
shown.

a. 𝑉𝐴 = 0
1 2𝑞 1
b. 𝑉𝐴 = 4𝜋𝜀 𝑙
(1 + 5) 𝑣𝑜𝑙𝑡𝑠
0 √
1 2𝑞 1
c. 𝑉𝐴 = (1 − ) 𝑣𝑜𝑙𝑡𝑠
4𝜋𝜀0 𝑙 √5
1 2𝑞
d. 𝑉𝐴 = 4𝜋𝜀0 𝑙
(1 + √5) 𝑣𝑜𝑙𝑡𝑠
e. None of these
4. Charges +𝑄, −𝑄, +𝑄 and −𝑄 are placed at
corners of square taken in order. At centre of
I. Find radius of the circle
square
a. 3.5 𝑛𝑚
a. 𝐸 = 0, 𝑉 = 0
b. 6 𝑛𝑚
b. 𝐸 = 0, 𝑉 ≠ 0
c. 7.5 𝑛𝑚
c. 𝐸 ≠ 0, 𝑉 = 0
d. 9 𝑛𝑚
d. 𝐸 ≠ 0, 𝑉 ≠ 0
e. None of these II. Find the 𝑥 co-ordinate of centre of the
circle is at
5. The electric potential at a point in free space
a. −2 𝑛𝑚
due to a charge 𝑄 is 𝑄 × 1011 𝑉. The electric
b. −3 𝑛𝑚
field at that point is
c. −4.5 𝑛𝑚
a. 4𝜋𝜀0 𝑄 × 1011 𝑉
d. −7.5 𝑛𝑚
b. 4𝜋𝜀0 𝑄 × 1022 𝑉
c. 2𝜋𝜀0 𝑄 × 1022 𝑉
d. 2𝜋𝜀0 𝑄 × 1011 𝑉
Electrostatics Vardan Patni’s Physics Classes – 9584120300

9. Electric Charges +10 𝜇𝐶, +5 𝜇𝐶, −3 𝜇𝐶 14. Charge of 1 𝜇𝐶 is placed at each of the four
and+8 𝜇𝐶 are placed at the corners of a square corners of side 2√2 𝑚. The potential at the
of side √2 𝑚. The potential at the centre of the point of interaction of the diagonals is
square is a. 18 × 103 𝑉
a. 1.8 𝑉 b. 1800 𝑉
b. 1.8 × 106 𝑉 c. 18√2 × 103 𝑉
c. 1.8 × 105 𝑉 d. None of these
d. 1.8 × 104 𝑉 15. At a certain distance from a point charge the
e. None of these 𝑉
electric field is 500 𝑚
and the potential is
10. Two charges of 4 𝜇𝐶 each are placed at the
3000 𝑉. What is this distance
corners 𝐴 and 𝐵 of an equilateral triangle of side
a. 6 𝑚
length 0.2 𝑚 in air. The electric potential at 𝐶 is
b. 12 𝑚
a. 9 × 104 𝑉 c. 36 𝑚
b. 18 × 104 𝑉 d. 144 𝑚
c. 36 × 104 𝑉 e. None of these
d. 36 × 10−4 𝑉 16. Charges are placed on the vertices of a square as
e. None of these
shown. Let 𝐸⃗⃗ be the electric field and 𝑉 the
11. Two point charges −𝑞 and +𝑞 are located at
potential at the centre. If the charges on 𝐴 and
points (0, 0, −𝑎) and (0, 0, 𝑎), respectively. The
𝐵 are interchanged with those on 𝐷 and 𝐶,
potential at a point (0, 0, 𝑧) where 𝑧 > 𝑎 is
𝑞𝑎 respectively, then
a. 4𝜋𝜀 𝑧2
0
𝑞
b.
4𝜋𝜀0 𝑎
2𝑞𝑎
c.
4𝜋𝜀0 (𝑧2 −𝑎2 )
2𝑞𝑎
d.
4𝜋𝜀0 (𝑧2 +𝑎2 )
e. None of these
12. A charge +𝑞 is fixed at each of the points a. 𝐸⃗⃗ remains unchanged, 𝑉 changes
𝑥 = 𝑥0 , 𝑥 = 3𝑥0 , 𝑥 = 5𝑥0 … … ∞, on the 𝑥-axis b. Both 𝐸⃗⃗ and 𝑉 change
and a charge −𝑞 is fixed at each of the points
c. 𝐸⃗⃗ and 𝑉 remains unchanged
𝑥 = 2𝑥0 , 𝑥 = 4𝑥0 , 𝑥 = 6𝑥0 … … ∞. Here 𝑥0 is a
d. 𝐸⃗⃗ changes, 𝑉 remains unchanged
positive constant. Take the electric potential at a
e. None of these
point due to a charge 𝑄 at a distance 𝑟 from it to
𝑄 17. An electric charge 10−3 𝜇𝐶 is placed at the
be 4𝜋𝜀 𝑟. Then the potential at the origin due to
0 origin (0, 0) of 𝑥-𝑦 co-ordinate system. Two
the above system of charge is points A and B are situated at (√2, √2) and
a. 0 (2, 0) respectively. The potential difference
𝑞
b. 8𝜋𝜀 𝑥 ln 2 between the points 𝐴 and 𝐵 will be
0 0
c. ∞ a. 9 𝑉
d.
𝑞 ln 2 b. 0
4𝜋𝜀0 𝑥0 c. 2 𝑉
e. None of these d. 3.5 𝑉
13. Three charges 2𝑞, −𝑞 and−𝑞 are located at the e. None of these
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
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

Potential due to charged sphere

1. A hollow metal sphere of radius 5 𝑐𝑚 is charged 6. Two spherical conductors 𝐴 and 𝐵 of radii
such that potential on its surface is 10 𝑉. The 1 𝑚𝑚 and 2 𝑚𝑚 are separated by a distance of
potential at centre of sphere will be 5 𝑐𝑚, are uniformly charged. The spheres are
a. 0 connected by a conducting wire. Then in
b. 10 𝑉 equilibrium condition, the ratio of magnitude of
c. Same as a point 5 𝑐𝑚 away from surface electric field at the surfaces 𝐴 and 𝐵 is
d. Same as a point 25 𝑐𝑚 away from a. 1 ∶ 2
surface b. 1 ∶ 3
e. None of these c. 2 ∶ 1
2. A spherical shell of radius 10 𝑐𝑚 is given a d. None of these
charge 𝑞. If the electric potential at distances 7. Three concentric metal shells 𝐴, 𝐵 and 𝐶 of
5 𝑐𝑚, 10 𝑐𝑚 and15 𝑐𝑚 from the centre of the respective radii 𝑎, 𝑏 and 𝑐 (𝑎 < 𝑏 < 𝑐) have
spherical shell is 𝑉1 , 𝑉2 and 𝑉3 respectively then surface charge densities +𝜎, −𝜎 and +𝜎,
a. 𝑉1 < 𝑉2 < 𝑉3 respectively. The potential of shell 𝐵 is
b. 𝑉1 = 𝑉2 < 𝑉3
c. 𝑉1 > 𝑉2 > 𝑉3
d. 𝑉1 = 𝑉2 > 𝑉3
e. None of these
3. The electrostatic potential of a uniformly
charged thin spherical shell of charge 𝑄 and
radius 𝑅 at a distance 𝑟 from the centre is
𝑄
a. for both points outside and inside
4𝜋𝜀0 𝑟
𝜎 𝑏2 −𝑐 2
of shell a. ( + 𝑎)
𝑄 𝑄 𝜀0 𝑏
b. 4𝜋𝜀0 𝑅
for points inside, 4𝜋𝜀0 𝑟
for points 𝜎 2
𝑎 −𝑏 2
b. 𝜀0
( 𝑏 + 𝑐)
outside
𝜎 𝑎 2 −𝑏2
c. Zero for point outside and 4𝜋𝜀
𝑄
for c. ( + 𝑏)
𝜀0 𝑐
0𝑟
𝜎 𝑎 2 −𝑏2
inside points d. 𝜀0
( 𝑎 + 𝑐)
d. Zero for both points inside and outside e. None of these
the shell 8. A charge 𝑄 is distributed over two concentric
e. None of these conducting thin spherical shells of radii 𝑟 and 𝑅
4. A conducting sphere of radius 𝑅 is given a (𝑅 >> 𝑟). If the surface charge densities on the
charge 𝑄. The electric potential and electric field two shells are equal, the electric potential at the
at the centre of the sphere respectively are common centre is
𝑄
a. Zero and 4𝜋𝜀 2 a. 𝑉 =
𝑄
(
𝑅1 +𝑅2
)
0𝑅 2𝜋𝜀0 𝑅1 2 +𝑅2 2
𝑄
b. 4𝜋𝜀0 𝑅
and zero b. 𝑉 =
𝑄 𝑅1 +𝑅2
(𝑅 2 −𝑅 2 )
4𝜋𝜀0 1 2
c. Zero and zero 𝑄 𝑅1 +𝑅2
𝑄 𝑄 c. 𝑉 = 4𝜋𝜀0
(𝑅 2 +𝑅 2 )
d. 4𝜋𝜀0 𝑅
and 4𝜋𝜀 2
1 2
0𝑅 𝑄 𝑅1 −𝑅2
e. None of these d. 𝑉 = 4𝜋𝜀0
(𝑅 2 +𝑅 2 )
1 2
5. A conducting sphere of radius 10 𝑐𝑚 is charged e. None of these
with 10 𝜇𝐶, another uncharged sphere of radius 9. Three concentric conducting spherical shells
20 𝑐𝑚 is allowed to touch it for some time. After carry charges +4𝑄 on inner shell, −2𝑄 on
that spheres are separated, then surface charge middle shell and +6𝑄 on outer shell. The charge
density on spheres will be in the ratio. on the inner surface of outer shell must be
a. 1 ∶ 2 a. +8𝑄
b. 1 ∶ 3 b. +2𝑄
c. 2 ∶ 1 c. +4𝑄
d. None of these d. −2𝑄
Electrostatics Vardan Patni’s Physics Classes – 9584120300

10. A charge 𝑄 is distributed over three concentric 13. A solid conducting sphere, having a charge 𝑄, is
spherical shells of radii 𝑎, 𝑏 and 𝑐 (𝑎 < 𝑏 < 𝑐), surrounded by an uncharged conducting hollow
such that their surface charge densities are spherical shell. Let the potential difference
equal to one another. The total potential at a between the surface of the solid sphere and that
point at distance 𝑟 from their common centre, of the outer surface of the hollow shell be 𝑉. If
where 𝑟 < 𝑎, would be the shell is now given a charge of −4𝑄, the new
𝑄 𝑎+𝑏+𝑐 potential difference between the same two
a. 4𝜋𝜀0
(𝑎2 −𝑏2 +𝑐 2 )
𝑄 𝑎−𝑏+𝑐
surface us
b. 4𝜋𝜀0
(𝑎2 +𝑏2 +𝑐 2 ) a. −2 𝑉
c.
𝑄 𝑎+𝑏−𝑐
(𝑎2 +𝑏2 +𝑐 2 ) b. 2 𝑉
4𝜋𝜀0 c. 4 𝑉
𝑄 𝑎+𝑏+𝑐
d. 4𝜋𝜀0
(𝑎2 +𝑏2 +𝑐 2 ) d. 𝑉
e. None of these e. None of these
11. Charges 𝑄, 2𝑄 and −𝑄 are given to three 14. The electric potential at the centre of two
conducting spherical shells 𝐴, 𝐵 and 𝐶, concentric half rings of radii 𝑅1 and 𝑅2 , having
respectively. The ratio of charge on inner and same linear charge density 𝜆 is
outer surface of shell will be
1
a. − 2
1
b. + 3
3
c. −
2
3
d. +2
e. None of these a.
2𝜆
12. Figure shows three concentric thin spherical 𝜀0
𝜆
shell 𝐴, 𝐵 and 𝐶 of radii 𝑅, 2𝑅 and 3𝑅. The shell b. 2𝜀0
𝐵 is earthed and 𝐴 and 𝐶 are given charge 𝑄 and 𝜆
c.
2𝑄, respectively. Find charges appearing on all 4𝜀0
𝜆
surface of 𝐴, 𝐵 and 𝐶. d. 𝜀0
e. None of these
15. Twenty seven drops of same size are charged at
220 𝑉 each. They combine to form a bigger
drop. Calculate the potential of the bigger drop
a. 1320 𝑉
b. 1520 𝑉
c. 1980 𝑉
d. 660 𝑉
e. None of these
7𝑄 4𝑄 2𝑄
16. Concentric metallic hollow spheres of radii 𝑅
a. ,− , and 4𝑅 hold charges 𝑄1 and 𝑄2 respectively.
3 3 3
7𝑄 4𝑄 2𝑄
b. − 3 , 3 , 3 Given that surface charge densities of the
7𝑄 4𝑄 2𝑄 concentric spheres are equal, the potential
c. − 3 ,− 3 , 3
difference 𝑉𝑅 − 𝑉4𝑅 is
d. None of these 𝑄2
a. 4𝜋𝜀0 𝑅
3𝑄2
b. 4𝜋𝜀0 𝑅
3𝑄1
c.
16𝜋𝜀0 𝑅
3𝑄1
d. 4𝜋𝜀0 𝑅
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

17. 𝑁 identical drops of mercury are charged 21. A hollow conducting spherical shell of radius 𝑅 is
simultaneously to 10 𝑣𝑜𝑙𝑡. When combined to charged with 𝑄 𝐶. The amount of work done for
form one large drop, the potential is found to be moving any charge 𝑞 from the centre to the
40 𝑣𝑜𝑙𝑡, the value of 𝑁 is surface of the shell will be
a. 4 𝑞𝑄
a. 4𝜋𝜀0 𝑅
b. 6
b. 0
c. 8 𝑞𝑄
d. 10 c. 𝜋𝜀0 𝑅
e. None of these 𝑞𝑄
d. 2𝜋𝜀0 𝑅
18. A hollow conducting sphere is placed in an
e. None of these
electric field produced by a point charge placed
22. If a charged spherical conductor of radius 10 𝑐𝑚
at 𝑃 as shown in figure. Let 𝑉𝐴 , 𝑉𝐵 , 𝑉𝐶 be the
has potential 𝑉 at a point distant 5 𝑐𝑚 from its
potentials at points 𝐴, 𝐵 and 𝐶 respectively.
centre, then the potential at a point distant
Then
15 𝑐𝑚 from the centre will be
1
a. 3
𝑉
2
b. 3
𝑉
3
c. 2
𝑉
d. 3 𝑉
e. None of these
a. 𝑉𝐶 > 𝑉𝐵 23. Two spheres of radii 𝑎 and 𝑏 respectively are
b. 𝑉𝐵 > 𝑉𝐶 charged and joined by a wire. The ratio of
c. 𝑉𝐴 > 𝑉𝐵 electric field of the spheres is
d. 𝑉𝐴 = 𝑉𝐶 𝑎
a.
e. None of these 𝑏
𝑏
19. A thin spherical conducting shell of radius 𝑅 has b. 𝑎
charge 𝑞. Another charge 𝑄 is placed at the 𝑎2
c.
𝑏2
centre of the shell. The electrostatic potential at 𝑏2
𝑅
a point 𝑃 a distance from the centre of the d. 𝑎2
2
shell is e. None of these
(𝑞+𝑄) 2 24. Two charged spheres of radii 𝑅1 and 𝑅2 having
a. 4𝜋𝜀0 𝑅 equal surface charge density. The ratio of their
2𝑄
b. potential is
4𝜋𝜀0 𝑅 𝑅1
2𝑄 2𝑞 a.
c. 4𝜋𝜀0 𝑅
− 4𝜋𝜀 𝑅 𝑅2
0 𝑅2
d.
2𝑄 𝑞
+ 4𝜋𝜀 𝑅 b.
𝑅1
4𝜋𝜀0 𝑅 0
𝑅 2
e. None of these c. ( 1 )
𝑅2
20. Two spherical conductors 𝐴 and 𝐵 or radii 1 𝑚𝑚 2
𝑅
and 2 𝑚𝑚 are separated by a distance of 5 𝑐𝑚 d. ( 2 )
𝑅1
and are uniformly charged. If the spheres are e. None of these
connected by a conducting wire, then in 3𝑅
25. The electric field at a distance 2
from the
equilibrium condition, the ratio of the
magnitude of the electric fields at the surfaces centre of a charged conducting spherical shell of
𝑅
of spheres 𝐴 and 𝐵 is radius 𝑅 is 𝐸. The electric field at a distance 2
a. 1 ∶ 2 from the centre of the sphere is
b. 2 ∶ 1 a. 0
c. 1 ∶ 4 b. 𝐸
d. 4 ∶ 1 𝐸
c. 2
e. None of these 𝐸
d.
3
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

26. Three concentric spherical shells have radii 𝑎, 𝑏

and 𝑐 (𝑎 < 𝑏 < 𝑐) and have surface charge
densities 𝜎, −𝜎 and 𝜎 respectively. If 𝑉𝐴 , 𝑉𝐵 and
𝑉𝐶 denote the potentials of the three shells,
then, for 𝑐 = 𝑎 + 𝑏, we have
a. 𝑉𝐶 = 𝑉𝐴 ≠ 𝑉𝐵
b. 𝑉𝐶 = 𝑉𝐵 ≠ 𝑉𝐴
c. 𝑉𝐶 ≠ 𝑉𝐴 ≠ 𝑉𝐵
d. 𝑉𝐶 = 𝑉𝐴 = 𝑉𝐵
e. None of these
27. Two metallic spheres of radii 1 𝑐𝑚 and 3 𝑐𝑚 are
given charges of −1 × 10−2 𝐶 and 5 × 10−2 𝐶,
respectively. If these are connected by a
conducting wire, the final charge on the bigger
sphere is
a. 2 × 10−2 𝐶
b. 3 × 10−2 𝐶
c. 4 × 10−2 𝐶
d. 1 × 10−2 𝐶
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

Potential difference in electric field

5. Figure shows three points 𝐴, 𝐵 and 𝐶 in a region
𝑁
1. An electric field of 20 𝐶
exists along 𝑥 direction of uniform electric field 𝐸⃗⃗ . the line 𝐴𝐵 is
in space. Calculate 𝑉𝐵 − 𝑉𝐴 where points 𝐴 and perpendicular and 𝐵𝐶 is parallel to the field
𝐵 are given by lines. Then which of the following holds good.
I. 𝐴 (0,0) and 𝐵 (4 𝑚, 2 𝑚) Where 𝑉𝐴 , 𝑉𝐵 and 𝑉𝐶 represent the electric
II. 𝐴 (4 𝑚, 2 𝑚) and 𝐵 (6 𝑚, 5 𝑚) potential at points 𝐴, 𝐵 and 𝐶 respectively
𝑉
2. A uniform electric field of 400 𝑚
is directed at
45° to 𝑥-axis as shown in figure. Find 𝑉𝐴 − 𝑉𝐵 .
The co-ordinate of point 𝐴 and 𝐵 are (0, 2 𝑚)
and (3 𝑚, 0).

a. 𝑉𝐴 = 𝑉𝐵 = 𝑉𝐶
b. 𝑉𝐴 = 𝑉𝐵 > 𝑉𝐶
c. 𝑉𝐴 = 𝑉𝐵 < 𝑉𝐶
d. 𝑉𝐴 > 𝑉𝐵 = 𝑉𝐶
e. None of these
6. The points resembling equal potentials are
a. 100√2 𝑉
b. 200√2 𝑉
c. 300√2 𝑉
d. 400√2 𝑉
e. None of these
a. 𝑃 and 𝑄
3. Some equipotential surfaces are shown in the
b. 𝑆 and 𝑄
figure. What can you say about magnitude and
c. 𝑆 and 𝑅
direction of electric field?
d. 𝑃 and 𝑅
e. None of these
7. Positive and negative point charges of equal
𝑎 −𝑎
magnitude are kept at (0,0, 2 ) and (0,0, 2
),
respectively. The work done by the electric field
when another positive point charge is moved
𝑉
a. 400 𝑚 from (−𝑎, 0,0) to (0, 𝑎, 0) is
𝑉 a. Positive
b. 300 𝑚
𝑉 b. Negative
c. 200
𝑚 c. Zero
𝑉
d. 100 d. Depends on the path connecting the
𝑚
e. None of these initial and final positions
4. On rotating a point charge having a charge e. None of these
𝑞 around a charge 𝑄 in a circle of radius 𝑟. The 8. A particle 𝐴 has charge +𝑞 and a particle 𝐵 has
work done will be charge +4𝑞 with each of them having the same
a. 𝑞 × 2𝜋𝑟 mass 𝑚. When allowed to fall from rest through
2𝜋𝑄 the same electric potential difference, the ratio
b. 𝑞 × 𝑟 𝑣
c. 0 of their speed 𝐴 will become
𝑣𝐵
𝑄 a. 2∶1
d. 2𝜀0 𝑟
b. 1∶2
e. None of these
c. 1∶4
d. 4∶1
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

9. The diagrams below show regions of 12. Four points 𝑎, 𝑏, 𝑐 and 𝑑 are set at equal
equipotential. A positive charge is moved from A distance from the centre of a dipole as shown in
to B in each diagram figure. The electrostatic potential 𝑉𝑎 , 𝑉𝑏 , 𝑉𝑐 and
𝑉𝑑 would satisfy the following relation

1 2 3 4

a. Maximum work is required to move 𝑞 in

figure 3. a. 𝑉𝑎 > 𝑉𝑏 > 𝑉𝑐 > 𝑉𝑑
b. In all the four cases the work done is the b. 𝑉𝑎 > 𝑉𝑏 = 𝑉𝑑 > 𝑉𝑐
same c. 𝑉𝑎 > 𝑉𝑐 = 𝑉𝑏 = 𝑉𝑑
c. Minimum work is required to move 𝑞 in d. 𝑉𝑏 = 𝑉𝑑 > 𝑉𝑎 > 𝑉𝑐
figure 1. 13. In moving from 𝐴 to 𝐵 along an electric field
d. Maximum work is required to move 𝑞 in line, the electric field does 6.4 × 10−19 𝐽 of work
figure 2. on an electron. If 𝜑1 and 𝜑2 are equipotential
10. A point charge is surrounded symmetrically by surfaces, then the potential difference (𝑉𝐶 − 𝑉𝐴 )
six identical charges at distance 𝑟 as shown in is
the figure. How much work is done by the forces
of electrostatic repulsion when the point charge
𝑞 at the centre is removed at infinity

a. −4 𝑉
b. 4𝑉
c. 0
d. 64 𝑉
e. None of these
a. 0
6𝑞2
b. 4𝜋𝜀0 𝑟
𝑞2
c.
4𝜋𝜀0 𝑟
12𝑞2
d. 4𝜋𝜀0 𝑟
e. None of these
11. A ball of mass 1 𝑔 and charge 10−8 𝐶 moves
from a point 𝐴 where potential is 600 𝑉 to the
point 𝐵 where potential is zero. Velocity of the
𝑐𝑚
ball at the point 𝐵 is 20 𝑠 . The velocity of the
ball at the point 𝐴 will be
𝑐𝑚
a. 22.8 𝑠
𝑐𝑚
b. 228 𝑠
𝑐𝑚
c. 16.8 𝑠
𝑐𝑚
d. 168
𝑠
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

Relation between electric field and

potential
6. The potential at a point 𝑥 (measured in 𝜇𝑚) due
1. The electric potential at a point (𝑥, 𝑦, 𝑧) is given
to some charges situated on the 𝑥-axis is given
by 𝑉 = −𝑥 2 𝑦 − 𝑥𝑧 3 + 4. The electric field at 20
that point is by 𝑉(𝑥) = (𝑥 2 −4) 𝑣𝑜𝑙𝑡𝑠. The electric field 𝐸 at
a. (𝑥𝑦 + 𝑧 3 )𝑖̂ + 𝑥 2 𝑗̂ + 3𝑥𝑧 2 𝑘̂ 𝑥 = 4 𝜇𝑚 is given by
b. (2𝑥𝑦 + 𝑧 3 )𝑖̂ + 𝑥 2 𝑗̂ + 4𝑥𝑧 2 𝑘̂ a.
5 𝑉
and in the −𝑣𝑒 𝑥 direction
3 𝜇𝑚
c. (2𝑥𝑦 + 𝑧 3 )𝑖̂ + 𝑥 2 𝑗̂ + 𝑥𝑧 2 𝑘̂ 5 𝑉
b. and in the +𝑣𝑒 𝑥 direction
d. (2𝑥𝑦 + 𝑧 3 )𝑖̂ + 𝑥 2 𝑗̂ + 3𝑥𝑧 2 𝑘̂ 3 𝜇𝑚
10 𝑉
e. None of these. c. and in the −𝑣𝑒 𝑥 direction
9 𝜇𝑚
2. Electric potential in a region is given by 10 𝑉
d. and in the +𝑣𝑒 𝑥 direction
−𝑥 3 𝑧 2 − 𝑥𝑦 3 + 8. Find 9 𝜇𝑚
a. Electric field at (1, 1,0) e. None of these
b. Electric force experienced by a 2 𝐶 7. The electric potential 𝑉 is given as a function of
charge placed at that point distance 𝑥 by 𝑉 = (5𝑥 2 + 10𝑥 − 9) 𝑣𝑜𝑙𝑡𝑠. Value
3. The variation of potential with distance 𝑅 from of electric field at 𝑥 = 1 is
𝑉
fixed point is shown in figure. The electric field a. −20
𝑚
at 𝑅 = 5 𝑐𝑚 is b. 6 𝑚
𝑉

𝑉
c. 11
𝑚
𝑉
d. −23
𝑚
e. None of these
8. The electric potential 𝑉 at any point 𝑂(𝑥, 𝑦, 𝑧) in
space is given by 𝑉 = 4𝑥 2 𝑣𝑜𝑙𝑡. The electric
𝑉
𝑉
field at the point (1𝑚, 0, 2𝑚) in is
𝑚
a. 3.5 𝑐𝑚 a. 8 along negative 𝑥-axis
𝑉
b. −4.5 𝑐𝑚 b. 8 along positive 𝑥-axis
c.
𝑉
2.5 𝑐𝑚 c. 16 along negative 𝑥-axis
𝑉
d. 16 along negative 𝑧-axis
d. −2.5 𝑐𝑚 e. None of these
e. None of these 9. The electric potential at a point (𝑥, 𝑦) in the 𝑥-𝑦
4. Electric potential is given by plane is given by 𝑉 = −𝑘𝑥𝑦. The field intensity
𝑉 = 6𝑥 − 8𝑥𝑦 2 − 8𝑦 + 6𝑦𝑧 − 4𝑧 2 then electric at a distance 𝑟 from the origin varies as
force acting on 2 𝐶 point charge placed on origin a. 𝑟 2
will be b. 𝑟
a. 2 𝑁 1
c.
𝑟
b. 6 𝑁 1
c. 8 𝑁 d. 𝑟2
d. 20 𝑁 e. None of these
e. None of these 10. The electric field in a certain region is given by
𝑘𝑉
5. Electric potential at any point is 𝐸⃗⃗ = (5𝑖̂ − 3𝑗̂) . The potential difference
𝑚
𝑉 = −5𝑥 + 3𝑦 + √15𝑧, then the magnitude of 𝑉𝐴 − 𝑉𝐵 between points 𝐴 and 𝐵, having
the electric field is coordinates (4, 0, 3) 𝑚 and (10, 3, 0) 𝑚
a. 3√2 respectively, is equal to
b. 4√2 a. 21 𝑘𝑉
c. 5√2 b. −21 𝑘𝑉
d. 7 c. 39 𝑘𝑉
e. None of these d. −39 𝑘𝑉
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

11. The figure gives the electric potential 𝑉 as a

function of distance through five regions on 𝑥-
axis. Which of the following is true for the
electric field 𝐸 in these region

a. 𝐸1 > 𝐸2 > 𝐸3 > 𝐸4 > 𝐸5

b. 𝐸1 = 𝐸3 = 𝐸5 and 𝐸2 < 𝐸4
c. 𝐸2 = 𝐸4 = 𝐸5 and 𝐸1 < 𝐸3
d. 𝐸1 < 𝐸2 < 𝐸3 < 𝐸4 < 𝐸5
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

Potential energy of system of charges

1. Three identical charges are placed at corners of 4. As per diagram, a point charge +𝑞 is placed at
an equilateral triangle of side 𝑙. If force between origin 𝑂. The work done in taking a point charge
any two charges is 𝐹. The work required to half 𝑄 from point 𝐴(𝑎, 0) to a point 𝐵(0, 𝑏) along
the dimension of triangle will be the straight line path 𝐴𝐵 is
a. 0.5 𝐹𝐿
b. 2 𝐹𝐿
c. 3 𝐹𝐿
d. 𝐹𝐿
e. None of these
2. A charge +𝑞 and −𝑞 are placed at points 𝐴 and 𝑞𝑄 𝑎−𝑏
a. ( )
𝐵 respectively which are at a distance 2𝐿 apart. 4𝜋𝜀0 𝑎𝑏
𝑞𝑄 𝑏−𝑎
𝐶 is the mid point between 𝐴 and 𝐵. The work b. ( )
4𝜋𝜀0 𝑎𝑏
done in moving charge +𝑄 along the semicircle 𝑞𝑄 𝑏 1
c. ( − 𝑏)
𝐶𝑅𝐷 is 4𝜋𝜀0 𝑎 2
𝑞𝑄 𝑎 1
d. ( − 𝑏)
4𝜋𝜀0 𝑏2
e. None of these
5. Two charges 𝑞1 and 𝑞2 are placed 30 𝑐𝑚 apart
as shown in figure. A third charge 𝑞3 is moved
along arc of radius 40 𝑐𝑚 from 𝐶 to 𝐷. The
𝑄𝑞 𝑞
a. change in potential energy of system is 3 𝑘,
2𝜋𝜀0 𝐿 4𝜋𝜀0
𝑄𝑞
b. 4𝜋𝜀0 𝐿
where 𝑘 is
𝑄𝑞
c. 6𝜋𝜀0 𝐿
𝑄𝑞
d. 8𝜋𝜀0 𝐿
e. None of these
3. As per diagram, a point charge 𝑞 is placed at
origin 𝑂. Work done in taking a point charge −𝑄
from point 𝐴(0, 𝑎) to a point 𝐵(𝑎, 0) along the a. 6𝑞2
straight line path 𝐴𝐵 is b. 6𝑞3
c. 8𝑞2
d. 8𝑞3
e. None of these
6. In the rectangle shown in figure, the two corners
have charge 𝑞1 = −5 𝜇𝐶 and 𝑞2 = +2 𝜇𝐶. The
work done in moving a charge of +3 𝜇𝐶 from 𝐵
1
−𝑄𝑞 𝑎 to 𝐴 is (4𝜋𝜀 = 1010 )
a. 4𝜋𝜀0 √2
0

𝑄𝑞 𝑎
b. 4𝜋𝜀0 √2
−𝑄𝑞 𝑎
c. 4𝜋𝜀0 2√2
d. 0
e. None of these
a. 3.5 𝐽
b. 4.5 𝐽
c. 2.8 𝐽
d. 0
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

7. Four equal charges (+𝑄) are placed at four 11. Two point charges 4𝑞 and −𝑞 are fixed on the 𝑥-
corners of a square side ‘𝑎’. Work done in 𝑑 𝑑
axis at 𝑥 = − 2 and 𝑥 = 2 , respectively. If a third
removing a charge −𝑄 from centre to ∞ is point charge ‘𝑞’ is taken from the origin to 𝑥 = 𝑑
𝑄2
a. along the semicircle as shown in the figure, the
𝜋𝜀0 𝐿
2√2𝑄2 energy of the charge will
b. 𝜋𝜀0 𝐿
2𝑄 2
c. 𝜋𝜀0 𝐿
√2𝑄 2
d. 𝜋𝜀0 𝐿
e. None of these 2𝑞2
8. Two point charges 𝑞1 = 𝑞2 = 2 𝜇𝐶 are held a. Increase by 3𝜋𝜀
0𝑑
fixed at 𝑥 = ±3 𝑚 on 𝑥-axis. Third particle of 3𝑞2
b. Increase by 4𝜋𝜀 𝑑
mass 1 𝑔𝑚 and charge −4 𝜇𝐶 is released from 0
4𝑞2
rest at 𝑦 = 4 𝑚. Find speed of charged particle c. Decrease by 3𝜋𝜀 𝑑
0
as it reaches origin. (Neglect gravity) 𝑞2
d. Decrease by
4𝜋𝜀0 𝑑
e. None of these
12. Three charges 𝑄, +𝑞 and +𝑞 are placed at the
vertices of a right-angled isosceles triangle as
shown below. The net electrostatic energy of
the configuration is zero if 𝑄 is equal to

𝑚
a. 2.5 𝑠
𝑚
b. 4.6
𝑠
𝑚
c. 6.3 𝑠
𝑚
d. 8.3 𝑠
√2𝑞
e. None of these a. −
√2+1
9. An alpha particle of kinetic energy 10 𝑀𝑒𝑉 is b. −2𝑞
heading towards a tin nucleus with atomic 𝑞
c. − 2+1
√
number 50. Calculate the distance of closest
d. +𝑞
approach if they were initially far apart.
e. None of these
a. 1.7 × 10−7 𝑚
13. Four equal point charges ′𝑄′ are placed in the
b. 1.5 × 10−12 𝑚
𝑥 − 𝑦 plane at (0, 2), (4, 2), (4, −2) and (0, −2).
c. 14.4 × 10−15 𝑚
The work required to put a fifth charge 𝑄 at the
d. 14.4 × 10−16 𝑚
origin of the coordinate system will be
e. None of these
𝑄2
10. An alpha particle and a proton are accelerated a. 2√2𝜋𝜀0
from rest through the same potential difference. 𝑄2 1
b. 4𝜋𝜀0
(1 + )
The ratio of linear momenta acquired by above √5
𝑄 2 1
two particles will be c. (1 + )
4𝜋𝜀0 √3
a. 2 ∶ 1 𝑄 2

b. 1 ∶ 2 d. 4𝜋𝜀0
c. 2√2 ∶ 1 e. None of these
d. 2 ∶ 3
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

14. As shown in the figure below, a charge +2 𝐶 is 𝑞 𝑞 2𝑞

17. Consider a system of three charges 3 , 3 and − 3
situated at the origin 𝑂 and another charge placed at points 𝐴, 𝐵 and 𝐶, respectively, as
+5 𝐶 is on the 𝑥-axis at the point 𝐴. The large shown in the figure. Take 𝑂 to be the centre of
charge from the point 𝐴 is then brought to a the circle of radius 𝑅 and angle 𝐶𝐴𝐵 = 60°
point 𝐵 on the 𝑦-axis. The work done is

𝑞
a. 45 × 109 𝐽 a. The electric field at point 𝑂 is 8𝜋𝜀 2
0𝑅
b. 90 × 109 𝐽
directed along the negative 𝑥-axis
c. 0
b. The potential energy of the system is
d. −45 × 109 𝐽
zero
e. None of these
c. The magnitude of the force between the
15. Three charges, each +𝑞, are placed at the 𝑞2
corners of an isosceles triangle 𝐴𝐵𝐶 of sides 𝐵𝐶 charges at 𝐶 and 𝐵 is 54𝜋𝜀 2
0𝑅
and 𝐶𝐴. The work done in taking a charge 𝑄 𝑞
d. The potential at point 𝑂 is 12𝜋𝜀
0𝑅
from 𝐷 to 𝐸 is
18. A square of side ‘𝑎’ has charge 𝑄 at its centre
and charge ‘𝑞’ at one of the corners. The work
required in moving the charge ‘𝑞’ from one
corner to the diagonally opposite corner is
a. 0
𝑄𝑞
b. 4𝜋𝜀0 𝑎
𝑄𝑞√2
a. 0 c. 4𝜋𝜀0 𝑎
3𝑞𝑄
b. d.
𝑄𝑞
4𝜋𝜀0 𝑎
2𝜋𝜀0 𝑎
3𝑞𝑄
c. 8𝜋𝜀0 𝑎 e. None of these
d.
𝑞𝑄 19. A charged particle 𝑞 is shot towards another
4𝜋𝜀0 𝑎
charged particle 𝑄 which is fixed, with a speed
e. None of these
𝑣. it approaches 𝑄 up to a closest distance 𝑟 and
16. If identical charges (−𝑞) are placed at each
then returns. If 𝑞 were given a speed 2𝑣, the
corner of a cube of side 𝑏, then potential energy
closest distances of approach would be
of charge (+𝑞) which is placed at centre of the
cube will be
8√2𝑞2
a. 4𝜋𝜀0 𝑏 a. 𝑟
8√2𝑞2 b. 2𝑟
b. − 𝜋𝜀 𝑏 𝑟
0 c.
4√2𝑞2 2
c. − 𝑟
𝜋𝜀0 𝑏 d. 4
4𝑞2 e. None of these
d. − 3𝜋𝜀 𝑏
√ 0
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

Capacitors
1. Capacitors are used in electrical circuits where 7. A capacitor is charged by a battery. The battery
appliances need more is removed and another identical uncharged
a. Current capacitor is connected in parallel. The total
b. Voltage electrostatic energy of resulting system
c. Watt a. Increases by a factor of 4
d. Resistance b. Decreases by a factor of 2
2. The net charge on capacitor is c. Remains the same
a. 2𝑞 d. Increases by a factor of 2
b. 𝑞/2 8. A capacitor is charged by using a battery which
c. 0 is then disconnected. A dielectric slab is then
d. ∞ slipped between the plates, which results in
3. If the charge on a capacitor is doubled, the value a. Reduction of charge on the plates and
of its capacitance 𝐶 will be increase of potential difference across
a. Doubled the plates
b. Halved b. Increase in the potential difference
c. Remains the same across the plate, reduction in stored
d. None of these energy, but no change in the charge on
4. The capaciatnce 𝐶 of a capacitor is the plates
a. Independent of the charge and potential c. Decrease in the potential difference
of the capacitor across the plates, reduction in the
b. Dependent on the charge and stored energy, but no change in the
Independent of potential charge on the plates
c. Independent of the geometrical d. None of the above
configuration of the capacitor 9. 𝐶, 𝑉, 𝑈 and 𝑄 are capacitance, potential
d. Independent of the dielectric medium diffrence, energy stored and charge of parallel
between the two conducting surfaces of plate capacitor respectively. The quantities that
the capacitor increases when a dielectric slab is introduced
5. Eight drops of mercury of equal radii possessing between the plates without disconnecting the
equal charges combine to form a big drop. Then battery are
the capacitance of bigger drop compared to a. 𝑉 and 𝐶
each individual small drop is b. 𝑉 and 𝑈
a. 8 times c. 𝑈 and 𝑄
b. 4 times d. 𝑉 and 𝑄
c. 2 times e. 𝑈 but not 𝑄
d. 32 times 10. A parallel plate capacitor has a uniform electric
6. If the charge on a capacitor is increased by 2 field 𝐸 in the space between the plates. If the
Coulombs, the energy stored in it increase by distance between the plates is 𝑑 and area of
21%. The original charge on the capacitor is each plate is 𝐴, the energy stored in the
a. 10 𝐶 capacitor is
1
b. 20 𝐶 a. 𝜀 𝐸2
2 0
c. 30 𝐶 𝐸 2 𝐴𝑑
d. 40 𝐶 b. 𝜀0
1
c. 𝜀 𝐸 2 𝐴𝑑
2 0
d. 𝜀0 𝐸𝐴𝑑
Electrostatics Vardan Patni’s Physics Classes – 9584120300

11. The energy required to charge a parallel plate 16. 𝑁 identical spherical drops charged to the same
condenser of plate separation 𝑑 and plate area potential 𝑉 are combined to form a big drop.
of cross-section 𝐴 such that the uniform electric The potential of the new drop will be
field between the plate is 𝐸, is a. 𝑉
𝑉
a. 𝜀0 𝐸 2 𝐴𝑑 b.
1 𝑁
b. 2 𝜀0 𝐸 2 𝐴𝑑 c. 𝑉 × 𝑁
2
𝜀0 𝐸 2
c. d. 𝑉 × 𝑁 3
2𝐴𝑑
𝜀0 𝐸 2 17. A parallel plate air capacitor of capacitance 𝐶 is
d. 𝐴𝑑 connected to a cell of emf 𝑉 and then
12. A spherical drop of capacitance 1 𝜇𝐹 is broken disconnected from it. A dielectric slab of
into eight drops of equal radius. Then the dielectric constant 𝐾, which can just fill the air
capacitance of each small drop is gap of the capacitor, is now inserted in it. Which
1
a. 8
𝜇𝐹 of the following is incorrect
b. 8 𝜇𝐹 a. The energy stored in capacitor
1 decreases K times
c. 𝜇𝐹
2
1 b. The change in energy stored is
d. 4
𝜇𝐹 1 1
𝐶𝑉 2 (𝐾 − 1)
13. A parallel plate air capacitor has capacity ‘𝐶’ 2

distance of separation between plates is ‘𝑑’ and c. The charge on the capacitor is not
potential difference ‘𝑉’ is applied between the conserved
plates. Force of attraction between the plates of d. The potential difference between the
the parallel plate air capacitor is plates decreases 𝐾 times
𝐶𝑉 2 18. 64 drops each having the capacity 𝐶 and
a.
2𝑑 potential 𝑉 are combined to form a big drop. If
𝐶𝑉 2
b. the charge on the small drop is 𝑞, then the
𝑑
𝐶 2𝑉 2 charge on the big drop will be
c.
𝑑2 a. 2𝑞
𝐶 2𝑉 2
d. b. 4𝑞
2𝑑 2
14. 1000 small water drops each of radius 𝑟 and c. 16𝑞
charge 𝑞 coalesce together to form one d. 64𝑞
19. 64 small drops of mercury, each of radius 𝑟 and
spherical drop. The potential of the big drop is
charge 𝑞 coalesce to form a big drop. The ratio
larger than that of the smaller drop by a factor
of the surface density of charge of each small
of
drop with that of the big drop is
a. 1000
b. 100 a. 1 ∶ 64
c. 10 b. 64 ∶ 1
d. 1 c. 4 ∶ 1
15. The Earth has volume ‘𝑉’ and surface area ‘𝐴’ d. 1 ∶ 4
20. 𝑛 identical droplets are charged to 𝑉 volt each.
then capacitance would be
𝐴 If they coalesce to form a single drop, then its
a. 4𝜋𝜀0 𝑉
potential will be
𝑉 2
b. 4𝜋𝜀0 𝐴
a. 𝑛3 𝑉
𝑉 1
c. 12𝜋𝜀0 b. 𝑛3 𝑉
𝐴
𝐴
d. 12𝜋𝜀0 𝑉 c. 𝑛𝑉
𝑉
d.
𝑛
Electrostatics Vardan Patni’s Physics Classes – 9584120300

21. A capacitor of capacitance 𝐶 is charged to a 26. A series combination of 𝑛1 capacitors each of

potential 𝑉. The flux of the electric field through value 𝐶1 , is charged by a source of potential
a closed surface enclosing the capacitor is difference 4 𝑉. When another parallel
𝐶𝑉 combination of 𝑛2 capacitors, each of value 𝐶2 ,
a. 𝜀0
2𝐶𝑉 is charged by a source of potential difference 𝑉,
b. it has the same total energy stored in it, as the
𝜀0
𝐶𝑉
c. first combination has. The value of 𝐶2 , in terms
2𝜀0
of 𝐶1 , is
d. 0 16𝐶1
22. If 𝑛 drops, each of capacitance 𝐶, coalesce to a.
𝑛1 𝑛2
form a single big drop, then the ratio of the 2𝐶1
b. 𝑛1 𝑛2
energy stored in the big drop to that in each 16𝑛2
small drop will be c. 𝐶1
𝑛1
a. 𝑛 ∶ 1 2𝑛2
d. 𝑛1 1
𝐶
1
b. 𝑛 ∶ 1
3
e. None of these
5
c. 𝑛 ∶ 1
3 27. The capacity of a parallel plate condenser is
d. 𝑛2 : 1 15 𝜇𝐹, when the distance between its plates is
23. Two metallic spheres of radii 1 𝑐𝑚 and 2 𝑐𝑚 are 6 𝑐𝑚. If the distance between the plates is
given charges 10−2 𝐶 and 5 × 10−2 𝑐𝑚 reduced to 2 𝑐𝑚, then the capacity of this
respectively. If they are connected by a parallel plate condenser will be
conducting wire, the final charge on the smaller a. 15 𝜇𝐹
sphere is b. 30 𝜇𝐹
a. 3 × 10−2 𝐶 c. 45 𝜇𝐹
b. 1 × 10−2 𝐶 d. 60 𝜇𝐹
c. 4 × 10−2 𝐶 28. A parallel plate capacitor with plates of area
d. 2 × 10−2 𝐶 1 𝑚2 each, area separation of 0.1 𝑚. If the
𝑁
24. A parallel plate capacitor is formed by two electric field between the plates is 100 𝐶 , the
plates each of area 30𝜋 𝑐𝑚2 separated by magnitude of charge on each plate is
1 𝑚𝑚. A material of dielectric strength a. 7.85 × 10−10 𝐶
𝑉
3.6 × 107 𝑚 is filled between the plates. If the b. 6.85 × 10−10 𝐶
maximum charge that can be stored on the c. 9.85 × 10−10 𝐶
plates. If the maximum charge that can be d. 8.85 × 10−10 𝐶
stored on the capacitor without causing any 29. Figure shows charge (𝑞) versus voltage (𝑉)
dielectric breakdown is 7 × 10−6 𝐶, the value of graph for series and parallel combination of two
dielectric constant of the material is given capacitors. The capacitances are
a. 1.66
b. 1.75
c. 2.25
d. 2.33
25. A parallel plate capacitor of capacitance 90 𝑝𝐹 is
connected to a battery of emf 20 𝑉. If a
5
dielectric material of dielectric constant 𝐾 = 3 is
inserted between the plates, the magnitude of
the induced charge will be a. 50 𝜇𝐶 and 30 𝜇𝐶
a. 0.3 𝑛𝐶 b. 20 𝜇𝐶 and 30 𝜇𝐶
b. 2.4 𝑛𝐶 c. 60 𝜇𝐶 and 40 𝜇𝐶
c. 0.9 𝑛𝐶 d. 40 𝜇𝐶 and 10 𝜇𝐶
d. 1.2 𝑛𝐶
Electrostatics Vardan Patni’s Physics Classes – 9584120300

Combination of Capacitors
1. A combination of capacitors is set up as shown 4. Plates of area 𝐴 are arranged as shown. The
in the figure. The magnitude of the electric field, distance between each plate is 𝑑, the net
due to a point charge 𝑄 (having a charge equal capacitance is
𝜀0 𝐴
to the sum of the charges on the 4 𝜇𝐹 and 9 𝜇𝐹 a. 𝑑
capacitors), at a point distance 30 𝑚 from it, b.
7𝜀0 𝐴
𝑑
would equal 6𝜀0 𝐴
c. 𝑑
5𝜀0 𝐴
d. 𝑑
5. The equivalent capacitance between 𝐴 and 𝐵 is
(in 𝜇𝐹)

𝑁
a. 360 𝐶
𝑁
b. 420 𝐶
𝑁
c. 480
𝐶
𝑁
d. 240
𝐶
2. In the adjoining figure the potential difference a. 25
between 𝑋 and 𝑌 is 60 𝑉. The potential b. 84/25
difference between the points 𝑀 and 𝑁 will be c. 9
d. 25/84
e. 1
6. Three equal capacitors, each with capacitance C
are connected as shown in figure. Then the
equivalent capacitance between A and B is
a. 𝐶
b. 3𝐶
a. 10 𝑉 𝐶
c.
b. 15 𝑉 3
3𝐶
c. 20 𝑉 d. 2
d. 30 𝑉 7. Four plates of the same area of cross-section are
3. The charge deposited on 4 𝜇𝐹 capacitor in the joined as shown in figure. The distance between
circuit is each plate is 𝑑. The equivalent capacity across A
and B will be
2𝜀0 𝐴
a. 𝑑
3𝜀0 𝐴
b. 𝑑
3𝜀0 𝐴
c.
2𝑑
𝜀0 𝐴
d. 𝑑

a. 6 × 10−6 𝐶
b. 12 × 10−6 𝐶
c. 24 × 10−6 𝐶
d. 36 × 10−6 𝐶
Electrostatics Vardan Patni’s Physics Classes – 9584120300

8. In the adjoining figure, four capacitors are 12. Four capacitors are connected in a circuit as
shown with their respective capacities and the shown in the figure. The effective capacitance in
P.D. applied. The charge across the 4 𝜇𝐹 𝜇𝐹 between points 𝐴 and 𝐵 will be
capacitor will be

28
a. 9
a. 600 𝜇𝐶; 150 𝑉 b. 4
b. 300 𝜇𝐶; 75 𝑉 c. 5
c. 800 𝜇𝐶; 200 𝑉 d. 18
d. 580 𝜇𝐶; 145 𝑉 13. The equivalent capacitance between A and B is
𝐶
9. All capacitors used in the diagram are identical a. 4
and each is of capacitance 𝐶. Then the effective 3𝐶
b. 4
capacitance between the point 𝐴 and 𝐵 is 𝐶
c. 3
4𝐶
d.
3
14. What is the effective capacitance between point
𝑋 and 𝑌
a. 1.5 𝐶
b. 6 𝐶
c. 𝐶
d. 3𝐶
10. Three plates of common surface area A are
connected as shown. The effective capacitance
will be
𝜀0 𝐴
a. 𝑑
3𝜀0 𝐴
b. 𝑑 A a. 24 𝜇𝐹
c.
3𝜀0 𝐴 b. 18 𝜇𝐹
2𝑑 c. 12 𝜇𝐹
2𝜀0 𝐴
d. d. 6 𝜇𝐹
𝑑
11. The charge on 4 𝜇𝐹 capacitor in the given circuit 15. In the figure shown below, the charge on the left
is plate of the 10 𝜇𝐹 capacitor is −30 𝜇𝐶. The
charge on the right plate of the 6 𝜇𝐹 capacitor is

a. −18 𝜇𝐶
b. −12 𝜇𝐶
a. 12 𝜇𝐶
c. +12 𝜇𝐶
b. 24 𝜇𝐶
d. +18 𝜇𝐶
c. 36 𝜇𝐶
d. 32 𝜇𝐶
Electrostatics Vardan Patni’s Physics Classes – 9584120300

16. In the figure shown, after the switch ‘𝑆’ is turned 20. In the circuit shown, charge on the 5 𝜇𝐹
from position ‘𝐴’ to Position ‘𝐵’, the energy capacitor is
dissipated in the circuit in terms of capacitance 120
a. 𝜇𝐶
11
‘𝐶’ and total 150
a. 𝜇𝐶
charge ‘𝑄’ is 11
90
3 𝑄2 b. 𝜇𝐶
a. 8 𝐶
11
180
3 𝑄2 c. 11
𝜇𝐶
b. 4 𝐶 21. The equivalent capacitance of the combination
1 𝑄2
c. 8 𝐶 shown in the figure is
5 𝑄2
d. 8 𝐶 a. 2 𝐶
17. In the circuit shown, find 𝐶 if the effective 𝐶
b.
capacitance of the whole circuit is to be 0.5 𝜇𝐹. 2
3𝐶
All values in the c.
2
circuit are in 𝜇𝐹 d. 3𝐶
7
a. 𝜇𝐹 22. The charge on capacitor of capacitance 15 𝜇𝐹 in
10
7 the figure given below is
b. 11
𝜇𝐹
6
c. 5
𝜇𝐹
d. 4 𝜇𝐹
18. The charge on 4 𝜇𝐹 capacitor in the given circuit
is

a. 60 𝜇𝐶
b. 130 𝜇𝐶
c. 260 𝜇𝐶
d. 585 𝜇𝐶
23. An infinite number of identical capacitors each
of capacitance 1 𝜇𝐹 are connected as shown in
a. 5.4 𝜇𝐶 the figure. Then, the equivalent capacitance
b. 24 𝜇𝐶 between 𝐴 and 𝐵 is
c. 13.4 𝜇𝐶
d. 9.6 𝜇𝐶
19. In the circuit shown in the figure, the total
charge in 750 𝜇𝐶 and the voltage across
capacitor 𝐶2 is 20 𝑉. Then the charge on
capacitor 𝐶2 is

a. 1 𝜇𝐹
b. 2 𝜇𝐹
1
c. 2
𝜇𝐹
d. ∞

a. 590 𝜇𝐶
b. 450 𝜇𝐶
c. 650 𝜇𝐶
d. 160 𝜇𝐶
Electrostatics Vardan Patni’s Physics Classes – 9584120300

24. In the circuit shown in the figure, the potential 28. Find capacitance between A and B
difference across the 4.5 𝜇𝐹 capacitor is

8
a. 𝑉
3
b. 4 𝑉 29. Find capacitance between A and B
c. 6 𝑉
d. 8 𝑉
25. The capacitor, whose capacitance is 6 𝜇𝐹, 3 𝜇𝐹
and 2 𝜇𝐹, respectively are connected with 12 𝑉
battery as shown in figure. The change on 3 𝜇𝐹
capacitor will be
a. 12 𝜇𝐶
b. 24 𝜇𝐶
c. 8 𝜇𝐶 30. Find capacitance between A and B
d. 16 𝜇𝐶
26. In the given circuit, find the heat produced
between 𝐴 and 𝐵 (given 𝐶 = 1 𝜇𝐹)

31. Find capacitance between A and B

a. 50 𝜇𝐽
b. 60 𝜇𝐽
c. 70 𝜇𝐽
d. 100 𝜇𝐽
27. The capacitance of a infinite circuit formed by
repetition of the same link consisting of two
identical capacitors, each with capacitance 𝐶 is

32. Find capacitance between A and B

a. 0
√5−1
b. 2
𝐶
√5+1
c. 2
𝐶
d. ∞
Electrostatics Vardan Patni’s Physics Classes – 9584120300

33. Find capacitance between A and B 38. Find charge on each capacitor

34. Find capacitance between A and B

35. Find capacitance between A and B

36. Find capacitance between A and B

37. Find 𝑉𝐴 − 𝑉𝐵
Electrostatics Vardan Patni’s Physics Classes – 9584120300

Capacitors with Dielectrics

5. A parallel plate condenser is filled with two
1. In a parallel plate capacitor, the separation dielectrics as shown. Area of each plate is 𝐴 𝑚2
between the plates is 3 𝑚𝑚 with air between and the separation is 𝑑 𝑚𝑒𝑡𝑟𝑒. The dielectric
them. Now, a dielectric of dielectric constant 2 is constants are 𝑘1 and 𝑘2 respectively. Its
introduced between the plates due to which the capacitance in farad
capacitance increases. In order to bring its will be
𝜀0 𝐴
capacitance of the original value, the separation a. (𝑘1 + 𝑘2 )
𝑑
between the plates must be made b.
𝜀0 𝐴 𝑘1 +𝑘2
( 2 )
𝑑
a. 1.5 𝑚𝑚 2𝜀0 𝐴
b. 2.5 𝑚𝑚 c. (𝑘1 + 𝑘2 )
𝑑
c. 4 𝑚𝑚 𝜀0 𝐴 𝑘1 −𝑘2
d. ( )
𝑑 2
d. 6 𝑚𝑚
6. Two dielectric slabs of constant 𝑘1 and 𝑘2 have
2. Two parallel plate of area 𝐴 are separated by
been filled in between the plates of a capacitor
two different dieletrics as shown in figure. The
as shown below. What will be the capacitance of
net capacitance is
4𝜀0 𝐴 the capacitor
a. 3𝑑
3𝜀0 𝐴
b. 4𝑑
2𝜀0 𝐴
c. 𝑑
𝜀0 𝐴
d. 𝑑
3. A parallel plate air capacitor has a capacitance 𝐶.
when it is half filled with a dielectric constant 5,
the percentage increase in
the capacitance will be 2𝜀0 𝐴
a. (𝑘1 + 𝑘2 )
𝑑
𝜀0 𝐴 𝑘1 +𝑘2
a. 400% b. (
𝑑 𝑘1 ×𝑘2
)
b. 66.6% 𝜀0 𝐴 𝑘1 ×𝑘2
c. ( )
c. 33.3% 𝑑 𝑘1 +𝑘2
2𝜀0 𝐴 𝑘1 ×𝑘2
d. 200% d. ( )
𝑑 𝑘1 +𝑘2
4. A parallel plate capacitor with air as the 7. A parallel plate capacitor of area 𝐴, plate
dielectric has capacitance 𝐶. A slab of dielectric separation 𝑑 and capacitance 𝐶 is filled with
constant 𝐾 and having the same thickness as the three different dielectric materials having
separation between the plates is introduced so dielectric constants 𝑘1 , 𝑘2 and 𝑘3 as shown. If a
as to fill one-fourth of the capacitor as shown in single dielectric material is to be used to have
the figure. The new capacitance will be the same capacitance 𝐶 in this capacitor, then
its dielectric constant 𝑘 is given by

𝐶
a. (𝐾 + 3) 4
𝐶
b. (𝐾 + 2) 4
𝐶
c. (𝐾 + 1) 4
1 1 1 1
𝐾𝐶 a. = 𝑘 + 𝑘 + 2𝑘
d. 𝑘 1 2 3
4 1 1 1
b. 𝑘
= 𝑘 +𝑘 + 2𝑘
1 2 3
𝑘 𝑘
c. 𝑘 = 𝑘 1+𝑘2 + 2𝑘3
1 2
d. 𝑘 = 𝑘1 + 𝑘2 + 2𝑘3
e. None of these
Electrostatics Vardan Patni’s Physics Classes – 9584120300

8. A parallel plate capacitor with square plates is 𝜀0 𝐴 1 2(𝐾1 +𝐾2 )

a.
𝑑 2
[ + 𝐾1 𝐾2
]
filled with four dielectrics of dielectric constants 𝜀0 𝐴 1 (𝐾1 +𝐾2 )
𝐾1 , 𝐾2 , 𝐾3 , 𝐾4 arranged as shown in the figure. b. 𝑑 2
[ + 𝐾1 𝐾2
]
The effective dielectric constant 𝐾 will be c.
𝜀0 𝐴 1
[ +
𝐾1 𝐾2
]
𝑑 2 𝐾1 +𝐾2
𝜀0 𝐴 1 𝐾1 𝐾2
d. 𝑑 2
[ + 2(𝐾1 +𝐾2 )
]
12. A parallel plate capacitor with plate area 𝐴 and
plate separation 𝑑 = 2𝑚 has a capacitance of
4 𝜇𝐹. The new capacitance of the system if half
(𝐾1 +𝐾2 ) (𝐾3 + 𝐾4 ) of the space between them is filled with a
a. 𝐾 =
2(𝐾1 +𝐾2 +𝐾3 +𝐾4 ) dielectric material of dielectric constant 𝐾 = 3
(𝐾1 +𝐾2 ) (𝐾3 + 𝐾4 )
b. 𝐾 = (as shown in figure) will be
(𝐾1 +𝐾2 +𝐾3 +𝐾4 )
(𝐾1 +𝐾4 ) (𝐾2 + 𝐾3 )
c. 𝐾 = 2(𝐾1 +𝐾2 +𝐾3 +𝐾4 )
(𝐾1 +𝐾3 ) (𝐾2 + 𝐾4 )
d. 𝐾 = (𝐾1 +𝐾2 +𝐾3 +𝐾4 )
9. A parallel plate capacitor is of area 6 𝑐𝑚2 and a
separation 3 𝑚𝑚. The gap is filled with three
dielectric materials of equal thickness with
dielectric constants 𝐾1 = 10, 𝐾2 = 12 and 𝐾3 =
14. The dielectric constant of a material which a. 2 𝜇𝐹
when fully inserted in above capacitor, gives b. 32 𝜇𝐹
same capacitance would be c. 6 𝜇𝐹
d. 8 𝜇𝐹
a. 12 13. Two thin dielectric slabs of dielectric constants
b. 4 𝐾1 and 𝐾2 (𝐾1 < 𝐾2 ) are inserted between
c. 36 plates of a parallel plate capacitor, as shown in
d. 14 the figure. The variation of electric filed 𝐸
10. In the reported figure, a capacitor is formed by between the plates with distance 𝑑 as measured
placing a compound dielectric between the from plate 𝑃 is correctly shown by
plates of parallel plate capacitor. The expression
for the capacity of the said capacitor will be
(Given area of the plates = 𝐴)
15 𝐾𝜀0 𝐴
a. 34 𝑑
15 𝐾𝜀0 𝐴
b. 6 𝑑
25 𝐾𝜀0 𝐴
c.
6 𝑑
9 𝐾𝜀0 𝐴
d. 6 𝑑
11. A parallel-plate capacitor with plate area 𝐴 has
separation 𝑑 between the plates. Two dielectric
slabs of dielectric constant 𝐾1 and 𝐾2 of same
𝐴 𝑑
area 2 and thickness 2 are inserted in the space
between the plates. The capacitance of the
capacitor will be given by