Tamanna
Chaudhary
, Electric Charges and Fields
1. A polythene piece, rubbed with wool, is found to have negative charge of 4 × 10!" C. the number of
electrons transferred from wool to polythene is
a) 1.5 × 10#$ b) 2.5 × 10#$ c) 2.5 × 10#% d) 3.5 × 10#%
2. The intensity of electric field at a point between the plates of a charged capacitor
a) Is directly proportional to the distance between the plates
b) Is inversely proportional to the distance between the plates
c) Is inversely proportional to the square of the distance between the plates
d) Does not depend upon the distance between the plates
3. Three charges – 𝑞# , +𝑞$ and −𝑞% are placed as shown in figure. The 𝑥 component of the force on – 𝑞# is
proportional to
& & & & &! & & &
a) '!! − '"! sin θ b) '!! − '"! cos θ c) '!
+ '"! sin θ d) '!! + '"! cos θ
4. According to Gauss’ Theorem, electric field of an infinitely long straight wire is proportional to
a) 𝑟 b) 1/𝑟 $ c) 1/𝑟 % d) 1/𝑟
5. Three charges each of + 1µC are placed at the corners of an equilateral triangle. If the force between any
two charges be F, then the net force on either charge will be
a) √2 𝐹 b) 𝐹√3 c) 2F d) 3F
6. Two point charge −𝑞 and +𝑞/2 are situated at the origin and at the point (𝑎, 0,0) respectively. The point
along the 𝑋-axis where the electric field vanishes is
𝑎 √2𝑎 √2𝑎
a) 𝑥 = b) 𝑥 = √2𝑎 c) 𝑥 = d) 𝑥 =
√2 √2 − 1 √2 + 1
7. A ring of radius 𝑟 carries a charge 𝑄 uniformly distributed over its length. A charge 𝑞 is placed at its centre
will experience a force equal to
𝑞𝑄 𝑞𝑄 c) Zero d) None of these
a) $ b) %
4𝜋𝜀( 𝑟 8𝜋𝜀( 𝑟
,8. In the given figure two tiny conducting balls of identical mass 𝑚 and identical charge 𝑞 hang from non-
conducting threads of equal length 𝐿. Assume that 𝜃 is so small that tan 𝜃 ≈ sin 𝜃, then for equilibrium 𝑥 is
equal to
q q
L L
q x q
# # # #
$ $ $ $ $
a) e 𝑞 𝐿 g b) e 𝑞𝐿 g c) e 𝑞 𝐿 g d) e 𝑞 𝐿 g
" " " "
2𝜋𝜀( 𝑚𝑔 2𝜋𝜀( 𝑚𝑔 4𝜋𝜀( 𝑚𝑔 4𝜋𝜀( 𝑚𝑔
9. Charge 𝑞$ of mass 𝑚 revolves around a stationary charge 𝑞# in a circular orbit of radius 𝑟. The orbital
periodic time of 𝑞$ would be
#/$ #/$
4𝜋 % 𝑚𝑟 $
#/$ 𝑘𝑞# 𝑞$ #/$ 4𝜋 $ 𝑚𝑟 * 4𝜋 $ 𝑚𝑟 $
a) h j b) k4𝜋 $ 𝑚𝑟 $ l c) h 𝑘𝑞 𝑞 j d) h 𝑘𝑞 𝑞 j
𝑘𝑞# 𝑞$ # $ # $
10. A hollow cylinder has a charge 𝑞 coulomb within it. If 𝜙 is the electric flux in units of 𝑣𝑜𝑙𝑡 − 𝑚𝑒𝑡𝑒𝑟
associated with the curved surface 𝐵, the flux linked with the plane surface 𝐴 in units of 𝑣𝑜𝑙𝑡 − 𝑚𝑒𝑡𝑒𝑟 will
be
1 𝑞 𝑞 𝜙 𝑞
a) v − 𝜙x b) c) d) −𝜙
2 ∈( 2 ∈( 3 ∈(
11. Two small conducting spheres of equal radius have charges +10 𝜇𝐶 and −20𝜇𝐶 respectively and placed at
a distance 𝑅 from each other experience force 𝐹# . If they are brought in contact and separated to the same
distance, they experience force 𝐹$ . The ratio of 𝐹# to 𝐹$ is
a) 1 : 8 b) −8: 1 c) 1 : 2 d) −2: 1
%+
12. The electric field at a distance from the centre of a charged conducting spherical shell of radius 𝑅 is 𝐸.
$
+
The electric field at a distance $ from the centre of the sphere is
a) Zero 𝐸 𝐸
b) 𝐸 c) d)
2 3
13. The unit of intensity of electric field is
a) 𝑁𝑒𝑤𝑡𝑜𝑛/𝐶𝑜𝑢𝑙𝑜𝑚𝑏 b) 𝐽𝑜𝑢𝑙𝑒/𝐶𝑜𝑢𝑙𝑜𝑚𝑏 c) 𝑉𝑜𝑙𝑡 − 𝑚𝑒𝑡𝑟𝑒 d) 𝑁𝑒𝑤𝑡𝑜𝑛/𝑚𝑒𝑡𝑟𝑒
14. An electric dipole is kept in non-uniform electric field. It experiences
a) A force and a torque b) A force but not a torque
c) A torque but not a torque d) Neither a force nor a torque
15. A metallic shell has a point charge ′𝑞′ kept inside its cavity. Which one of the following diagrams correctly
represents the electric lines of forces
a) b) c) d)
, 16. An electron enters in an electric field with its velocity in the direction of the electric lines of force. Then
a) The path of the electron will be a circle b) The path of the electron will be a parabola
c) The velocity of the electron will decrease d) The velocity of the electron will increase
17. Two equal charges are separated by a distance 𝑑. A third charge placed on a perpendicular bisector at 𝑥
distance will experience maximum coulomb force when
𝑑 𝑑 𝑑 𝑑
a) 𝑥 = b) 𝑥 = c) 𝑥 = d) 𝑥 =
√2 2 2√2 2√3
18. A simple pendulum of period 𝑇 has a metal bob which is negatively charged. If it is allowed to oscillate
above a positively charged metal plate, its period will
a) Remains equal to 𝑇 b) Less than 𝑇 c) Greater than 𝑇 d) Infinite
19. Figures below show regular hexagons, which charges at the vertices. In which of the following cases the
electric field at the centre is not zero
q q q –q
q q q q
q q q –q
2q 2q +qq
2q
q q q Q2q
2q 2q 2q aq
(3) (4)
a) 1 b) 2 c) 3 d) 4
20. A total charge 𝑄 is broken in two parts 𝑄# and 𝑄$ and they are placed at a distance 𝑅 from each other. The
maximum force of repulsion between them will occur, when
𝑄 𝑄 𝑄 2𝑄 𝑄 3𝑄 𝑄 𝑄
a) 𝑄$ = , 𝑄# = 𝑄 − b) 𝑄$ = , 𝑄# = 𝑄 − c) 𝑄$ = , 𝑄# = d) 𝑄# = , 𝑄$ =
𝑅 𝑅 4 3 4 4 2 2
21. A charge q is placed at the corner of a cube of side𝑎. The electric flux through the cube is
𝑞 𝑞 𝑞 𝑞
a) b) c) d)
𝜀( 3𝜀( 6𝜀( 8𝜀(
22. If Ea be the electric field strength of a short dipole at a point on its axial line and Ee that on equatorial line
at the same distance, then
a) Ee = 2Ea b) Ea = 2Ee c) Ea = Ee d) None of these
23. 𝑞# , 𝑞$ , 𝑞% and 𝑞* are point charges located at points as shown in the figure and 𝑆 is a spherical Gaussian
surface of radius 𝑅. Which of the following is true according to the Gauss’s law
S
q1 R
q4
q2 q3
𝑞# + 𝑞$ + 𝑞%
a) • •𝐸‘⃗# + 𝐸‘⃗$ + 𝐸‘⃗% “. 𝑑𝐴⃗ =
- 2𝜀(
(𝑞# + 𝑞$ + 𝑞% )
b) • •𝐸‘⃗# + 𝐸‘⃗$ + 𝐸‘⃗% “. 𝑑𝐴⃗ =
- 𝜀(
(𝑞# + 𝑞$ + 𝑞% + 𝑞* )
c) • •𝐸‘⃗# + 𝐸‘⃗$ + 𝐸‘⃗% “. 𝑑𝐴⃗ =
- 𝜀(
d) None of the above
Chaudhary
, Electric Charges and Fields
1. A polythene piece, rubbed with wool, is found to have negative charge of 4 × 10!" C. the number of
electrons transferred from wool to polythene is
a) 1.5 × 10#$ b) 2.5 × 10#$ c) 2.5 × 10#% d) 3.5 × 10#%
2. The intensity of electric field at a point between the plates of a charged capacitor
a) Is directly proportional to the distance between the plates
b) Is inversely proportional to the distance between the plates
c) Is inversely proportional to the square of the distance between the plates
d) Does not depend upon the distance between the plates
3. Three charges – 𝑞# , +𝑞$ and −𝑞% are placed as shown in figure. The 𝑥 component of the force on – 𝑞# is
proportional to
& & & & &! & & &
a) '!! − '"! sin θ b) '!! − '"! cos θ c) '!
+ '"! sin θ d) '!! + '"! cos θ
4. According to Gauss’ Theorem, electric field of an infinitely long straight wire is proportional to
a) 𝑟 b) 1/𝑟 $ c) 1/𝑟 % d) 1/𝑟
5. Three charges each of + 1µC are placed at the corners of an equilateral triangle. If the force between any
two charges be F, then the net force on either charge will be
a) √2 𝐹 b) 𝐹√3 c) 2F d) 3F
6. Two point charge −𝑞 and +𝑞/2 are situated at the origin and at the point (𝑎, 0,0) respectively. The point
along the 𝑋-axis where the electric field vanishes is
𝑎 √2𝑎 √2𝑎
a) 𝑥 = b) 𝑥 = √2𝑎 c) 𝑥 = d) 𝑥 =
√2 √2 − 1 √2 + 1
7. A ring of radius 𝑟 carries a charge 𝑄 uniformly distributed over its length. A charge 𝑞 is placed at its centre
will experience a force equal to
𝑞𝑄 𝑞𝑄 c) Zero d) None of these
a) $ b) %
4𝜋𝜀( 𝑟 8𝜋𝜀( 𝑟
,8. In the given figure two tiny conducting balls of identical mass 𝑚 and identical charge 𝑞 hang from non-
conducting threads of equal length 𝐿. Assume that 𝜃 is so small that tan 𝜃 ≈ sin 𝜃, then for equilibrium 𝑥 is
equal to
q q
L L
q x q
# # # #
$ $ $ $ $
a) e 𝑞 𝐿 g b) e 𝑞𝐿 g c) e 𝑞 𝐿 g d) e 𝑞 𝐿 g
" " " "
2𝜋𝜀( 𝑚𝑔 2𝜋𝜀( 𝑚𝑔 4𝜋𝜀( 𝑚𝑔 4𝜋𝜀( 𝑚𝑔
9. Charge 𝑞$ of mass 𝑚 revolves around a stationary charge 𝑞# in a circular orbit of radius 𝑟. The orbital
periodic time of 𝑞$ would be
#/$ #/$
4𝜋 % 𝑚𝑟 $
#/$ 𝑘𝑞# 𝑞$ #/$ 4𝜋 $ 𝑚𝑟 * 4𝜋 $ 𝑚𝑟 $
a) h j b) k4𝜋 $ 𝑚𝑟 $ l c) h 𝑘𝑞 𝑞 j d) h 𝑘𝑞 𝑞 j
𝑘𝑞# 𝑞$ # $ # $
10. A hollow cylinder has a charge 𝑞 coulomb within it. If 𝜙 is the electric flux in units of 𝑣𝑜𝑙𝑡 − 𝑚𝑒𝑡𝑒𝑟
associated with the curved surface 𝐵, the flux linked with the plane surface 𝐴 in units of 𝑣𝑜𝑙𝑡 − 𝑚𝑒𝑡𝑒𝑟 will
be
1 𝑞 𝑞 𝜙 𝑞
a) v − 𝜙x b) c) d) −𝜙
2 ∈( 2 ∈( 3 ∈(
11. Two small conducting spheres of equal radius have charges +10 𝜇𝐶 and −20𝜇𝐶 respectively and placed at
a distance 𝑅 from each other experience force 𝐹# . If they are brought in contact and separated to the same
distance, they experience force 𝐹$ . The ratio of 𝐹# to 𝐹$ is
a) 1 : 8 b) −8: 1 c) 1 : 2 d) −2: 1
%+
12. The electric field at a distance from the centre of a charged conducting spherical shell of radius 𝑅 is 𝐸.
$
+
The electric field at a distance $ from the centre of the sphere is
a) Zero 𝐸 𝐸
b) 𝐸 c) d)
2 3
13. The unit of intensity of electric field is
a) 𝑁𝑒𝑤𝑡𝑜𝑛/𝐶𝑜𝑢𝑙𝑜𝑚𝑏 b) 𝐽𝑜𝑢𝑙𝑒/𝐶𝑜𝑢𝑙𝑜𝑚𝑏 c) 𝑉𝑜𝑙𝑡 − 𝑚𝑒𝑡𝑟𝑒 d) 𝑁𝑒𝑤𝑡𝑜𝑛/𝑚𝑒𝑡𝑟𝑒
14. An electric dipole is kept in non-uniform electric field. It experiences
a) A force and a torque b) A force but not a torque
c) A torque but not a torque d) Neither a force nor a torque
15. A metallic shell has a point charge ′𝑞′ kept inside its cavity. Which one of the following diagrams correctly
represents the electric lines of forces
a) b) c) d)
, 16. An electron enters in an electric field with its velocity in the direction of the electric lines of force. Then
a) The path of the electron will be a circle b) The path of the electron will be a parabola
c) The velocity of the electron will decrease d) The velocity of the electron will increase
17. Two equal charges are separated by a distance 𝑑. A third charge placed on a perpendicular bisector at 𝑥
distance will experience maximum coulomb force when
𝑑 𝑑 𝑑 𝑑
a) 𝑥 = b) 𝑥 = c) 𝑥 = d) 𝑥 =
√2 2 2√2 2√3
18. A simple pendulum of period 𝑇 has a metal bob which is negatively charged. If it is allowed to oscillate
above a positively charged metal plate, its period will
a) Remains equal to 𝑇 b) Less than 𝑇 c) Greater than 𝑇 d) Infinite
19. Figures below show regular hexagons, which charges at the vertices. In which of the following cases the
electric field at the centre is not zero
q q q –q
q q q q
q q q –q
2q 2q +qq
2q
q q q Q2q
2q 2q 2q aq
(3) (4)
a) 1 b) 2 c) 3 d) 4
20. A total charge 𝑄 is broken in two parts 𝑄# and 𝑄$ and they are placed at a distance 𝑅 from each other. The
maximum force of repulsion between them will occur, when
𝑄 𝑄 𝑄 2𝑄 𝑄 3𝑄 𝑄 𝑄
a) 𝑄$ = , 𝑄# = 𝑄 − b) 𝑄$ = , 𝑄# = 𝑄 − c) 𝑄$ = , 𝑄# = d) 𝑄# = , 𝑄$ =
𝑅 𝑅 4 3 4 4 2 2
21. A charge q is placed at the corner of a cube of side𝑎. The electric flux through the cube is
𝑞 𝑞 𝑞 𝑞
a) b) c) d)
𝜀( 3𝜀( 6𝜀( 8𝜀(
22. If Ea be the electric field strength of a short dipole at a point on its axial line and Ee that on equatorial line
at the same distance, then
a) Ee = 2Ea b) Ea = 2Ee c) Ea = Ee d) None of these
23. 𝑞# , 𝑞$ , 𝑞% and 𝑞* are point charges located at points as shown in the figure and 𝑆 is a spherical Gaussian
surface of radius 𝑅. Which of the following is true according to the Gauss’s law
S
q1 R
q4
q2 q3
𝑞# + 𝑞$ + 𝑞%
a) • •𝐸‘⃗# + 𝐸‘⃗$ + 𝐸‘⃗% “. 𝑑𝐴⃗ =
- 2𝜀(
(𝑞# + 𝑞$ + 𝑞% )
b) • •𝐸‘⃗# + 𝐸‘⃗$ + 𝐸‘⃗% “. 𝑑𝐴⃗ =
- 𝜀(
(𝑞# + 𝑞$ + 𝑞% + 𝑞* )
c) • •𝐸‘⃗# + 𝐸‘⃗$ + 𝐸‘⃗% “. 𝑑𝐴⃗ =
- 𝜀(
d) None of the above
