ELECTRIC CHARGES AND FIELDS

VIDYAPEETH 1

1 2q 1 3q
PHYSICS (c) .
40 3 3R2
(d) .
40 2 3R2
ELECTRIC CHARGES AND FIELDS 7. An insulated sphere of radius R has charge
1. Figure shows the electric field lines around three 4. Figure shows the electric lines of force energy density p. The electric field at a distance r from
point charge A, B and C. Which charge has the from a charge body. If the electric field at A and the centre of the sphere (r < R)
largest magnitude? B are E A and E B , respectively and the
r R
displacement between A and B is r, then (a) (b)
30 30
(a) 1 (b) 2
r R
(c) (d)
0 0 (c) 3 (d) 4

8. For a uniformly charged ring of radius R, the 11. A point charge + q is placed at a distance d from
electric field on its axis has the largest magnitude an isolated conducting plane. The field at a point
at a distance h from its centre. Then, value of h is P on the other side of the plane is

R (a) directed perpendicular to the plane and

(a) Charge A (b) Charge B (a) (b) R 2 away from the plane
2
(c) Charges A and B (d) Charge C (b) directed perpendicular to the plane but
R
2. In the electric field shown in figure, the electric (c) R (d) towards the plane
5
lines in the left have twice the separation as that (a) EA  EB (b) EA  EB (c) directed radially away from the point
between those on right. If the magnitude of the
field at point A is 40 NC–1, the force experienced (c) EA = EB (d) E A = 2 EB
9. Two point charge q1 ( )
10C and q2 ( −25C ) charge

by a proton placed at point A is are placed on the X-axis at x = 1m and x = 4 m, (d) directed radially towards the point charge
5. Two point charges –q and +q/2 are situated at the respectively. The electric field (in V/m) at a point
origin and at the point (a, 0, 0), respectively. The 12. A hemisphere is uniformly charged positively.
y = 3m on Y-axis is
point along the X-axis, where the electric field The electric field at a point on a diameter away
vanished, is 1 from the centre is directed
(Take, = 9 109 N − m2C −2 )
40
2a (a) perpendicular to the diameter
(a) x=
2 −1 (a) ( 63iˆ − 27 ˆj ) 10 2
(b) parallel to the diameter

X = 2a − 2 − 1
(81iˆ − 81 ˆj ) 10
(b) 2
(c) at an angle tilted towards the diameter
(a) 6.4 10−18 N (b) 3.2 10−13 N (b)
(c) X= ( 2 −1) 2a (d) at an angle tilted away from the diameter
(c) 5.0 10−12 N (d) 1.2 10−18 N (c) (81iˆ + 81 ˆj ) 10 2
13. A point positive charge brought near an isolated
3. Two conducting sphere of radii r1 and r2 are (d) None of these conducting sphere (figure). The electric field is
charged to the same surface charge density. The 6. The maximum field intensity on the axis of a
(d) ( −63iˆ + 27 ˆj ) 10 2
best given by
ratio of electric field near their surface is uniformly charged ring of charge q and radius R
10. A metallic solid sphere is placed in a uniform
will be (a)
(a) r12 / r22 (b) r22 / r12 electric field. The lines of force follow the paths
1 q 1 2q shown in figure
(c) r1 / r2 (d) 1:1 (a) . (b) .
40 3 3R2 40 3R2

ELECTRIC CHARGES AND FIELDS ELECTRIC CHARGES AND FIELDS

17. In finding the electric field using Gauss’s law, the Q

(b) (a) zero (b)
q 40 x2
formula E = ene is applicable. In the formula,
0 A
Q
0 is permittivity of free space, A is the area of (c) (d) None of these
0 x 2
Gaussian surface and qene is charge enclosed by
(c)
the Gaussian surface. This equation can be used 21. Infinite parallel plane sheet of a metal is charged
in which of the following situation? to charge density  coulomb per square metre in
a medium of dielectric constant K. Intensity of
(a) Only when the Gaussian surface is an
electric field near the metallic surface will be
equipotential surface and E is constant Which of the following statements is correct?
(d)  K
on the surface.
(a) E on the LHS of the above equation will (a) E= (b) E=
0 K 30
(b) Only when the Gaussian surface is an have a contribution from q1 , q2 and q3 on
equipotential surface. the RHS will have a contribution from q2  K
14. In a region of space, the electric field is given by (c) E= (d) E=
20 K 20
E = 8iˆ + 4 ˆj + 3k . The electric flux through a (c) For any choice of Gaussian surface and q4 only.
surface of are of 100 units XY-plane is (b) E on the LHS of the above equation will 22. A long charged cylinder of linear charged density
(d) Only when E = constant on the surface.
have a contribution from all charges while  is surrounded by a hollow co-axial conducting
(a) 800 units (b) 300 units
18. The electric flux through the surface q on the RHS will have a contribution from cylinder. What is the electric field in the space
(c) 400 units (d) 1500 units q2 and q4 only. between the two cylinders?
15. A cylinder of radius R and length L is placed in a (c) E on the LHS of the above equation will  r
(a) (b)
uniform electric field E parallel to the cylinder
have a contribution from all charges while 20 r 2 0
axis. The total flux for the surface of the cylinder q on the RHS will have a contribution from
is given by
q1 , q3 and q5 only. 
(c) (d) None of these
2 0 r
(a) zero (b) R2 / E (a) In Fig. (iv) is the largest (d) Both E on the LHS and q on the RHS will
(c) 2R 2 / E (d) None of these have contributions from q2 and q4 only. 23. A spherical charged conductor has  as the
(b) in Fig. (iii) is the least
surface density of charge. The electric field on its
16. Suppose an imaginary cube is with a charge (c) in Fig. (ii) is same as fig. (iii) but is smaller 20. The adjacent diagram shows a charge +Q held on surface is E. If the radius of the sphere is doubled,
situated at the centre of it. The total electric flux than Fig. (iv) an insulating support S and enclosed by a hollow keeping the surface density of the charge
passing through each of the faces of the cube will spherical conductor, O represents the centre of unchanged, what will be the electric field on the
(d) is the same for all the figure the spherical conductor and P is a point such that
be surface of the new sphere?
19. Five charges q1 , q2 , q3 , q4 and q5 are fixed at OP = x and SP = r The electric field at point, P
q will be E E
(a) their positions as shown in figure, S is a Gaussian (a) (b)
60 4 2
surface. The Gauss’s law is given by
q q (c) E (d) 2E
(b)
20
 E.dS = 0 .
24. Which one of the following graphs shows the
variation of electric field strength E with distance
q
(c) d from the centre of the hollow conducting
120
sphere?
(d) None of the above
ELECTRIC CHARGES AND FIELDS ELECTRIC CHARGES AND FIELDS

30. Figure shows three concentric metallic spherical

shells. The outermost shell has charge q2 , the
inner most shell has charge q1 , and the middle
(a) (b)
shell is uncharged. The charge appearing on the
inner surface of outermost shell is

EB
(c) (d) (a) EA  EB (b) EA =
r

EB
(c) EA  EB (d) EA = (a) Both negative
25. Figure shows three electric field lines. If FA , FB r2
and FC are force on a test charge q at position A, (b) Q1 positive and Q2 negative
28. A sphere of radius R carries charge density  such
B and C respectively, then that  = kr 2 , where k is positive constant and r is (c) Both positive
q2
distance from centre. Find the magnitude of (a) q1 + q2 (b) (d) Q1 negative and Q2 positive
electric field at distance R/2 from centere. 2

kR 3
kR3 (c) − q1 (d) Zero 33. The figure shows electric field lines. If E A and
(a) (b) E B are electric fields at A and B and distance is
200 100
r, then
3 3
kR kR 31. The magnitude of electric field strength E such
(c) (d)
50 400 that an electron placed in it would experience an
(a) FA  FB  FC (b) FA  FB  FC electrical force equal to its weight is given by
29. q1 , q2 , q3 and q4 are point charge located at
(c) FA  ( FB = FC ) (d) FA  ( FB = FC ) (a) mge (b)
mg (a) EA  EB (b) E A  EB / r
points as shown in figure. S is the spherical e
Gaussian surface of radius R. Which of the (c) EA  EB (d) E A = EB / r 2
26. There is a point charge +q inside a hollow sphere
and a point charge –q outside its surface. Find the following is true according to Gauss’s law? e e2 g
(c) (d) 34. If the electric field intensity in a fair weather
total flux passing through the sphere. mg 2m
q +q +q atmosphere is 100 V/m, then the total charge on
−q q
(a) ( )
E1 + E2 + E3 .dA = 1 2 3
20 32. The figure shown is a plot of electric field lines the earth’s surface is (radius of the earth is 6400
(a) (b) km)
0 0 due to two charges Q1 and Q2 . The sign of
q1 + q2 + q3 (a) 4.55 107 C (b) 4.55 108 C
 (E + E ) charges is
2q (b) + E3 .dA = (c) 4.55 105 C (d) 4.55 106 C
0
1 2
(c) Zero (d)
0
35. Charge 2Q and –Q are placed as shown in figure.
q1 + q2 + q3
27. Figure shows the electric lines of force emerging (c)  (E + E 1 2 )
+ E3 + E4 .dA =
0
The point at which electric field intensity is zero
will be somewhere
from a charged body. If electric field at A and B
are E A and E B respectively and distance
q1 + q2 + q3 + q4
between A and B is r then (d)  (E + E 1 2 )
+ E3 + E4 .dA =
0
(a) Between –Q and 2Q
(b) On the left of –Q

ELECTRIC CHARGES AND FIELDS ELECTRIC CHARGES AND FIELDS

(c) On the right of 2Q (b)  particle trajectory is more curved 43. An electric dipole consists of two opposite (c) One
(d) On the perpendicular bisector of line (c) Both trajectories are equally curved and in charges each of magnitude 1C separated by a
(d) Nothing certain can be said
joining the charges same direction distance of 2 cm. The dipole is placed in an
external field of 105 N / C . The maximum torque 48. An electric dipole is placed in non-uniform
(d) Both trajectories are equally curved and in
36. Figure shows electric field lines due to a charge on the dipole is electric field. It may experience
same direction
configuration, from this we conclude that (a) Resultant force and couple
39. Electric field in a region is uniform and is given (a) 2  10−4 N m (b) 2  10−3 N m
by E = aiˆ + bjˆ + ckˆ . Electric flux associated with −3 −3
(b) Only resultant force
(c) 4  10 N m (d) 10 N m
a surface of area A = R 2iˆ is (c) Only couple
44. A charge Q is situated at the centre of a cube. The
(a) aR 2 (b) 3aR2 electric flux through one of the faces of the cube (d) All of these
is 49. The given figure shows, two parallel plates A and
(c) 2abR (d) acR
(a) q1 and q2 are positive and q2  q1 Q Q B of charge density + and – respectively.
40. A small conducting sphere is hanged by an (a) (b)
(b) q1 and q2 are positive and q1  q2 0 20 Electric intensity will be zero in region.
insulating thread between the plates of a parallel
(c) q1 and q2 are negative and q1  q2 plate capacitor as shown in figure. The net force
Q Q
(d) q1 and q2 are negative and q2  q1 on the sphere is (c) (d)
40 60
37. Six point charges are placed at the vertices of a
hexagon of slide 1 m as shown in figure. Net 45. A charge q is placed at the centre of the open end
electric field at the centre of the hexagon is of a cylindrical vessel. The flux of the electric
field through the surface of the vessel is (a) I only (b) II only
q (c) III only (d) Both (1) & (3)
(a) Zero (b)
0
50. A sphere of radius R has a uniform distribution of
(a) Towards plate A (b) Towards plate B q 2q electric charge in its volume. At a distance x from
(c) (d) its centre for x < R, the electric field is directly
(c) Upwards (d) Zero 20 0
proportional to
6q 41. Electric charge q, q and –2q are placed at the 46. A charged body has an electric flux  associated
(a) Zero (b) 1 1
corners of an equilateral triangle ABC of side L. with it. The body is now placed inside a metallic (a) (b)
40 x2 x
The magnitude of electric dipole moment of the container. The flux , outside the container will
q q system is
(c) (d) be (c) x (d) x2
0 40
38. A proton and an  particle having equal kinetic
(a) qL (b) 2qL (a) Zero (b) Equal to  51. The electric field at 20 cm from the centre of a
energy are projected in a uniform transverse uniformly charged non-conducting sphere of
(c) 3qL (d) 4qL (c) Greater than  (d) Less than  radius 10 cm is E. Then at a distance 5 cm from
electric field as shown in figure
47. A charge of 1 coulomb is located at the centre of the centre it will be
42. The torque  acting on an electric dipole of dipole
a sphere of radius 10 cm and a cube of side 20 cm. (a) 16 E (b) 4E
moment p in an electric field E is
The ratio of outgoing flux from the sphere and
cube will be (c) 2E (d) Zero
(a)  = p.E (b)  = p E
(a) More than one 52. If a small sphere of mass m and charge q is hung
(c)  = pE (d)  = pE from a silk thread at an angle  with the surface
(a) Proton trajectory is more curved (b) Less than one
ELECTRIC CHARGES AND FIELDS ELECTRIC CHARGES AND FIELDS

of a vertical charged conducting plate, then for then the electric field at a point in between the 60. In which of the following cases electric field at (a) iˆ (b) − iˆ
equilibrium of sphere, the surface charge density plates is given by point P is non-zero?
of the place is (c) ĵ (d) − ĵ
Q Q
(a) (b) (a)
 mg   2mg  A0 2 A0 63. If electric field in a region is given by
(a) 0   tan  (b) 0   tan 
 q   q 
Q E0 .x ˆ E0 . y 2 ˆ E0 .z 3 ˆ
(c) (d) Zero E= i + 2 j+ 3 k
 mg  4 A0 l l l
(c) 0 ( mgq) tan  (d) 0   tan 
 3q  57. If atmospheric electric field is approximately 150 Where E0 = 5  103 N / C , l = 2cm .
(b)
53. Two long thin charged rods with charged density volt/m and radius of the earth is 6400 km, then
then electric flux passing through the plane x = 2
 each are placed parallel to each other at a the total charge on the earth’s surface is
cm. The plane is a square of side 2 cm.
distance d apart. The force per unit length exerted (a) 6.8 105 coulomb (c)
on one rod by the other will be N .m2 N .m 2
(a) 2 (b) 3
 1  (b) 6.8 106 coulomb C C
 Where k = 
 40 
(c) 6.8 104 coulomb N .m2
(c) 5 (d) None of these
(d) C
k 2 k 2 2 (d) 6.8 10 coulomb
9
(a) (b)
d d 64. Which of the following is true, when a dipole is
58. Three particles are projected in a uniform electric 61. For two equal and opposite charges placed at placed in non-uniform electric field?
k 2 k 2 2 field with same velocity perpendicular to the field distance d, then electric field will be zero at
(c) (d)
d2 d2 as shown. Which particle has highest charge to (a) Net force on it is equal to zero
mass ratio? (b) Torque may or may not be zero
54. Two isolated metallic spheres of radii 2 cm and 4
cm are given equal charge, then the ratio of (c) Torque must be zero
charge density on the surface of the sphere will be
(d) All of these
(a) 1:2 (b) 4:1
(a) Mid way 65. Which of the following is true for electric flux
(c) 8:1 (d) 1:4 through a Gaussian surface?
(b) Distance d from (–q) and to the left
55. Gauss’s law can help in easy calculation of (a) It depends on magnitude of net charge
electric field due to (c) Distance d from (+q) and to the right
(a) A enclosed by Gaussian surface
(a) Moving charge only (d) No finite distance
(b) B (b) Electric flux is a scalar quantity
(b) Any charge configuration 62. The linear charge density upon the semi-circular
(c) C (c) Electric flux is independent of shape of
ring, on both side is same in magnitude, the
(c) Any symmetrical charge configuration electric field at O is along Gaussian surface enclosing the charge
(d) All have same charge to mass ratio
(d) Some special symmetric charge (d) All are true
59. The dimensional formula of linear charge density
configuration  is 66. A small spherically symmetric charge q is placed
56. Each of two large conducting parallel plates has at one vertex of a cube as shown. The flux
 M L T A  M L T A
−1 −1 +1 0 −1 +1
(a) (b) through the faces ABCD and HGEF are,
one sides surface area A. If one of the plates is
given a charge Q whereas the other is neutral, respectively,
(c)  M −1L−1T +1 A−1  (d)  M 0 L−1T +1 A−1 

ELECTRIC CHARGES AND FIELDS

69. The magnitude of dipole moment of the following

system is n aq. The value of n is

q q q
(a) , (b) 0,
240 240 80

q q (a) 11 (b) 17
(c) ,0 (d) ,0
80 240
(c) 21 (d) 25
67. Five identical charges +q are placed at five corner 70. Two short dipoles, each of dipole moment p, are
of a regular hexagon of side a. The magnitude of placed at origin. The dipole moment of one dipole
q is along x-axis, while that of other is along y-axis.
electric field at centre is . The value of n
n0 a2 The electric field at a point (a, 0) is given by
is np
. The value of n is
(a) 1 (b) 2 40 a3

(c) 3 (d) 4 (a) 1 (b) 2

68. The electric field at point O, due to the segment (c) 3 (d) 5
of a ring, whose linear charge density is 8 C/cm
is n× 1013 V/m . The value on n is
71. If the electric field is given by 3iˆ + 2 ˆj + 6kˆ . The
(a) 10 (b) 16
electric flux through a surface area 20 unit lying
(c) 13 (d) 18 in xy plane is n unit. The value of n is

(a) 90 (b) 100

(c) 120 (d) 150