VIDYAPEETH 1

PHYSICS
Electric charges and Field
1. In hydrogen like system, the ratio of coulombian sphere C is first placed in contact with A and then
force and gravitational force between an electron in contact with B and finally placed at midpoint
and a proton is in the order of between spheres A and B. The force experienced
by sphere C will be
(a) 1019 (b) 1029
(a) 3F/2 (b) 3F/4
(c) 1039 (d) 1036
(c) F (d) 2F
2. Two identical conducting spheres P and S with
charge Q on each, repel each other with a force 6. A certain charge Q is divided into two parts q and
16N. A third identical uncharged conducting (Q − q) . How should the charges Q and q be
sphere R is successively brought in contact with divided so that q and (Q – q) placed at a certain
the two spheres. The new force of repulsion distance apart experience maximum electrostatic
between P and S is repulsion?
(a) 4N (b) 1N
q
(a) Q = 2q (b) Q=
(c) 12 N (d) 6N 2

3. A 10C charge is divided into two parts and (c) Q = 4q (d) Q = 3q

placed at 1 cm distance so that the repulsive force
between them is maximum. The charges of the 7. Two identical tennis balls each having mass m
two parts are and charge q are suspended from a fixed point by
threads of length l. What is the equilibrium
(a) 9 C (b) 7 C, 3 C separation when each thread makes a small angle
 with the vertical?
(c) 8 C, 2 C (d) 5 C, 5 C
1/3
4. A charge of 4 C is to be divided into two. The  q 2l 2 
(a) x = 2 2 
distance between the two divided charges is  20 m g 
constant. The magnitude of the divided charges
1/2
so that the force between them is maximum, will  q 2l 
(b) x = 
 20 mg 
be

(a) 1 C and 3 C 1/3

 q 2l 2 
(b) 2 C and 2 C (c) x= 2 
 20 m g 
(c) 0 and 4 C 1/3
 q 2l 
(d) 1.5 C and 2.5 C (d) x = 
 20 mg 
5. Two identical metallic spheres A and B when
placed at certain distance in air repel each other 8. Two identical conducting spheres A and B, carry
with a force of F. Another identical uncharged equal charge. They are separated by a distance
Electric charges and Field

much larger than their diameters, and the force be in equilibrium (at rest) the height
between them is F. A third identical conducting h = x 10−3 m .
sphere, C, is uncharged. Sphere C is first touched
to A, then to B, and then removed. As a result, the The value of x is _______
force between A and B would be equal to
 1 
 Take = 9 109 m2C −2 , g = 10ms −1 
3F F  40 
(a) (b)
8 2

3F
(c) (d) F
4

9. Under the influence of the Coulomb field of

charge +Q, a charge –q is moving around it in an
elliptical orbit. Find out the correct statement(s).

(a) The angular momentum of the charge –q is

12. Three point charges q, –2q and 2q are placed on
constant.
3
x-axis at a distance x = 0 , x = R and x = R
(b) The linear momentum of the charge –q is 4
constant. respectively from origin as shown. If
q = 2  10−6 C and R = 2 cm , the magnitude of
(c) The angular velocity of the charge –q is
constant. net force experienced by the charge –2q is ___N.

(d) The linear speed of the charge –q is

constant.

10. A thin metallic wire having cross sectional area

of 10–4 m² is used to make a ring of radius 30 cm.
A positive charge of 2 C is uniformly distributed 13. A point charge q1 = 4q0 is placed at origin.
over the ring, while another positive charge of 30 Another point charge q2 = −q0 is placed at
pC is kept at the centre of the ring. The tension in
x = 12cm . Charge of proton is q0 . The proton is
the ring is _____N; provided that the ring does
not get deformed (neglect the influence of placed on x axis so that the electrostatic force on
gravity). the proton is zero. In this situation, the position of
the proton from the origin is ____ cm.
 1 
 given = 9 109 SI units  14. An infinite number of point charges, each
 40  carrying 1 C charge, are placed along the y-axis
11. As shown in the figure, a configuration of two at y = 1 m, 2 m, 4 m, 8 m ______. The total force
equal point charges ( q0 = +2C ) is placed on an
on a 1 C point charge, placed at the origin, is
x  103 N . The value of x, to the nearest integer,
inclined plane. Mass of each point charge is 20g.
Assume that there is no friction between charge is ______.
and plane. For the system of two point charges to
Electric charges and Field

 1  20. Three identical charged balls each of charge 2C

Take = 9 109 Nm2 /C2 
 40 
are suspended from a common point P by silk
threads of 2 m each (ash shown in figure). They
15. Two small spheres each of mass 10 mg are form an equilateral triangle of side 1 m. The ratio
suspended from a point by threads 0.5 m long. of net force on a charged ball to the force between
They are equally charged and repel each other to any two charged balls will be
a distance of 0.20 m. The charge on each of the
a
sphere is 10−8 C . The value of ‘a’ will be ___
21
[Given = 10 m s–2]

16. Two identical conducting spheres with negligible

volume have 2.1 nC and –0.1 nC charges,
respectively. They are brought into contact and
then separated by a distance of 0.5m. The
electrostatic force between the spheres is
 1  (a) 1:1 (b) 1:4
_____10−9 . Given :40 = SI unit 
 9 109

(c) 3:2 (d) 3:1
–3
17. A small ball of mass 2×10 kg having a charge
21. The charges +Q, q, +Q are placed respectively, at
of 1C is suspended by a string of length 0.8 m.
distance, 0 d/2 and d from the origin, on the x-
Another identical ball having the same charge is
axis. If the net force experienced by +Q, placed at
kept at the point of suspension. Determine the
x = 0, is zero, then value of q is
minimum horizontal velocity which should be
imparted to the lower ball so that it can make (a) +Q / 4 (b) −Q / 2
complete revolution.
(c) +Q / 2 (d) −Q / 4
18. Two small balls having equal positive charge Q
(coulomb) on each are suspended by two 22. A charge Q is placed at each of the opposite
insulating string of equal length L (metre) from a corners of a square. A charge q is placed at each
hook fixed to a stand. The whole setup is taken in of the other two corners. If the net electrical force
a satellite into space where there is no gravity on Q is zero, then the Q/q equals
(state of weightlessness). The angle between the
two string is ____ and the tension in each string (a) −2 2 (b) –1
is ____ newton. 1
(c) 1 (d) −
19. A point charge 2×10–2 C is moves from P to S in 2
a uniform electric field of 30 N C–1 directed
23. Four charges equal to –Q are placed at the four
along positive x-axis. If co-ordinates of P and S
corners of a square and a charge q is at its centre.
are (1, 2, 0) m and (0, 0, 0) m respectively, the
If the system is in equilibrium the value of q is
work done by electric field will be

(a) 1200 mJ (b) 600 mJ (a) −

Q
4
(
1+ 2 2 ) (b)
Q
4
(
1+ 2 2 )
(c) –600 mJ (d) –1200 mJ
Electric charges and Field

( ) ( )
1/ N
−
Q
1+ 2 2
Q
1+ 2 2  q2 
(c) (d) equilibrium, and a = k   , where k is a
 
2 2

24. Three charges − q1 , + q2 and −q3 are placed as constant. Then N is ______.
shown in the figure. The x-component of the force 28. Four charges Q1 , Q2 , Q3 and Q4 of same
on − q1 is proportional to
magnitude are fixed along the x-axis at
x = −2a, − a, + a and +2a respectively. A
positive charge q is placed on the positive y-axis
at a distance b > 0 Four options of the signs of
these charges are given in List I. The direction of
the forces on the charge q is given in List II.
Match List I with List II and select the correct
answer using the code given below the lists.

q2 q3 q2 q3
(a) − cos  (b) + sin 
b2 a 2 b2 a 2

q2 q3 q2 q3
(c) + cos  (d) – sin 
b2 a 2 b2 a 2
List I List II
25. Two equal positive point charges are separated by P. Q1, Q2, Q3, Q4 all 1. +x
a distance 2a. The distance of a point from the positive
centre of the line joining two charge on the Q. Q1, Q2, positive Q3, Q4 2. –x
equatorial line (perpendicular bisector) at which negative
force experienced by a test charge q0 , become R. Q1, Q4 positive; Q2, Q3 3. +y
a negative
maximum is . The value of x is ________
x S. Q1, Q3 positive; Q2, Q4 4. –y
negative
26. Three point charges of magnitude 5 C, 0.16 C
and 0.3 C are located at the vertices A, B, C of a
right angled triangle whose sides are AB = 3cm , (a) P-3, Q-1, R-4, S-2

BC = 3 2 cm and CA = 3cm and point A (b) P-4, Q-2, R-3, S-1

experiences ____ N of electrostatic force due to (c) P-3, Q-1, R-2, S-4
the other two charges.
(d) P-4, Q-2, R-1, S-3
27. Four point charges, each of +q, are rigidly fixed
at the four corners of a square planar soap film of 29. Three particles, each of mass 1 g and carrying a
side a. The surface tension of the soap film is  . charge q, are suspended from a common point by
The system of charges and planar film are in insulated massless strings, each 100 cm long. If
the particles are in equilibrium and are located at
the corners of an equilateral triangle of side
Electric charges and Field

length 3 cm, calculate the charge q on each

particle. (Take g = 10 m/s²)

30. A rigid insulated wire frame in the form of a right (a) (b)
angled triangle ABC, is set in a vertical plane as
shown in figure. Two beads of equal masses m
each and carrying charges q1 and q2 are
connected by a cord of length l and can slide
(c) (d)
without friction on the wires. Considering the
case when the beads are stationary, determine 33. Force between two point charges q1 and q2
placed in vacuum at ‘r’ cm apart is F. Force
between them when placed in a medium having
dielectric constant k = 5 at ‘r/5’ cm apart will be

(a) 25F (b) F/5

(c) 5F (d) F/25

34. If two charges q1 and q2 are separated with

(a) (i) The angle  distance ‘d’ and placed in a medium of dielectric
constant k. What will be the equivalent distance
(ii) The tension in the cord between charges in air for the same electrostatic
(iii) The normal reaction on the beads. force?

(b) If the cord is now cut what are the value of (a) k d (b) 1.5d k
the charges for which the beads continue to
remain stationary? (c) 2d k (d) d k

31. Five point charges, each of value +q coulomb, are 35. Two identical charged spheres are suspended by
placed on fiver vertices of a regular hexagon of strings of equal lengths. The strings make and
side I. metre. The magnitude of the force on the angle of 30º with each other. When suspended in
point charge of value –q coulomb place at the a liquid of density 0.8 g cm–3, the angle remains
centre of the hexagon is____ newton. the same. If density of the material of the sphere
is 1.6 g cm–3, the dielectric constant of the liquid
32. An infinitely long positively charged straight
is
thread has a linear charge density  Cm–1. An
electron revolves along a circular path having (a) 1 (b) 4
axis along the length of the wire. The graph that
(c) 3 (d) 2
correctly represents the variation of the kinetic
energy of electron as a function of radius of 36. Two identical non-conducting solid spheres of
circular path from the wire is same mass and charge are suspended in air from
a common point by two non-conducting,
massless string of same length. At equilibrium,
Electric charges and Field

the angle between he strings is . The spheres are 40. A uniform electric field, E= –400 3 yˆ N C−1 is
now immersed in a dielectric liquid of density applied in a region. A charged particle of mass m
800 kg m–3 and dielectric constant 21. If the angle carrying positive charge q is projected in this
between the strings remains the same after the
region with an initial speed of 2 10 106 ms−1 .
immersion, then
This particle is aimed to hit a target T, which is 5
(a) electric force between the spheres remains away from its entry point into the field as shown
unchanged schematically in the figure.
(b) electric force between the spheres remains q
unchanged Take = 1010 C kg −1 . Then
m
(c) mass density of the spheres is 840 kg m–

(d) the tension in the string holding the spheres

remains same.

37. Two identical charged spheres are suspended by

strings of equal lengths. The strings make an
angle  with each other. When suspended in
water, the angle remains the same. If density of
the material of the sphere is 1.5 g/cc, the dielectric
constant of water will be (Take density of water
= 1 g/cc)
(a) the particle will hit T if projected at an
38. Two identical charges spheres are suspended by angle 45º from the horizontal
strings of equal lengths. The strings make an
angle if 37º with each other. When suspended in (b) the particle will hit T if projected either at
a liquid of density 0.7 g cm³, the angle remains an angle 30º or 60º from the horizontal
same. If density of material of the sphere is 1.4 g (c) time taken by the particle to hit T could be
cm³, the dielectric constant of the liquid is ___.
5 5
 3 s and s
 tan37º = 4  6 2
 
5
39. If g E and g M are the accelerations due to (d) time taken by the particle to hit T is s
3
gravity on the surfaces of the earth and the moon
respectively and if Millikan's oil drop experiment 41. A charge q is placed at the centre of one of the
could be performed on the two surfaces, one will surface of a cube. The flux linked with the cube
find the ratio is
electronic charge on the moon
to be q q
electronic charge on the earth (a) (b)
80 40
(a) g M /g E (b) 1
q
(c) (d) zero
(c) 0 (d) g E /g M 20
Electric charges and Field

42. Five charges +q, +5q, –2q, +3q and –4q are
situated as shown in the figure. The electric flux
due to this configuration through the surface S is

3q q q q
(a) (b)
0 0 (a)
80
(b)
480
5q 4q q q
(c) (d) (c) (d)
0 0 40 240
43. Figure shows a rod AB, which is bent in a 120º 45. Two charged thin infinite plane sheets of uniform
circular arc of radius R. A charge (–Q) is
surface charge density  + and  − , where
uniformly distributed over rod AB. What is the
+  – , intersect at right angle. Which of the
electric field E at the centre of curvature O?
following best represents the electric field lines
for this system

(a) (b)

(c) (d)

(a)
3 3Q ˆ
820 R2
()
i (b)
3 3Q ˆ
80 R 2
()
i 46. Two infinite planes each with uniform surface
charge density + are kept in such a way that the
angle between them is 30º. The electric field in
(c)
3 3Q ˆ
820 R2
()
i (d)
3 3Q ˆ
1620 R 2
i () the region shown between them is given by

44. A charge ‘q’ is placed at one corner of a cube of

a cube as shown in figure. The flux of
electrostatic field E through the shaded area is
Electric charges and Field

  3 xˆ 
(a) 1 +  yˆ + 
0  2  2 

(b)
 

20 
( ) xˆ 
1 + 3 yˆ + 
2

(c)
 

20 
( ) xˆ 
1 + 3 yˆ − 
2

  3 xˆ 
(d) 1 −  yˆ − 
20  2  2 
L
(a) 2
 qE 
g − m 
47. Consider a sphere of radius R which carries a
R  
uniform charge density . If a sphere of radius
2
L
EA (b) 2 2
is carved out of it, as shown, the ratio of  qE 
EB g − 
2

 m
magnitude of electric field E A and EB
respectively, at points A and B due to the L
(c) 2
remaining portion is  qE 
g + 
 m

L
(d) 2
q2 E 2
g2 −
m2

49. Chages –q and +q located at A and B,

respectively, constitute and electric dipole.
Distance AB = 2a, O is the mid point of the dipole
and OP is perpendicular to AB. A charge Q is
placed at P where OP = y and y >> 2a. The charge
21 18 Q experiences an electrostatic force F. If Q is now
(a) (b) moved along the equatorial line to P’ such that the
34 54
 y
17 18 OP ' =   , force on Q will be close to
(c) (d) 3
54 34
y 
48. A simple pendulum of length L is placed between  3  2a 
 
the plates of a parallel plate capacitor having
electric field E, as shown in figure. Its bob has
mass m and charge q. The time period of the
pendulum is given by
Electric charges and Field

Q Q
(a) (b)
30 60

(a) 27 F (b) 3F Q Q
(c) (d)
F 0 20
(c) (d) 9F
3
52. A solid ball of radius R has a charge density 
50. Determine the electric dipole moment of the  r
given by  = 0 1 −  for 0  r  R . The
system of three charges, placed on the vertices of  R
an equilateral triangle, as shown in the figure. electric field outside the ball is

 0 R3  40 R3
(a)  2 
(b)
 120 r  30 r 2

30 R3 0 R3
(c) (d)
40 r 2 0 r 2

53. A wooden block performs SHM on a frictionless

surface with frequency, u0 . The block carries a
charge +Q on its surface. If now a uniform
iˆ + ˆj electric field E is switched on as shown, then the
(a) 2ql ˆj (b) ( ql ) SHM of the block will be
2

ˆj − iˆ
(c) 3 al (d) − 3 ql ˆj
2

51. A charge Q is placed at a distance a/2 above the

centre of the square surface of edge a as shown in (a) of the same frequency and with shifted
the figure. The electric flux the square surface is mean position.

(b) of the same frequency and with the same

mean position

(c) of changed frequency and with shifted

mean position
Electric charges and Field

(d) of changed frequency and with the same −2C 2C

(a) (b)
mean position. 0 0

54. Let the there be spherically symmetric charge

10C 12C
distribution with charge density varying as (c) (d)
0 0
5 r 
 ( r ) = 0  −  upto r = R , where r is the
4 R 56. A charged ball B hangs from a silk thread S,
distance from the origin is given by which makes an angle  with a large charged
conducting sheet P, as shown in the figure. The
0 r   r  surface charge density  of the sheet is
−
30  4 R 
(a)
proportional to

40 r  5 r 
−
30  3 R 
(b)

0 r  5 r 
−
40  3 R 
(c)

40 r  5 r 
−
30  4 R 
(d)

(a) sin (b) tan

55. A disk of radius a/4 having a uniformly
distributed charge 6 C is placed in the x-y plane (c) cos (d) cot
with its centre at ( −a / 2,0,0) . A rod of length a 57. Three infinitely long charge sheets are placed as
carrying a uniformly distributed charge 8 C is shown in figure. The electric field at point P is
placed on the x-axis from x = a / 4 to x = 5a / 4 .
Two point charges –7 C and 3 C are placed at
( a / 4, −a / 4,0) and ( −3a / 4,3a / 4,0) ,
respectively. Consider a cubical surface formed
by six surfaces x  a / 2, y = 2, z = a / 2 . The
electric flux through this cubical surface is

2 4
(1) k̂ (2) k̂
0 0

2 4
(3) − k̂ (4) − k̂
0 0
 VIDYAPEETH 11

58. A charged oil drop is suspended in a uniform field (a) 3.3 10−18 C (b) 3.3 10−18 C
of 3  104 V / m so that it neither falls nor rises.
(c) 1.6 10−18 C (d) 4.8 10−18 C
The charge on the drop will be (take the mass of
the charge = 9.9 10−15 kg and g = 10 m / s 2 )
Electric charges and Field

ANSWER KEY

1. (C) 22. (A) 39. (B)

2. (D) 23. (B) 40. (B, C)
3. (D) 24. (B) 41. (C)
4. (B) 25. (2) 42. (D)
5. (B) 26. (17) 43. (A)
6. (A) 27. (3) 44. (D)
7. (D) 28. (A) 45. (B)
8. (A) 29. 3.16×10–9 46. (D)
9. (A) 30. (i)  = 60 47. (D)
10. (3) q1q2 48. (B)
(ii) T = + mg
11. (54) I2 49. (A)
12. (5440) (iii) R1 = 3mg, R2 = mg 50. (D)
13. (24) 1 q2 51. (B)
31. N
14. (12) 40 L2 52. (A)
15. (20) 32. (B) 53. (A)
16. (36) 33. (C) 54. (C)
17. (5.86 m/s) 34. (D) 55. (A)
18. 180º 35. (D) 56. (B)
19. (C) 36. (B,C) 57. (C)
20. (D) 37. (3) 58. (D)
21. (D) 38. (2)