QUESTIONS FOR SHORT ANSWER
1. The charge on a proton is + 1.6 × 10–19 C and that on an electron is –1.6 × 10–19 C. Does it mean that the electron has a charge 3.2 × 10–19 C less than the charge of a proton ?
2. Is there any lower limit to the electric force between two particles placed at a separation of 1 cm ?
3. Consider two particles A and B having equal charges and placed at some distance. The particle A is slightly displaced towards B. Does the force on B increase as soon as the particle A is displaced ? Does the force on the particle A increase as soon as it is displaced ?
4. Can a gravitational field be added vectorially to an electric field to get a total field ?
5. Why does a phonograph-record attract dust particles just after it is cleaned ?
6. Does the force on a charge due to another charge depend on the charges present nearby ?
7. In some old texts it mentioned that 4p lines of force originate from each unit positive charge. Comment on the statement in view of the fact that 4p is not an integer.
8. Can two equipotential surface cut each other ?
9. If a charge is placed at rest in an electric field, will its path be along a line of force ? Discuss the situation when the lines of force are straight and when they are curved.
10. Consider the situation shown in figure. What are the signs of q1 and q2 ? If the lines are drawn in proportion to the charge, what is the ratio q1/q2 ?
11. A point charge is taken from a point A to a point B in an electric field. Does the work done by the electric field depend on the path of the charge ?
12. It is said that the separation between the two charges forming an electric dipole should be small. Small compared to what ?
13. The number of electrons in an insulator is of the same order as the number of electrons in a conductor. What is then the basic difference between a conductor and an insulator ?
14. When a charged comb is brought near a small piece of paper, it attracts the piece. Does the paper become charged when the comb is brought near it ?
OBJECTIVE – I
1. Fig. shown some of the electronic field lines corresponding to an electric to an electric field. The figure suggests that -
(A) EA > EB > EC (B) EA = EB = EC
(C) EA = EC > EB (D) EA = EC < EB
2. When the seperation between two charges is incresased, the electric potential energy of the charges
(A) increases (B) decresaes
(C) remains the same (D) may increase or decrease
3. If a positive charge is shifted from a low-potential region to a high-potential region, the electric potential energy
(A) increases (B) decresaes
(C) remains the same (D) may increase or decrease
4. Two equal positive charges are kept at points A and B. The electric potential at the points between A and B
(excluding these points) is studied while moving from A to B. The potential [HCV_Chp.29_Obj_4]
(A) continuously increases (B) continuosly decreases
(C) increases then decreases (D) decreases than increases
5. The electric field at the origin is along the positive X-axis. A small circle is drawn with the centre at the origin
cutting theaxes at points A, B, C and D having coordinates (a,0), (0,a), (-a,0), (0,-a) respectively. Out of the points
on the periphery of the circle, the potential is minimum at -
(A) A (B) B (C) C (D) D
6. If a body is charged by rubbing it, is weight -
(A) remains precisely constant (B) increases slightly
(C) decreases slightly (D) may increase slightly or may decrease slightly
7. An electric dipole is placed in a uniform electric field. The net electric force on the dipole -
(A) is always zero (B) depends on the orientation of the dipole
(C) can never be zero (D) dependw on the strength of the dipole
8. Consider the situtaion fig. The work done in taking a point charge from P to A is WA, from P to B is WB and from P to C is WC
(A) WA < WB < WC (B) WA > WB > WC
(C) WA = WB = WC (D) none of these
9. A point charge q is rotated along a circle in the electric field generated by another point charge Q. The work done by the electric field on the roatating charge in one complete revolution is
(A) zero (B) positive (C) negative
(D) zero if the charge Q is at the centre and nonzero otherwise
OBJECTIVE – II
1. Mark out the correct options.
(A) The total charge of the universe is constant.
(B) The total positive charge of the universe is constant.
(C) The total negative charge of the universe is constant
(D) The total number of charged particles in the universe is constant
2. A point charge is brought in an electric field. The electric field at a nearby point
(A) will increase if the charge is positive (B) will decrease if the charge is negative
(C) may increase if the charge is positive (D) may decrease if the charge is negative
3. The electric field and the electric potential at a point are E and V respectively
(A) If E = 0, V must be zero (B) If V = 0, E must be zero
(C) If E = 0, V cannot be zero (D) If V= 0, E cannot be zero
4. The electric potential decreases uniformly from 120 V to 80 V as one moves on the X-axis from
x = – 1 cm to x = + 1 cm. The electric field at the origin
(A) must be equal to 20V/cm (B) may be equal to 20V/cm
(C) may be greater than 20V/cm (D) may be less than 20V/cm
5. Which of the following quantites do not depend on the choice of zero potential or zero potential energy
(A) potential at a point
(B) potential difference between two points
(C) potential energy of a two - charge system
(D) change in potential energy of a two-charge system
6. An electric dipole is placed in an electric field generated by a point charge
(A) The net electric force on the dipole must be zero
(B) The net electric force on the dipole may be zero
(C) The torque on the dipole due to the field must be zero
(D) The torque on the dipole due to the field may be zero
7. A proton and an electron are placed in a unifrorm electric field.
(A) The electric forces acting on them will be equal
(B) The magnitudes of the forces will be equal
(C) Their acelerations will be equal
(D) The magnitudes of the accelerations will be equal.
8. The electric field in a region is directed outward and is propertional to the distance r
form the origin. Taking the electric potential at the origin to be zero
(A) it is uniform in the region (B) it is proportional to r
(C) it is proportional to r2 (D) it increases as one goes away from the origin
EXERCISES
1. Find the dimensional formula of e0.
Ans. I2M–1 L–3T4
2. A charge of 1.0 C is placed at the top of the your college building and another equal charge at the top
of your house. Take the separation between the two charges to be 2.0 km. Find the force exerted by the
charges on each other. How many times of your weight is this force ?
Ans . 9/4 × 103 N = 2.25 × 103 N
3. At what separations should two equal charges, 1.0 C each, be placed so that the force between them
equals the weight of a 50 kg person ? (g = 9.8 m/s2)
(g = 9.8 m/s2)
Ans. 30/7 × 103 m
4. Two equal charges are placed at a separation of 1.0 m. What should be the magnitude of the charges
so that the force between them equals the weight of a 50 kg person ? (g = 9.8 m/s2)
Ans. × 10–4 C
5. Find the electric force between two protons separated by a distance of 1 fermi (1 fermi = 10–15 m).
The protons in a nucleus remain at a separation of this order.
Ans. 230.4 N
6. Two charges 2.0 × 10–6 C and 1.0 × 10–6 C are placed at a separation of 10 cm. Where should a
third charge be placed such that it experiences no net force due to these charges ?
7. Suppose the second charge in the previous problem is – 1.0 × 10–6 C. Locate the position where a
third charge will not experience a net force.
8. Two charged particles are placed at a distance 1.0 cm apart. What is the minimum possible magnitude
of the electric force acting on each charge ?
Ans. 2.3 × 10–24 N
9. Estimate the number of electrons in 100 g of water. How much is the total negative charge on these electrons ?
Ans. 3.35 × 1025, 5.35 × 106 C
10. Suppose all the electrons of 100 g water are lumped together to form a negatively charged particle and all the nuclei are
lumped together to form a positivively charged particle. If these two particles are placed 10.0 cm away from each other,
find the force of attraction between them. Compare it with your weight.
Ans. 2.56 × 1025 N
11. Consider a gold nucleus to be a sphere of radius 6.9 fermi in which protons and neutrons are distributed. Find the force
of repulsion between two protons situated at largest separation. Why do these protons not fly apart under this repulsion ?
Ans. 1.2 N
12. Two insulating small spheres are rubbed aganist each other and placed 1 cm apart. If they attract each other with a force
of 0.1 N, how many electrons were transferred from one sphere to the other during rubbing ?
Ans. 2 × 1011
13. NaCl molecule is bound due to the electric force between the sodium and the chlorine ions when one electron of sodium
is transferred to chlorine. Taking the separation between the ions to be
2.75 × 10–8 cm, find the force of attraction between them. State the assumptions (if any) that you have made.
Ans. 3.05 × 10–9 N
14. Find the ratio of the electric and gravitational forces between two protons.
Ans. 1.23 × 1036
15. Suppose an attractive nuclear force acts between two protons which may be written as
F = Ce–kr/r2. (a) Write down the dimensional formulae and appropriate SI units of C and k. (b) Suppose that k = 1 fermi–1 and that the repulsive electric force between the protons is just
balanced by the attractive nuclear when the separation is 5 fermi. Find the value of C.
Ans. (a) ML3T–2, L–1, N–m2, (b) 3.4 × 10–26 N–m2
16. Three equal charges, 2.0 × 10–6 C each, are held fixed at the three corners of an equilateral triangle of side 5 cm. Find the coulomb force experienced by one of the charges due to the rest two.
Ans. 24.9 N at 30° with the extended sides from the charge under consideration.
17. Four equal charges 2.0 × 10–6 C each are fixed at the four corners of a square of side 5 cm. Find the coulomb force experienced by one of the charges due to the rest three.
Ans. 27.5 N at 45° with the extended sides of the square from the charge under consideration.
18. A hydrogen atom contains one proton and one electron. It may be assumed that the electron revolves in a circle of radius
0.53 angstrom (1 angstrom = 10–10 m and is abbreviated as Å) with the proton at the centre. The hydrogen atom is said to be
in the ground state in this case. Find the magnitude of the electric force between the proton and the electron of a hydrogen atom in its ground state.
Ans. 8.2 × 10–8 N
19. Find the speed of the electron in the ground state of a hydrogen atom. The description of ground state is given in the previous problem.
Ans. 2.18 × 106 m/s
20. Ten positively charged particle are kept fixed on the X-axis at points x = 10 cm, 20 cm, 30 cm, ....., 100 cm.
The first particle has a charge 1.0 × 1.0–8 C, the second 8 × 10–8 C, the third 27 × 10–8 C and so on.
The tenth particle has a charge 1000 × 10–8 C. Find the magnitude of the electric force acting on a 1 C charge placed at the origin.
Ans. 4.95 × 105 N
21. Two charged particles having charge 2.0 × 10–8 C each are joined by an insulating string of length 1 m and the system is
kept on a smooth horizontal table. Find the tension in the string.
Ans. 3.6 × 10–6 N
22. Two identical balls, each having a charge of 2.00 × 10–7 C and a mass of 100 g, are suspended from a common point
by two insulating strings each 50 cm long. The balls are held at a separation 5.0 cm apart and then released.
Find (a) the electric force on one of the charged balls (b) the components of the resultant force on it along and perpendicular
to the string (c) the tension in the string (d) the acceleration of one of the balls. Answers are to be obtained only for the instant just after the release.
Ans. (a) 0.144 N
(b) zero, 0.095 N away from the other charge
(c) 0.986 N and
(d) 0.95 m/s2 perpendicular to the string and going away from the other charge
23. Two identical pith balls are charged by rubbing against each other. They are suspended from a horizontal rod through two strings
of length 20 cm each, the separation between the suspension points being 5 cm. In equilibrium, the separation between the balls is
3 cm. Find the mass of each ball and the tension in the strings. The charge on each ball has a magnitude 2.0 × 10–8 C.
Ans. 8.2 g, 8.2 × 10–2 N
24. Two small spheres, each having a mass of 20 g, are suspended from a common point by two insulating strings of length
40 cm each. The spheres are identically charged and the separation between the balls at equilibrium is found to be 4 cm.
Find the charge on each sphere.
Ans. 4.17 × 10–8 C
25. Two identical pith balls, each carrying a charge q, are suspended from a common point by two strings of equal length l.
Find the mass of each ball if the angle between the strings is 2q in equilibrium.
26. A particle having a charge of 2.0 × 10–4 C is placed directly below and at a separation of 10 cm from the bob of a
simple pendulum at rest. The mass of the bob is 100 g. What charge should the bob be given so that the string becomes loose.
Ans. 5.4 × 10–9 C
27. Two particles A and B having charges q and 2q respectively are placed on a smooth table with a separation d.
A third particle C is to be clamped on the table in such a way that the particles A and B remain at rest on the
table under electrical forces. What should be the charge on C and where should it be clamped ?
28. Two identically charged particles are fastened to the two ends of a spring of spring constant 100 N/m and natural
length 10 cm. The system rests on a smooth horizontal table. If the charge on each particle is 2.0 × 10–8 C, find the
extension in the length of the spring. Assume that the extension is small as compared to the natural length. Justify
this assmuption after you solve the problem.
Ans. 3.6 × 10–6 m
29. A particle A having a charge of 2.0 × 10–6 C is held fixed on a horizontal table. A second charged particle of mass
80 g stays in equilibrium on the table at a distance of 10 cm from the first charge. The coefficient of friction between
the table and this second particle is m = 0.2. Find the range within which the charge of this second particle may lie.
Ans. between ± 8.71 × 10–8 C
30. A particle A having a charge of 2.0 × 20–6 C and a mass of 100 g is placed at the bottom of a smooth inclined plane
of inclination 30° Where should another particle B, having same charge and mass, be placed on the incline so that it
may remain in equilibrium ?
Ans. 27 cm from the bottom
31. Two particles A and B, each having a charge Q, are placed a distance d apart. Where should a particle of charge q be
placed on the perpendicular bisector of AB so that it experiences maximum force ? What is the magnitude of this maximum force ?
32. Two particles A and B, each carrying a charge Q, are held fixed with a separation d between them. A particle C having mass m
and charge q is kept at the middle point of the line AB. (a) If it is displaced through a distance x perpendicular to AB, what would
be the electric force experiencd by it. (b) Assuming x << d, show that this force is proportional to x. (c) Under what conditions
will the particle C execute simple harmonic motion if it is released after such a small displacement ? Find the time period of the
oscillations if these conditions are satisfied.
34. The electric force experienced by a charge of 1.0 × 10–6 C is 1.5 × 10–3 N. Find the magnitude of the electric field at the position of the charge.
Ans. 1.5 × 103 N/C
35. Two particles A and B having charges of + 2.00 × 10–6 C and of – 4.00 × 10–6 C respectively are held fixed at a separation
of 20.0 cm. Locate the point(s) on the line AB where (a) the electric field is zero (b) the electric potential is zero.
Ans. (a) 48.3 cm from A along BA
(b) 20 cm from A along BA and cm from A along AB
36. A point charge produces an electric field of magnitude 5.0 N/C at a distance of 40 cm from it. What is the magnitude of the charge ?
Ans. 8.9 × 10–11 C
37. A water particle of mass 10.0 mg and having a charge of 1.50 × 10–6 C stays suspended in a room. What is the magnitude
of electric field in the room ? What is its direction ?
Ans. 65.3 N/C, upward
38. Three identical charges, each having a value 1.0 × 10–8 C, are placed at the corners of an equilateral triangle of side 20 cm.
Find the electric field and potential at the centre of the triangle.
Ans. zero 2.3 × 103 V
39. Positive charge Q is distributed uniformly over a circular ring of radius R. A particle having a mass m and a negative charge q,
is placed on its axis at a distance x from the centre. Find the force on the particle. Assuming x << R, find the time period of oscillation
of the particle if it is released from there.
40. A rod of length L has a total charge Q distributed uniformly along its length. It is bent in the shape of a semicircle. Find the
magnitude of the electric field at the centre of curvature of the semicircle.
41. A 10 cm long rod carries a charge of + 50 mC distributed uniformly along its length, Find the
magnitude of the electric field at a point 10 cm from both the ends of the rod.
Ans. 5.2 × 107 N/C
42. Consider a uniformly charged ring of radius R. Find the point on the axis where the electric field is maximum.
43. A wire is bent in the form of a regular hexagon and a total charge q is distributed uniformly on it. What is the
electric field at the centre ? You may answer this part without making any numerical calculations.
Ans. zero
44. A circular wire-loop of radius a carries a total charge Q distributed uniformly over its length. A small length dL
of the wire is cut off. Find the electric field at the centre due to the remaining wire.
45. A positive charge q is placed in front of a conducting solid cube at a distance d from its centre.
Find the electric field at the centre of the cube due to the charges appearing on its surface. [2]
Sol. 
Due to presence of +q charge, charge is redistributed on conducting solid sphere in such a way that net electric
field inside conducting sphere is zero.
46. A pendulum bob of mass 80 mg and carrying a charge of 2 × 10–8 C is at a distance d from its centre.
Find the electric field at the centre of the cube due to the charges appearing on its surface.
Ans. 8.8 × 10–4 N
47. A particle of mass m and charge q is thrown at a speed u against a uniform electric field E.
How much distance will it travel before coming to momentary rest ?
Ans. mu2/2qE
48. A particle of mass 1 g and charge 2.5 × 10–4 C is released from rest in an electric field of
1.2 × 104 N/C. (a) Find the electric force and the force of gravity acting on this particle. Can one of these
forces be neglected in comparison with the other for approximate analysis ? (b) How long will it take for the particle to travel a distance of 40 cm ?
(c) What will be the speed of the particle after travelling this distance ? (d) How much is the work done by the electric force on the particle during this pariod ?
Ans. (a) 3.0 N, 9.8 × 10–3 N, (b) 1.63 × 10–2 s
(c) 49.0 m/s (d) 1.20 J
49. A ball of mass 100 g and having a charge of 4.9 × 10–5 C is releasd from rest in a region where a horizontal electric field of
2.0 × 104 N/C exists. (a) Find the resultant force acting on the ball. (b) What will be the path of the ball ? (c) Where will the ball be at the end of 2s ?
Ans. (a) 1.4 N making an angle of 45° with and
(b) straight line along the resultant force
(c) 28 m from the starting point on the line of motion
50. The bob of a simple pendulum has a mass of 40 g and a positive charge of 4.0 × 10–6 C. It makes 20 oscillations in 45 s.
A vertical electric field pointing upward and of magnitude 2.5 × 104 N/C is switched on. How much time will it now take to complete 20 oscillations ?
Ans. 52 s
51. A block of mass m and having a charge q is placed on a smooth horizontal table and is connected to a wall through an
unstressed spring of spring constant k as shown in figure. A horizontal electric field E parallel to the spring is switched on.
Find the amplitude of the resulting SHM of the block.
Ans. qE/k
52. A block of mass m containing a net positive charge q is placed on a smooth horizontal table which terminates in a vertical wall
as shown in figure. The distance of the block from the wall is d. A horizontal electric field E towards right it switched on.
Assuming elastic collisions (if any) find the time period of the resulting oscillatory motion. Is it a simple harmonic motion ?
53. A uniform electric field of 10 N/C exists in the vertically downward direction. Find the increase in the electric potential as one goes up through a height of 50 cm.
54. 12 J of work has to be done against an existing electric field to take a charge of 0.01 C from A to B. How much is the potential difference VB – VA ?
Ans. 1200 volts
55. Two equal charges, 2.0 × 10–7 C each, are held fixed at a separation of 20 cm. A third charge of equal magnitude is placed midway
between the two charges. It is now moved to a point 20 cm from both the charges. How much work is done by the electric field during the process ?
Ans. 3.6 × 10–3 J
56. An electric field of 20 N/C exists along the X-axis in space. Calculate the potential difference
VB – VA where the points A and B are given by,
(a) A = (0, 0) ; B = (4m, 2m)
(b) A = (4m, 2m) ; B = (6m, 5m)
(c) A = (0, 0) ; B = (6m, 5m).
Do you find any relation between the answers of parts (a), (b) and (c) ?
Ans. (a) – 80 V (b) – 40 V (c) – 120 V
57. Consider the situation of the previous problem. A charge of –2.0 × 10–4 C is moved from the point A to the point B.
Find the change in electrical potential energy VB – VA for the cases (a), (b) and (c).
Ans. 0.016 J, 0.008 J, 0.024 J
58. An electric field N/C exists in the space. If the potential at the origin is taken to be zeror, find the potential at (2m, 2m).
Ans. –100 V
59. An electric field exists in the space, where A = 10 V/m2. Take the potential at (10 m, 20 m) to be zero. Find the potential at the origin.
Ans. 500 V
60. The electric potential existing in space is V(x, y, z) = A(xy + yz + zx). (a) Write the dimensional formula of A.
(b) Find the expression for the electric field. (c) If A is 10 SI units, find the magnitude of the electric field at (1 m, 1 m, 1 m).
61. Two charged particles, having equal charges of 2.0 × 10–5 C each, are brought from infinity to within a separation of 10 cm.
Find the increase in the electric potential energy during the process.
Ans. 36 J
62. Some equipotential surfaces are shown in figure. What can you say about the magnitude and the direction of the electric field ?
Ans. (a) 200 V/m making an angle 120° with the X-axis
(b) radially outward, decreasing with distance as
E = 6V - m / r2
63. Consider a circular ring of radius r, uniformly charged with linear charge density l. Find the electric potential at a point on
the axis at a distance x from the centre of the ring. Using this experssion for the potential, find the electric field at this point.
64. An electric field of magnitude 1000 N/C is produced between two parallel plates having a separation of 2.0 cm as shown in figure.
(a) What is the potential difference between the plates ?
(b) With what minimum speed should an electron be projected from the lower plate in the direction of the field so that it may reach the upper plate ?
(c) Suppose the electron is projected from the lower plate with the speed calculated in part. (b) and the direction of projection makes an angle of 60º
with the field. Find the maximum height reached by the electron. (Neglect gravity)
Sol. 
E = 1000 N/C
(a) V = E.d. = 1000 × 2/100 = 20 volt
(b) by work energy theorem
65. A uniform field of 2.0 N/C exists in space in x-direction.
(a) Taking the potential at the origin to be zero, write an expression for the potential at a general point (x, y, z). (b) At which points,
the potential is 25 V ? (c) If the potential at the origin is taken to be 100 V, what will be the expression for the potential at a general point ?
(d) What will be the potential at the origin if the potential at infinity is taken to be zero ? Is it practical to choose the potential at infinity to be zero ?
Ans. (a) –(2.0 V/m) x (b) points on the plane x = –12.5 m
(c) 100 V – (2.0 V/m) x (d) infinity
66. How much work has to be done in assembling three charged particles at the vertices of an equilateral triangle as shown in figure ?
Ans. 234 J
67. The kinetic energy of a charged particle decreases by 10 J as it moves from a point at potential 100 V to a point at potential 200 V. Find the charge on the particle.
Ans. 0.1 C
68. Two identical particles, each having a charge of 2.0 × 10–4 C and mass of 10 g, are kept at a separation of 10 cm and then released.
What would be the speeds of the particles when the separation becomes large ?
Ans. 600 m/s
69. Two particles have equal masses of 5.0 g each and opposite charges of +4.0 × 10–5 C and
–4.0 × 10–5 C. They are released from rest with a separation of 1.0 m between them. Find the speeds of the particles when the separation is reduced to 50 cm.
Ans. 54 m/s for each particle
70. A sample of HCl gas is placed in an electric field of 2.5 × 104 N/C. The dipole moment of each HCl molecule is 3.4 × 10–30 C–m. Find the maximum torque that can act on a molecule.
Ans. 8.5 × 10–26 N–m
71. Two particles A and B, having opposite charges 2.0 × 10–6 C and –2.0 × 10–6 C, are placed at a separation of 1.0 cm.
(a) Write down the electric dipole moment of this pair. (b) Calculate the electric field at a point on the axis of the dipole 1.0 cm away from the centre .
(c) Calculate the electric field at a point on the perpendicular bisector of the dipole and 1.0 m away from the centre.
Ans. (a) 2.0 × 10–8 C–m (b) 360 N/C (c) 180 N/C
72. Three charges are arranged on the vertices of an equilateral triangle as shown in figure. Find the dipole moment of the combination.
Ans. , along the bisector of the angle at 2q, away from the triangle
73. Find the magnitude of the electric field at the point P in the configuration shown in figure for
d >> a. Take 2qa = p.
.
74. Two particles, carrying charges – q and +q and having equal masses m each, are fixed at the ends of a light rod of length a to form a dipole.
The rod is clamped at an end and is placed in a uniform electric field E with the axis of the dipole along the electric field.
The rod is slightly tilted and then released. Neglecting gravity find the time period of small oscillations.
75. Assume that each atom in a copper wire contributes one free electron. Estimate the number of free electrons in a copper wire
having a mass of 6.4 g (take the atomic weight of copper to be
64 g/mol).
Ans. 6 × 1022