electrostatics-i physics

ELECTROSTATICS-I PHYSICS

59

CLASS ASSIGNMENT

Questions Based on Charge & Coulomb’s law

1. A polythene piece rubbed with wool is found to have a negative charge of 3.2 10-7

C

(i) Estimate the number of electrons transferred.

(ii) Is there a transfer of mass from wool to polythene?

2. The electrostatic force of repulsion between two positively charged ions carrying equal charges is 3.7

10-9

N, when they are separated by a distance of 5Å. How many electrons are missing from each ion?

3. A pith ball A of mass 9 10-5

kg carries a charge of 5 μC. What must be the magnitude and sign of the

charge on a pith ball B held 2cm directly above the pith–ball A, such that the pith–ball A remains

stationary?

4. The distance between the electron and proton in hydrogen atom is 5.3 10-11

m. Determine the magnitude

of the ratio of electrostatic and gravitational force between them.

Given me = 9.1 10-31

kg, mp = 1.67 10-27

kg, e = 1.6 10-19

C and G = 6.67 10–11

Nm2kg

-2.

5. (a) Two insulated charged copper spheres A and B have their centres separated by a distance of

50 cm. What is the mutual force of electrostatic repulsion if the charge on each is 6.5 10-7

C? The radii

of A and B are negligible compared to the distance of separation.

(b) What is the force of repulsion if (i) each sphere is charged double the above amount, and the distance

between them is halved. (ii) the two spheres are placed in water? (Dielectric constant of water = 80)

6. Suppose the spheres A and B in above question have identical sizes. A third sphere of the same size but

uncharged is brought in contact with the first, then brought in contact with the second, and finally

removed from both. What is the new force of repulsion between A and B?

7. Three charges +Q, q, + Q are placed respectively, at distance, 0, d/2 and d from the origin, on the x-axis.

If the net force experienced by + Q, placed at x = 0, is zero, then value of q is : [JEE (M) 2019]

(A) +Q/2 (B) –Q/2

(C) –Q/4 (D) +Q/4

8. Two identical spheres, having charges of opposite sign attract each other with a force of 0.108 N when

separated by 0.5 m. The spheres are connected by a conducting wire, which then removed, and thereafter

they repel each other with a force of 0.036 N. What were the initial charges on the spheres?

9. Two similar balls each having mass m and charge q are hung from silk threads of length l. Prove that

equilibrium separation

3/1

0

2

2

mg

lqx

When each thread makes a small angle θ with the vertical.

10. Five point charges, each of value +q coulomb are placed on five vertices of a regular hexagon of side L

metres. Find the magnitude of force on a charge –q coulomb placed at the centre of the hexagon.

11. A charge Q is placed at each of the opposite corners of a square. A charge of q is placed at each of the

other two corners. (a) if the resultant force on Q is zero, how are Q and q related? (b) Could q be chosen

to make the resultant force on every charge zero?

12. Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of

30o with each other. When suspended in a liquid of density 800 kg m

-3, the angle remains the same. What

is the dielectric constant of medium? The density of the material of the sphere is 1600 kg m-3

.

PHYSICS ELECTROSTATICS-I

60

13. Calculate the coloumb force on charge q0 due to uniform linear charge distribution as shown.

Questions Based on Electric Field

14. A pendulum of mass 80 milligram carrying a charge of 2 10-8 C is at rest in a horizontal uniform electric

field of 2 104 Vm

-1. Find the tension in the thread of the pendulum and the angle it makes with the vertical.

15. A copper ball of density 8.6 g cm-3, 1cm in diameter is immersed in oil of density 0.8 g cm

-3. What is the

charge on the ball, if it remains just suspended in oil in an electric field of intensity 3600 Vm-1 acting in the

downward direction?

16. An oil drop of 12 excess electrons is held stationary under a constant electric field of

2.55 104 Vm

-1 in Millikan’s oil drop experiment. The density of the oil is 1.26 g cm

-3. Estimate the

radius of the drop. (g = 9.81 m/s2, e = 1.60 10

-19 C)

17. Two point charges of +16µC and –9µC are placed 8 cm apart in air. Determine the position of the point

at which the resultant field is zero.

18. Four charges +q, +q, –q, –q are placed respectively at the four corners A, B, C and D of a square of side

a. Calculate the electric field at the centre of the square.

Questions Based on Electric Dipole

19. Two charges ±10µC are placed 5.00 mm apart. Determine electric field at (a) a point P on the axis of the

dipole 15 cm away from its centre O on the side of the positive charge, (b) a point Q, 15 cm away from O

on a line passing through O and normal to the axis of the dipole.

20. A test charge placed on the axis of an electric dipole at a distance of 25 cm from its midpoint experiences

a force of 5 dyne. The same test charge, when placed at a distance of 15 cm, experiences a force of 27

dyne. Calculate the length of the electric dipole.

21. Calculate electric dipole moment due to following arrangement of charges.

(a) (b)

22. An electric dipole of length 2cm is placed with its axis making an angle of 60o to a uniform electric field

of 105 N/C. If it experiences a torque of magnitude 8√3 Nm, calculate the

(i) Magnitude of the charge on the dipole, and

(ii) Potential energy of the dipole

23. A molecule of a substance has permanent electric dipole moment equal to 10-29

Cm. A mole of this

substance is polarized (at low temperature) by applying a strong electrostatic field of magnitude (106

V/m). The direction of the field is suddenly changed by an angle of 60o. Estimate the heat released by the

substance in aligning its dipoles along the new direction of the field. For simplicity assume 100%

polarization of the sample.

24. In a certain region of space, electric field is along the z –direction throughout. The magnitude of electric

field, is however, not constant but increases uniformly along the +ve z–direction at the rate of 105 NC

-1m

-1.

What are the force and torque experienced by a system having a total dipole moment equal to 10-7

Cm in

the –ve z-direction?


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25. A point particle of mass M is attached to one end of massless rigid non –conducting rod of length L.

Another particle of same mass is attached to other end of the rod. The two particles carry charges +q and

–q respectively. This arrangement is held in a region of uniform electric field E such that the rod makes a

small angle θ (≈50) with the field direction. Find the expression for the minimum time needed for the rod

to become parallel to the field after it is set free.

Questions Based on Electric Field lines

26. Draw electric field lines for the charge arrangements shown in the diagram.

(a) (b)

27. A particle of mass m and charge (–q) enters the region between the two charged plates initially moving

along x-axis with speed vx as shown. A uniform electric field is maintained between the plates. Show that

the vertical deflection of the particle at the far edge of the plate is

2

22 x

qEL

mv. Where will the charged

particle strike the upper plate for the following data. 6 1 2 1 19 31

2.0 10 ms ; 0.5 cm; E 9.1 10 NC , 1.6 10 C; 9.1 10 kgx

v d q m

Questions Based on Electric Flux & Gauss’s Theorem

28. Find the ratio of electric flux from S1 and S2.

29. Calculate the number of electric field lines starting from 1 C charge.

30. If the electric field is given by ⃗ ̂ ̂ ̂ N/C, calculate the electric flux through a surface of area

100 units lying in the X –Y plane

31. Five thousand lines of force enter a certain volume of space and three thousand lines emerge from it.

What is the total charge in coulomb within this volume?

32. A point charge +10 µC is a distance 5cm directly above the centre of a square of side 10cm as shown in

figure. What is the magnitude of the electric flux through the square?

33. The length of each side of a cubical closed surface is l. If charge q is situated on one of the vertices of the

cube then the flux passing through each face of the cube will be:

(A) q/6 ε0 (B) q/10ε0

(C) q/24 ε0 (D) q/16 ε0


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34. The electric field components in figure are Ex = α x1/2

, Ey = Ez =0, in which α = 800 N/Cm2. Calculate (i)

the flux φE through the cube and (ii) the charge within the cube. Assume that a = 0.1m.

35. A charge Q is distributed uniformly on a ring of radius r. A sphere of equal radius r is constructed with

its centre at the periphery of the ring. Find the electric flux through the sphere.

36. A long string with charge per unit length λ on it passes through the opposite faces of a cube of side a. The

electric flux through the cube is:

(A) λa/ε0 (B) √2 λa/ε0

(C) √3 λa/ε0 (D) 2 λa/ε0

37. In the above problem, the maximum flux through the cube can be

(A) λa/ε0 (B) √2 λa/ε0

(C) √3 λa/ε0 (D) 2 λa/ε0

38. Calculate electric flux through one of the circular faces of the cylinder as shown

39. Prove that equilibrium of test charge in the presence of electric fields only is necessarily unstable.

40. Prove that electric field in a small cavity on the surface of a spherical shell with surface charge density

is 02

in the outward direction.

41. For a charged soap bubble if inside and outside pressure are equal then calculate the charge on the

bubble.

42. Charge q is placed on the vertex of a cone. Calculate the flux through the circular face of the curve.

43. A solid ball of radius R has a charge density given by 0 1

r

R

for 0 r R . The electric

field outside the ball is: [JEE (M) 2018]

(A)

3

0

2

012

R

r

(B)

3

0

2

0

4

3

R

r

(C)

3

0

2

0

3

4

R

r

(D)

3

0

2

0

R

r


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HOME ASSIGNMENT

Questions Based on Properties of Charges

Objective Problems

1. Which one of the following statement regarding electrostatics is wrong?

(A) Charge is quantized

(B) Charge is conserved

(C) There is an electric field near an isolated charge at rest

(D) A stationary charge produces both electric and magnetic fields

2. If linear charge density of a wire of length L depends on distance x from one end as 0 x

L

(A) 0L (B) 0

2

L

(C) 0

4

L (D) NOT

3. Surface charge density of a thin disc having radius R varies with distance r from centre as

0 , 0R

rr

then total charge of disc is:

(A) 3

02 R (B) 2

02 R

(C) 2

02 2 R (D) 2

02 R

4. Linear charge density of a half ring varies with as 0 cos , then find total charge of ring.

(A) 0R (B) Zero

(C) 02 R (D) 02 R

Subjective Problems

5. Design an experiment which proves that electric force dominates the gravitational force.


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6. If electric force between two charged particles were independent of distance, would the charged glass rod

still cause polarization of neutral papers? Why or why not? Would the neutral paper still be attracted to

the glass rod? Why or why not?

7. When a hard rubber rod is given a negative charge by rubbing it with wool, how will the charge transfer take place?

8. The leaves of a positively charged electroscope diverge more when an object is brought near the knob of

the electroscope. What is the nature of the object?

9. Two objects A and B are attracted to each other. Objects B and C are also attracted to each other. If A

and C are held close together what type of force exist between them?

10. How does the charge of an electron differ from the charge of a proton?

11. A soap bubble is given a negative charge. What happens to its radius?

12. Two identical metal balls with similar charges are brought in contact. The charge of one of the balls

increases by 40%. Find the ratio of initial charges of balls.

13. How many coulombs of charge are on the electrons in cupronicle coin? Use the following method to find

the answer.

(a) Find the number of atoms in cupronickel coin. A cupronickel coin has a mass of about 5 g.

Cupronickel is 75 percent Cu and 25 percent Ni, so each mole of the coin’s atoms will have a mass

of about 62 g.

(b) Find the number of electrons in the coin. On average, each atom has 28.75 electrons.

(c) Find the charge on the electrons.

14. Electrons and positrons are produced by the nuclear transformations of protons and neutrons known as

beta decay.

(a) If a proton transforms into a neutron, is an electron or a positron produced?

(b) If a neutron transforms into a proton, is an electron or a positron produced?

15. If a cat repeatedly rubs against your cotton slacks on a dry day, the charge transfer between the cat hair

and the cotton can leave you with an excess charge of 2.00 mC.

(a) How many electrons are transferred between you and the cat?

You will gradually discharge via the floor, but if instead of waiting, you immediately reach toward a

faucet, a painful spark can suddenly appear as your fingers near the faucet.

(b) In that spark, do electrons flow from you to the faucet or vice versa?

(c) Just before the spark appears, do you induce positive or negative charge in the faucet?

(d) If, instead, the cat reaches a paw toward the faucet, which way do electrons flow in the resulting spark?

16. Calculate protonic charge in 100 cc of water.

17. Does charge depend on the frame of reference?

18. Earth’s atmosphere is constantly bombarded by cosmic ray protons that originate somewhere in space. If

the protons all passed through the atmosphere, each square meter of Earth’s surface would intercept

protons at the average rate of 1500 protons per second. What would be the electric current intercepted by

the total surface area of the planet?

19. Some of the free electrons in the conductor say Copper move very rapidly at the speed of 106

ms–1

or

more. Why do not these electrons fly out of the conductor completely?

20. Can two similarly charged bodies attract each other?

21. Identify the element denoted by X in the following reaction 1 12

1 6H + C X .


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22. What does q1 + q2 = 0 signify in electrostatics? (2001)

Questions Based on Method of Charging

Objective Problems

23. A positively charged rod is brought close to L, but not touching it, as shown. The two spheres are slightly

separated and the rod is then withdrawn. As a result:

(A) both spheres are neutral (B) both spheres are positive

(C) both spheres are negative (D) L is negative and M is positive

Subjective Problems

24. Tyres of aeroplanes are made slightly conducting. Why?

25. Before putting oil in oil tank of aeroplane, nozzle is touched to its body from distance. Why?

26. Why do we prefer gold leaves in gold leaf electroscope?

27. Why cotton swabs are readily used in surgical procedures?

28. If a neutral object made of substance A rubs a neutral object made of substance B, then A becomes

positively charged and B becomes negatively charged. If, however, a neutral object made of substance A

is rubbed against a neutral object made of substance C, then A becomes negatively charged. What will

happen if a neutral object made of substance B is rubbed against a neutral object made of substance C?

29. Fig shows an uncharged, insulated conductor AB, which is in contact with gold leaf electroscope C. A

positively charged rod is brought near the end A. Answer the following questions.

(i) What charge is developed at A and why?

(ii) What charge is present at B, C and D?

(iii) How are gold leaves affected?

(iv) If positively charged rod is taken away, give your observations.

30. We cannot charge a copper rod held in our hand by rubbing. Why?

31. Give a simple method to distinguish between a conductor and an insulator.

32. A broad metal plate is connected to Earth through an ammeter and grounded through it, A positively

charged body passes along a straight path very close to the plate. How will the current vary with time?


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33. Taking off a nylon shirt sometimes gives crackling sound or sparking in dry weather why?

34. White paper strip when ironed is attracted by T.V screen. Why?

35. An ironed paper strip, when folded, the two parts repel each other. Why?

36. A trolley in operation theatre carrying ether has metallic ropes attached to it and touching the ground. Why?

37. Why are fan blades more dusty at the edges?

38. Why do gramophone record or mirror becomes dusty immediately after it is rubbed with dry cloth?

39. Explain the principle of electrostatic paint spraying and powder coating in case of vehicles.

40. How are ash particles collected in chimneys?

41. If you peel two strips of transparent tape off the same roll and immediately let them hang near each other,

will they attract or repel each other? Now if you then stick the sticky side of one to the shiny side of the

other and rip them apart, will they attract or repel each other? Explain your answers. [Hint: Tear off one strip and it leaves electrons behind, and so the strip is positively charged. The roll though is not negatively charged because it is

earthed by the hand holding it. The excess negatives repel each other away through the hand. Tear off the next strip and once more it leaves electrons

behind, the new strip is also positively charged and will repel the first strip. Tear two strips apart and one will leave electrons behind on the other. Meaning

that one strip is positive and the other is negative and they will attract each other.]

42. (a) It is difficult to carry out electrostatic experiments on humid days. Why?

(b) A neutral object is brought closer to the disc of the charged electroscope without touching the two to

each other. Will the divergence of the leaves of the electroscope increase? Explain.

Questions Based on Coulomb’s law

Objective Problems

43. The proton in the nucleus of the Hydrogen atom attracts the electron that orbits it with electric force.

Relative to this force, how does the electron attracts the proton?

(A) greater force (B) lesser force

(C) same force (D) depends on the position of electron

44. If a proton at a particular distance from a charged particle is repelled with a given force, F. what will be

the new force if the proton is three times farther away from the particle?

(A) F

9 (B)

F

8

(C) F

3 (D)

F

2

45. Two charges equal in magnitude and similar in polarity are placed at a certain distance apart and force acting

between them is F. If 75% charge of one is transferred to another. What is the new force between the charges?

(A)7

F8

(B)7

F4

(C)7

F16

(D) F


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46. If the separation of the charged particles is increased by 1%, then what will be the change in force of the

interaction between them?

(A) 1 % (B) –1 %

(C) 2 % (D) –2 %

47. The force between two point charges placed in vacuum at distance 1 mm is 18 N. If a glass plate of

thickness 1mm and dielectric constant 6, is introduced between the charges then what would be the new

force between them?

(A) 9 N (B) 18 N

(C) 3 N (D) 108 N

48. Two point charges are kept separated by 4 cm of air and 6 cm of a dielectric of relative permittivity 4.

The equivalent air separation between them so far their coulombian interaction is conserved is

(A) 10 cm (B) 8 cm

(C) 5 cm (D) 16 cm

49. Is the force between two charged particles affected due to the presence of third charge?

(A) Yes (B) No

(C) depends on the position of charges (D) Insufficient data

50. The electrostatic force between an -particle and an electron separated by a distance of 1 Å is

(A) 2.3 × 10–8

N attractive (B) 2.3 × 10–8

N repulsive

(C) 4.6 × 10–8

N attractive (D) 4.6 × 10–8

repulsive

51. Two point charges in air at a distance of 20 cm from each other interact with a certain force. At what

distance from each other should these charges be placed in oil of relative permittivity 5 to obtain the

same force of interaction?

(A) 8.94 × 10–2

m (B) 0.894 × 10–2

m

(C) 89.4 × 10–2

m (D) 8.94 × 102 m

52. The force between two point charges in vacuum is 15N. If a brass plate is introduced between the two

charges, then force between them

(A) Becomes zero (B) Remains the same

(C) Becomes 30 N (D) Becomes 60 N

53. Four point charges qA = 2µC, qB = –5µC, qC = 2µC, qD = –5µC are located at the corners of a square ABCD of

side 10cm. What is the magnitude of force on a charge of 1µC placed at the centre of the square?

(A) 31.8 10 N (B)

21.8 10 N

(C) 11.8 10 N (D) 0 N

54. Charges of +5µC, +10µC and –10µC are placed in air at the corners A, B and C of an equilateral triangle

ABC, having each side equal to 5cm. What is the magnitude of the resultant force on the charge at A?

(A) 31.8 10 N (B) 180 N

(C) 11.8 10 N (D) 0 N


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55. Two pieces of copper each weighing 10 g are placed at a distance of 10cm from each other. One electron

from per 1000 atoms of one piece is transferred to the other piece of copper. What will be the Coulomb

force between the two pieces after the transfer of electrons? The atomic mass of copper is 63.5g mol-1

.

Avogadro’s number, N = 6 1023

, charge on electron, e = –1.6 10-19

C

(A) 82.056 10 N (B)

92.056 10 N

(C) 142.056 10 N (D) 0 N

56. A negative point charge 2q and a positive charge q are fixed at a distance l apart. At what distance from

positive charge q, a negative charge of magnitude q be placed on the line connecting the charges for the

positive charge to be in equilibrium?

(A) l (B) 2l

(C)2

l (D) 3l

57. Mid way between the two equal and similar charges, we place the third equal and similar charge. Which

of the following statements is correct, concerned to the equilibrium along the line joining the charges?

(A) The third charge experienced a net force inclined to the line joining the charges

(B) The third charge is in stable equilibrium

(C) The third charge is in unstable equilibrium

(D) The third charge experiences a net force perpendicular to the line joining the charges

58. Two fixed charges, q1 = +1.00 C and q

2 = –4.00 C, are 0.200 m apart. Where should be a test charge q

be placed so that net force on it will be zero?

(A) 0.40 m to the right of q1 (B) 0.13 m to the right of q

1

(C) 0.20 m to the left of q1 (D) 0.067 m to the left of q

1

59. The three charges each of magnitude 5 × 10–6

C and similar in nature are placed at vertices of an equilateral

triangle of side 10cm. The force exerted on the charge of 1 C placed at centre of triangle in newton will be

(A) 13.5 (B) zero

(C) 4.5 (D) 6.75

60. ABC is a right angle triangle AB = 3cm, BC = 4cm. Charges + 15, +12, –12 esu are placed at A, B and C

respectively. The magnitude of the force experienced by the charge at B in dyne is-

(A) 125 (B) 35

(C) 22 (D) 0

61. Two identical point charges are held on a smooth horizontal floor at a distance d apart by a non-

conducting string with tension T. If a third identical point charge is fixed vertically above at a distance of

d from both the point charges then what will be the new tension in the string.

(A) T (B) 2T

(C) 3T/2 (D) none


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62. Two small spheres each having mass m kg and charge q coulomb are suspended from a point by

insulating threads each l meter long but of negligible mass. If θ is the angle, each thread makes with the

vertical when equilibrium has been attained, then what is the value of q2?

(A) (mgl2sin

2θ tanθ) 4πε0 (B) (2 mgl

2sin

2θ tanθ) 4πε0

(C) (4 mgl2sin

2θ tanθ) 4πε0 (D) (8 mgl

2sin

2θ tanθ) 4πε0

63. Two identical spheres each of radius R are kept at centre-to-centre spacing 4R as shown in the figure.

They are charged and the electrostatic force interaction between them is first calculated assuming them

point like charges at their centres and the force is also measured experimentally. The calculated and

measured forces are denoted by Fc and Fm respectively. (Fc and Fm denote magnitude of force):

(A) When they carry charges of the same sign Fc > Fm and when they carry charges of opposite signs Fc <

Fm only when they are insulators

(B) When they carry charges of the same sign Fc > Fm and when they carry charges of opposite signs Fc <

Fm only when they are conductors.

(C) When they carry charges of the same sign Fc < Fm and when they carry charges of opposite signs Fc >

Fm irrespective of their material.

(D) When they carry charges of the same sign Fc > Fm and when they carry charges of opposite signs Fc <

Fm irrespective of their material.

64. Three charges are separated from each other as shown below. Choose correct statement(s):

(a) If q1 and q2 are in equilibrium then entire system will be in equilibrium

(b) If q0 is in equilibrium then entire system is in equilibrium

(c) For equilibrium of system q1 and q2 must have opposite sign

(d) For equilibrium of system q1 and q2 must have same sign

(A) Only A & B (B) Only A, B & C

(C) Only A & D (D) All

65. Two particles which have masses m, 2m and charges 2q, q respectively are hung by massless threads

from a point as shown in equilibrium particles are on same horizontal line what can be the relation in 1

& 2. (1 & 2 are not upto scale in figure)

(A) 1 > 2 (B) 1 < 2

(C) 1 = 2 (D) More information is required


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Subjective Problems

66. Gravitational force is very weak compared to electric force. Even then it is pervasive/dominant in daily life. Why?

67. Two point charges q1 and q2 are placed close to each other. What is the nature of force between the

charges when q1q2 < 0?

68. Why is it difficult to take large number of electrons from copper penny?

69. What is the dielectric constant of a medium?

70. Force of attraction between two point charges placed at a distance d apart in a medium is F. What would

be the distance apart in the same medium so that the force of attraction between them becomes one-

fourth its pervious value?

71. Two point charges +10 C and + 20 C are separated by a distance ‘r’ in air. If an additional charge of –

8 C is given to each, by what factor does the force between the charges, change?

72. Two conducting identical sized spheres A and B carrying charges +30 C and –10 C separated by a

distance of 1 metre in air, are made to touch each other. They are then again separated by the same

distance. Compare the forces between them in the two cases.

73. Is there any difference between coulomb’s force between two free protons and two free electrons

separated by similar distances?

74. Two point charges having equal charges separated by 1 m distance experience force of 8 N. What will be

force experienced by them, if they are held in water, at same distance? (2011 C)

75. Two equal balls having equal positive charge q are suspended by two insulating strings of equal length.

What would be the effect on the force when a plastic sheet is inserted between the two? (2014)

76. Plot a graph showing the variation of coulomb force F versus 2

1

r, where r is the distance between the

two charges of each pair of charges: (1C, 2C) and (2C, –3C). Interpret the graphs obtained.

(2011)

77. Two point charges are 3m apart and their combined charge is 20 .C If the force between them is 0.075

N, what are the charges?

Questions Based on Electric field

Objective Problems

78. A small metallic ball is suspended freely in a uniform electric field with the help of an insulating thread.

If high energy X –rays are made incident on the ball then

(A) the ball gets displaced in a direction opposite to that of electric field

(B) the ball gets displaced in the direction of electric field

(C) the ball will not get displaced

(D) nothing can be said

79. A particle of mass m and carrying charge q is placed at point P between the plates P1 and P2 (figure). A

constant electric field exists from P1 to P2. The path of particle when released will be:

(A) (B)


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(C) (D)

80. A copper ball of density c and diameter d is immersed in oil of density 0. What charge should be

present on the ball, so that it could be suspended in the oil, if a homogeneous electric field E is applied

vertically upward?

(A) 2

0

6

cd gQ

E

(B)

3

0

6

cd gQ

E

(C) 3

0cd gQ

E

(D) None of these

Subjective Problems

81. Which physical quantity has unit NC-1

? Is it a vector or a scalar quantity? (2003)

82. In an electric field an electron is kept freely. If a proton replaces this electron, what will be the

relationship between the forces experienced by then? (2000)

83. (i) Define electric field intensity. Write its S.I. unit. Write the magnitude and direction of electric field

intensity due to an electric dipole of length 2a at the mid point of the line joining the two charges.

(2005)

(ii) The electric field E due to any point charge near is defined as 0

limq

FE

q where q is the test charge

and F is the force acting on it. What is the physical significance of 0

limq

in this expression? (1995, 2007)

Draw the electric lines of point charge Q when (i) Q> 0 and (ii) Q < 0.

Questions Based on Electric field due to point charge

Objective Problems

84. ABC is a right angled triangle, the right angle being at B. Charges of –256, +288 and +81 esu are placed

at A, B and C respectively. If AB = 4cm, BC = 3cm, what is the magnitude of electric field at the foot of

the perpendicular drawn from B on the side AC?

(A) 100 (B) 50

(C) 50 2 (D) 50 3

85. If mass of the electron = 9.1 × 10–31

kg, charge on the electron = 1.6 × 10–19

coulomb and g = 9.8 m/s2,

then the intensity of the electric field required to balance the weight of an electron is

(A) 5.6 × 10–9

N/C (B) 5.6 × 10–11

N/C

(C) 5.6 × 10–8

N/C (D) 5.6 × 10–7

N/C

86. A charge q is lying at the mid –point of the line –joining the two similar charges Q. The system will be in

equilibrium if the value of q is :

(A) Q/2 (B) –Q/2

(C) Q/4 (D) –Q/4

87. There are n electrons on a drop of oil. It is in equilibrium in an electric field of intensity E. If the density

of oil is ρ, the radius of drop will be :


72

(A)

1

33

4

neE

g

(B)

1

34

3

g

neE

(C)

1

33

4

n g

eE

(D)

1

34

3

eE

g

88. Four charges +q, +q, – q and – q are placed respectively at the corners A, B, C and D of a square of side

a, arranged in the given order. Calculate the electric field intensity at, the centre of the square.

(A)

2

04

4 2

a

q

(B)

2

0

4 2

4

q

a

(C)

2

0

4 2

a

q

(D)

2

0

4 2q

a

89. Four points +ve charges of same magnitude(Q) are placed at four corners of a rigid square frame as

shown in figure. The plane of the frame is perpendicular to Z-axis. If a –ve point charge is placed at a

distance z away from the above frame (z << L) then:

(A) –ve charge oscillates along the Z-axis

(B) It moves away from the frame

(C) It moves slowly towards the frame and stays in the plane of the frame

(D) It passes through the frame only one

90. Electric field v/s distance graph is drawn along the joining line of charges then choose correct statement:

(A) q1 and q2 both are positive & q1 > q2 (B) q1 and q2 both are negative & q1 > q2

(C) q1 is negative and q2 is positive & q1 > q2 (D) q1 & q2 both are negative and q1 < q2

91. Two point charges Q1 and Q2 of equal magnitude are placed at a certain distance from each other.

Assuming the field strength to be positive in the positive direction of x–axis


73

The signs of the charges Q1 and Q2 for given graphs are

(A) +,+ ; +,– ; –,+ ; –,– (B) +,– ; +,+ ; –,+ ; –,–

(C) –,+ ; +,– ; +,+ ; –,– (D) +,+ ; +,– ; –,– ; –,+

92. In the given diagrams the direction of electric field at point O is given in list-II (O is circumcenter of the given

regular polygon). Charge Q is positive. Match the direction of electric field for the given arrangement:

List-I List-II

Code:

P Q R S P Q R S


74

(A) 2 1 4 3 (B) 3 1 2 4

(C) 3 2 1 4 (D) 1 4 3 2

93. For the arrangement shown in the figure below, mark out the correct statement.

(A) For +ve test charge, P is a position of stable equilibrium for displacement along AB.

(B) For +ve test charge, P is a position of unstable equilibrium for displacement along CD.

(C) For –ve test charge, P is a position of unstable equilibrium for displacement along AB.

(D) All of the above

Questions Based on Electric field due to circular arc/disc

Objective Problems

94. A small circular ring has a uniform charge distribution. On a far-off axial point distance x from the centre

of the ring, the electric field is proportional to-

(A) 2x

(B)

3

2x

(C) 3x (D)

5

4x

95. The maximum electric field at a point on the axis of a uniformly charged ring is E0.At how many points

on the axis will the magnitude of electric field be E0/2?

(A) 1 (B) 2

(C) 3 (D) 4

96. Find electric field vector at origin. The wire of radius R has uniform linear charge density +2and – on

its two semi-circular portion as shown in figure.

(A)2k

iR

(B)

2ki

R

(C)6k

iR

(D)

6ki

R

Questions Based on Electric field due to straight charged wire

Objective Problems


75

97. Three sides of a square of side l are occupied by positive charges of density C/m. The net electric field

at the centre O is:

(A)2k

l

(B)

2 2k

l

(C) 2k

l

(D)

k

l

98. Two plates A and B are placed one above the other in the gravitational field and a block of mass m is

connected to the upper plate by a spring of spring constant k. Its time period is found to be T. Now the

space between the plates is made gravity free and a charge +q is given to the block of mass m and an

electric field E is produced in the direction shown. Calculate the new time period.

(A) T (B) 2T

(C) 3T (D) 4T


76

99. A thin semi-circular ring of radius r has a positive charge q distributed uniformly over it. The net field E

at the centre O is:

(A) 2 2

0

ˆ2

qj

r (B)

2 2

0

ˆ4

qj

r

(C) 2 2

0

ˆ4

qj

r (D)

2 2

0

ˆ2

qj

r

Questions Based on Electric dipole

Objective Problems

100. The ratio of the electric field due to an electric dipole of short length on its axis and on the perpendicular

bisector of the dipole is

(A) 1 : 2 (B) 2 : 1

(C) 1 : 4 (D) 4 : 1

101. An electric dipole is placed at the origin O such that its equator is y-axis. At a point P far away from the

dipole, the electric field direction is along y-direction. OP makes an angle with the x-axis. What is the

value of tan

(A) 3 (B) 2

(C) 1 (D)1

2

102. The electric dipole is situated in an electric field as shown in the figure. The dipole and electric field are

both in the plane of the paper. The dipole is rotated about an axis-perpendicular to plane of paper passing

through its centre in anticlockwise direction. If the angle of rotation is measured with respect to the

direction of electric field, then the torque experienced by the dipole for different values of the angle of

rotation will be represented in figure by which curve?

(A) 1 (B) 2

(C) 3 (D) 4

103. An electric dipole is placed in an electric field generated by a point charge. Then which of the following

statements is/are correct?

(A) The net force on the dipole must be zero.

(B) The net force on the dipole may be zero.


77

(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.

104. A certain electric dipole is placed in a uniform electric field of magnitude 40 N/C. Figure gives the

magnitude of the torque on the dipole versus the angle between field E and the dipole moment p .

The vertical axis scale is set by 28100 10s N.m. What is the magnitude of p ?

(A) 1.25 10–28

C.m (B) 2.5 10–28

C.m

(C) 5 10–28

C.m (D) 7.5 10–28

C.m

105. Given below are four arrangement of charges. Let F1, F2, F3 and F4 be the magnitudes of force

experienced by the charge q placed at O in the respective cases. Find the correct order of these

magnitudes of forces.

(i) (ii)

(iii) (iv)

(A) (i) > (ii) > (iii) > (iv) (B) (iv) > (ii) > (i) > (iii)

(C) (iv) > (i) > (ii) > (iii) (D) (iv) < (ii) < (i) < (iii)

Subjective Problems

106. (i) What orientation of an electric dipole in a uniform electric field corresponds to its (a) stable and (b)

unstable equilibrium? (2001, 2010)

(ii) Two point electric charges of unknown magnitude and sign are placed at distance ‘d’ apart. The

electric intensity is zero at a point, not between the charges but on the joining them. Write two essential

conditions for this to happen. (1997)

(iii) The distance of the field point, on the equatorial plane of small electric dipole is halved. By what

factor does the electric field due to the dipole change? (2004)

107. Find an expression for the electric field strength at a distant point situated (i) on the axis and (ii) along the

equatorial line of an electric dipole. (1994, 2009)

108. Find expressions for the force and torque on an electric dipole kept in a uniform electric

(1998, 2008)

OR

Find an expression for the maximum torque acting on an electric dipole when it is placed in a uniform

electric field. (2002)

OR


78

An electric dipole is held in a uniform electric field (i) using suitable diagram shown that it does not

undergo any translator motion, and (ii) derive an expression for torque acting on it and specify its

direction. (2005)

Find an expression for the work done in rotating an electric dipole in a uniform electric field.

(1995)


79

Questions Based on Electric field lines

Objective Problems

109. Which of the electric fields can be responsible for the proton’s trajectory as shown below?

(A) (B)

(C) (D)

110. What among the curves shown in figure. Can possibly represent electrostatic field lines?

(A) (B)

(C) (D)

111. For the figure shown, what is the ratio of the charges q1/q2, where the figure shown has a representation

of the field lines in the space.

(A) 3

2 (B)

2

3

(C) 4

3 (D)

5

2

Subjective Problems

112. Consider the situation shown in the figure. What is the signs of q1 and q2? (2002)


80

113. An electrostatic field line cannot be discontinuous, why? (2005)

114. (i) Sketch the electric lines of force for two point charges q1 and q2 for q1 = q2 and q1> q2 separated by a

distance d. (1997)

(ii) What is the angle between the directions of electric field at any

(I) axial point and (CBSE SAMPLE PAPER)

(II) equatorial point due to an electric dipole?

115. Sketch the electric field lines for a uniformly charged hollow cylinder shown in figure.

116. A point charge (+Q) is kept in the vicinity of uncharged conducting plate. Sketch electric field lines

between the charge and the plate.

Questions Based on Electric flux

Objective Problems

117. A cylinder of radius R and length L is placed in an uniform electric field E parallel to the cylinder axis.

The total flux for the surface of the cylinder is given by:

(A) 2R2E (B) R

2/E

(C) (R2/R)/E (D) Zero

118. If electric field flux coming out of a closed surface is zero, the electric field at the surface will be-

(A) zero (B) same at all places

(C) dependent upon the location of points (D) infinite

119. If three electric dipoles are placed in some closed surface, then the electric flux emitting from the surface

will be

(A) zero (B) positive

(C) negative (D) None


81

120. A rectangular surface of 2 metre width and 4 metre length, is placed in an electric field of intensity 20

N/C, there is an angle of 60º between the perpendicular to surface and electrical field intensity. Then total

flux emitted from the surface will be - (In Volt - metre)

(A) 80 (B) 40

(C) 20 (D) 160

121. In figure, a butterfly net is in a uniform electric field of magnitude E = 3.0 m N/C. The rim, a circle of

radius a = 11 cm, is aligned perpendicular to the field. The net contains no net charge. Find the electric

flux entering through the netting.

(A) –1.1×10–4

N.m2/C (B) 1.1×10

–4 N.m

2/C

(C) –2.2×10–4

N.m2/C (D) 2.2×10

–4 N.m

2/C

122. The cube in figure has sides of length L = 10 cm. The electric field is uniform, of magnitude 4 103 N/C

and is parallel to the xy-plane at an angle of 53o measured from the +x-axis toward the +y-axis. What is

the total electric flux through all faces of the cube?

(A) –24 N.m2/C (B) 32 N.m

2/C

(C) 24 N.m2/C (D) 0 N.m

2/C .

123. Calculate electric flux through the surface of the following figure

(A) 0

2

(B)

0

6

(C) 0

3

(D)

0

3

124. Three objects are placed in a region of uniform electric field of magnitude E. The dimensions of the

objects are given in the figure. The inward flux through the objects 1, 2 and 3 (counted from left) follows

the relation. (Assume H = R, r < R)


82

(A) 1 = 2 = 3 (B) 1 = 3 < 2

(C) 2 < 1 =3 (D) 1 > 2 > 3

Subjective Problems

125. (a) A charge Q C is placed at the centre of a cube. What would be the flux through one face?

[CBSE (F) 2010]

(b) Define electric flux. Write its S.I. unit.

A spherical rubber balloon carries a charge that is uniformly distributed over its surface.

As the balloon is blown up and increases in size, how does the total electric flux coming out of the

surface change? Give reason. [CBSE (D) 2008C, 2007]

Questions Based on Gauss theorem

Objective Problems

126. 2C charge is in some Gaussian surface, giving outward flux What additional charge is needed if we

want that 6 flux enters the Gaussian surface?

(A) –10 C (B) 12 C

(C) 10 C (D) –14 C

127. Electric charge is uniformly distributed along a long straight wire of radius 1 mm. The charge per cm

length of the wire is Q. Another cylindrical surface of radius 50 cm and length 1 m symmetrically

encloses the wire as shown in the figure. What is the total electric flux passing through the cylindrical

surface?

(A) 0

Q

(B)

0

10Q

(C) 0

100Q

(D)

0

1000Q

128. If Coulomb’s law involved 3

1

r dependence (instead of

2

1

r), would Gauss’s law be still true?

(A) Yes (B) No

(C) Yes, only in some cases (D) Cannot be determined


83

129. A hollow cylinder has a charge q coulomb placed at center. If is the electric flux in units of V-m

associated with the curved surface B, then the flux linked with the plane surface A in units of V-m will

be :

(A)02

q

(B)

3

(C)0

q

(D)

0

1

2

q

130. A thin conducting spherical shell carries a charge of surface charge density . A small elemental part of the

shell is removed from it. Consider two points P and Q located very close to the spherical shell. The point P is

in the neighborhood of the elementary cavity formed and Q is just outside the shell as shown. Let EP and EQ

be the magnitudes of electric field strength at P and Q respectively. Then the ratio of EP/EQ is equal to:

(A) zero (B) 1

(C) 0.5 (D) 2

131. A charge is placed at the centre of spherical Gaussian surface. The flux through the sphere is . In which

of the following cases, will change.

(A) The sphere is replaced by a cube of one tenth the volume

(B) The charge is moved off-centre in the original sphere, still remaining inside

(C) The charge is moved just outside the original sphere.

(D) A second charge is placed near and outside, the original sphere.

132. Two charges q and 2q are placed at heights a/2 and a respectively from plane of the square surface

ABCD. Then flux through the square surface is:

(A) 03

q

(B)

04

q

(C) 0

5

24

q

(D) None of these


84

Subjective Problems

133. Two infinitely large plane thin parallel sheets having surface charge densities 1 and 2 (1 > 2) are

shown in the figure.

Write the magnitudes and directions of the net fields in the regions marked II and III.

134. A point charge q is placed at the center of a shell carrying a charge Q uniformly distributed over its

surface. Calculate electric field at a point (i) inside (ii) outside the shell at a radial distance r from the

center (iii) Plot the variation of electric field

135. Two concentric shell of radii a and b carry charge q1 and q2 (uniformly distributed) respectively (a < b).

Calculate electric field at radial distance r from the center for (i) r < a (ii) b > r > a (iii) r > b. Represent

this field graphically.

136. Electric field in a region of space is radially outwards from origin and varies with distance ‘r’ from origin

as E = kr. Find the charge enclosed in a sphere of radius ‘a’ centered at origin.

137. A ball of radius R carries a positive charge throughout its volume, such that the volume density of charge

depends on distance r from the ball’s center as 0 1

r

R

, where 0 is a constant. Assuming the

permittivity of the ball to be one, find the magnitude of electric field as a function of distance r, both

inside and outside the ball.

138. (a) A spherical conducting cell of inner radius r, and outer radius r2 has a charge ‘Q’. A charge ‘q’ is

placed at the centre of shell.

(1) What is the surface charge density on the (i) inner surface (ii) outer surface of the shell?

(2) Write expression for the electric field at a point 2x r from the centre of the shell.

[CBSE Al 2010]


85

(b) A small metal sphere carrying charge +Q is located at the centre of a spherical cavity in a large

uncharged metal sphere as shown in fig. Use Gauss’s theorem to find electric field at points P1 and P2.

[CBSE 2005]

139. A uniform electric field ˆ N/CxE E i for 0x and ˆ N/CxE E i for 0x are given. A right

circular cylinder of length l cm and radius r cm has its centre at the origin and its axis along the X-axis.

Find out the net outward flux. Using Gauss’s law, write the expression for the net charge within the

cylinder. [CBSE 2008 (C)]

140. (i) Using Gauss’s Theorem show mathematically that for any point outside shell, the field due to a

uniformly charged spherical shell is same as the entire charged shell is concentrated at the centre. (ii)

Why do you expect the electric field inside the shell to be zero according to this theorem.

[CBSE Al 2005]

OR

A thin conducting spherical shell of radius R has charge Q spread uniformly over its surface. Using

Gauss’s theorem, derive and expression for the electric field at a point outside the shell.

[CBSE 2009]

Draw a graph of electric field E r with distance r from the centre of the shell for 0 .r

OR

(i) Using Gauss’s theorem derive the expression for the electric field intensity at a point outside a

uniformly charged thin spherical shell for radius R and surface density C/m2.

(ii) Use Gauss’s theorem to find the value of electric field intensity at a point inside this shell (or hollow

charged conducting sphere)?

141. State Gauss theorem in electrostatics. Apply this theorem to obtain the expression for the electric field at

a point due to an infinitely long, thin uniformly charged straight wire of linear charge density Cm–1

.

[CBSE 2009; CBSE sample Paper, CBSE Al 2008, 07, 05]

142. State Gauss theorem in electrostatics. Apply Gauss theorem to find the electric field straight near an

infinite plane sheet of charge. [CBSE 2007, 2005, 2004, 1995]

143. A uniformly charged conducting sphere of diameter 2.5 m has a surface charge density 100 C/m2.

Calculate

(i) charge on the sphere and

(ii) total electric flux passing through the sphere. [CBSE 2008]

144. A point charge 17.7 C is located at the centre of the cube of side 0.03 m. Find the electric flux through

each face of cube. [CBSE 1997]


86

145. The flux of electrostatic field through the closed spherical surface S is found to be four times that

through the closed spherical surface S. Find the magnitude of the charge Q. Given

1 2 31μC, 2μC, 9.84μC.q q q [CBSE 2004C]

146. In the figure shown, calculate the total flux of the electrostatic field through the spheres S1 and S2. The

wire AB shown here has a linear charge density given kx where x is distance measured along the

wire, from the end A. [CBSE Al 2004C]

Questions Based on Conductors

Objective Problems

147. A point charge +q is at rest inside a thin metallic uncharged spherical shell, but not at its centre (as shown

in figure). The electric force acting on the charge.

(A) zero (B) directed in rightward direction

(C) directed in leftward direction (D) information are insufficient to decide

148. A point charge q is placed at the centre of a spherical metallic shell of radius R. Another point charge Q

is placed at a distance 2R from the centre of the shell. The force exerted by the induced charges of the

shell on the charge q is:

(A) zero (B)2

04

Qq

R

(C)2

016

Qq

R (D) None of these


87

149. An ellipsoidal cavity is carved within a perfect conductor. A positive charge is placed at the centre of the

cavity. The points A and B are on the cavity surface as shown in the figure. Then choose correct option:

(A) Electric field near A in the cavity = Electric field near B in the cavity

(B) Charge density at A = Charge density at B

(C) Potential at A = Potential at B

(D) Total electric field flux through the Gaussian surface taken in the material portion of the conductor is q/0

150. Charge on both surfaces of middle metal plate :

(A) x = – 2Q, x' = 0 (B) x = + 2Q, x' = 0

(C) x = – 2Q, x' = + 4 Q (D) x = – 4Q, x' = + 2Q

151. A sensitive instrument is to be shielded from strong electrostatic field in its environment then it must be

enclosed fully by:

(A) non conducting surface (B) metallic surface

(C) Gaussian surface (D) Dielectric surface

152. A point charge q = 2 × 10–7

C is placed at the centre of a spherical cavity of radius 3 cm in a metal piece.

Points a and b are situated at distances 1.5 cm and 4.5 cm respectively from the centre of cavity. The

electric intensities at a and b are:

(A) 8 × 106 N/C and zero (B) Zero and zero

(C) Zero and 8.9 × 105 N/C (D) None of the above

(4) All the above

153. Identify the correct statement related to the properties of conductor.


88

(A) Since volume charge exists inside a conductor, therefore, E inside conductor is zero.

(B) E inside a conductor is non zero.

(C) Since conductor is an equipotential surface, therefore, E = 0 inside a conductor is zero.

(D) All the above

154. Identify the correct statement related to the properties of conductor.

(A) The amount of charge on a surface is inversely proportional to the radius of curvature.

(B) The surface charge density is proportional to the radius of curvature.

(C) The surface charge density is inversely proportional to the curvature of the surface.

(D) None of these.

155. Two metallic concentric shells are shown. Before closing the switch charge on inner shell is Q and

charge on outer shell is 2Q. Potential at point 'A' is V. What will be potential at same point after closing

the switch:

(A) V (B) 2V

(C) 3

4V (D)

2

3V

156. In given figure charge given to outer sphere is Q. Inner sphere is grounded. What will be charge on inner

sphere after earthing:

(A) 2

Q (B) Q

(C) 2

Q (D)

3

2

Q

157. Initially the spheres A and B are at potential VA and VB respectively. Now sphere B is earthed by closing

the switch. The potential of A will now become:


89

(A) 0 (B) VA

(C) VA–VB (D) VB


90

ANSWER KEY

Question

s Answers Questions Answers

Questio

ns Answers

1 D 71 0.12 118 C

2 B 72 3

if

FF 119 A

3 D 74 0.1 N 120 A

4 B 76 or

121 A

12 9/5 77 1 215μC; 5μCq q 122 D

13

224.857 10 atoms ; 22139.63 10 ;

52.234 10 C

78 B 123 B

15 (a) 1.25 1016 e 79 B 124 C

16 9.636 106 C 80 B 126 D

18 1.234 10-1 A 84 C 127 C

23 D 85 B 128 B

43 C 86 D 129 D

44 A 87 A 130 C

45 C 88 B 131 C

46 D 89 A 132 B

47 C 90 B 136 3

04encq k a

48 D 91 B 137

3

0

2

012out

RE

r

;

2

0

0

4 3

12in

rR rE

R

49 B 92 B 139 2 115.56 10 CxE r

50 C 93 D 143 (i) 1.96 mC

(ii) 2.21 108 Nm2 C–1

51 A 94 A 144 6 2 13.33 10 Nm C

52 A 95 D 145 26.52 C

53 D 96 D 146 1

0

QS

;

2

2

0

1

2Q kl

S

54 B 97 B 147 A

55 C 98 A 148 C

56 C 99 D 149 C

57 B 100 B 150 A

58 C 101 B 151 B

59 B 102 B 152 A

60 C 103 D 153 C

61 C 104 B 154 C

62 C 105 B 155 C

63 D 109 D 156 A

64 C 110 C 157 C

65 A 111 A

70 2d 117 D


91

OBJECTIVE QUESTIONS BANK

1. An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius r. The coulomb

force F between the two is (Where 0

1

4K

)

(A)

2

3ˆ

eK r

r (B)

2

3

eK r

r

(C) 3

eK r

r

(D)

2

2ˆ

eK r

r

2. One metallic sphere A is given positive charge where as another identical metallic sphere B of exactly

same mass as of A is given equal amount of negative charge. Then

(A) Mass of A and mass of B still remain equal (B) Mass of A increases

(C) Mass of B decreases (D) Mass of B increases

3. Three equal charges are placed on the three corners of a square. If the force between 1Q and 2Q is 12F

and that between 1Q and 3Q is 13F , then the ratio of magnitudes 12

13

F

F

(A) 1

2 (B) 2

(C) 1

2 (D) 2

4. A glass rod rubbed with silk is used to charge a gold leaf electroscope then charged electroscope is

exposed to X-rays for a short period. Then

(A) The divergence of leaves will not be affected (B) The leaves will diverge further

(C) The leaves will collapse (D) The leaves will melt

5. Three point charges are placed at the corners of an equilateral triangle. Assuming only electrostatic forces

are acting

(A) The system can never be in equilibrium

(B) The system will be in equilibrium if the charge rotate about the centre of the triangle

(C) The system will be in equilibrium if the charges have different magnitudes and different signs

(D) The system will be in equilibrium if the charges have the same magnitudes but different signs

6. The distance between charges 5 10–11

C and – 2.7 10–11

C is 0.2 m. The distance at which a third

charge should be placed from – 2.7 10–11

C charge in order that it will not experience any force along

the line joining the two charges is

(A) 0.44 m (B) 0.65 m

(C) 0.556 m (D) 0.350

7. Three charges 4q, Q and q are in a straight line in the position of 0, l/2 and l respectively. The resultant

force on q will be zero. If Q =

(A) – q (B) – 2q

(C) 2

q (D) 4q


92

8. Two particle of equal mass m and charge q are placed at a distance of 16 cm. They do not experience any

force. The value of q

m is

(A) 40G (B) 0

G

(C) 04

G

(D)

04 G

9. Is it possible to get complete stable equilibrium in electrostatics?

(A) Yes (B) No

(C) it is possible to get unstable equilibrium only (D) Insufficient data

10. A regular polygon has n sides each of length l. Each corner of the polygon is at a distance r from the

centre. Identical charges each equal to q are placed at (n – 1) corners of the polygon. What is the electric

field at the centre of the polygon?

(A) 2

04

n q

r (B) 2

04

n q

l

(C) 2

0

1

4

q

r (D) 2

0

1

4

q

l

11. Two spheres A and B of gold (each of mass 1 kg.) are hung from two pans of a sensitive physical balance.

If A is given 1 faraday of positive charge and B is given 1 F of negative charge, then to balance the

balance we have to put a weight of (1F = 96500 C)

(A) 0.6 g on the pan of A (B) 0.6 g on the pan of B

(C) 1.09 milligram on the pan of A (D) 1.2 milligram on the pan of B

12. Two point charges placed at a distance of 20 cm in air repel each other with a certain force. When a

dielectric slab of thickness 8 cm and dielectric constant K is introduced between these point charges,

force of interaction becomes half of it’s previous value. Then K is approximately

(A) 2 (B) 4

(C) 2 (D) 1

13. Inside a uniformly charged spherical shell of radius r the electric field is

(A) Zero (B) Non-zero constant

(C) Varies with r (D) Inversely varies with r

14. There is a solid dielectric sphere of radius ‘R’ having uniformly distributed charge. What is the relation

between electric field ‘E’ inside the sphere and radius of sphere ‘R’ is

(A) 2E R (B) 1E R

(C) 3

1E

R (D) 2E R

15. Two infinite plane parallel sheets separated by a distance d have equal and opposite uniform charge

densities . Electric field at a point between the sheets is

(A) Zero (B) 0

(C) 02

(D) Depend on the nature of the material


93

16. A simple pendulum has a metal bob, which is negatively charged. If it is allowed to oscillate above a

positively charged metallic plate, then its time period will

(A) Increases (B) Decreases

(C) Become zero (D) Remain the same

17. In the figure distance of the point from A, where the electric field is zero is

(A) 20 cm (B) 10 cm

(C) 33 cm (D) None of these

18. In the diagram shown electric field intensity will be zero at a distance

(A) Between – q and +2q charges (B) Towards +2q on the line drawn

(C) Away from the line towards 2q (D) Away from the line towards – q

19. If an electron has an initial velocity in a direction different from that of an electric field, the path of the

electron is

(A) A straight line (B) A circle

(C) An ellipse (D) A parabola

20. A pendulum bob of mass 80 mg and carrying a charge of 2 10–8

C is at rest in a horizontal uniform

electric field of 20,000 V/m. The tension in the thread of the pendulum is

(A) 2.2 10–4

N (B) 4.4 10–4

N

(C) 8.8 10–4

N (D) 17.6 10–4

N

21. An electric dipole has the magnitude of its charge as q and its dipole moment is p. It is placed in a

uniform electric field E. If its dipole moment is along the direction of the field, the force on it and its

potential energy are respectively

(A) q.E and p.E (B) Zero and minimum

(C) q.E and maximum (D) 2q.E and minimum

22. Shown below is a distribution of charges. The flux of electric field due to these charges through the

surface S is

(A) 0

3q

(B)

0

2q

(C) 0

q

(D) Zero

80 cm

10 C

A B

20 C

– q 2q

+q

S

+q

+q


94

23. The distance between a proton and electron both having a charge 1.6 10–19

coulomb, of a hydrogen

atom is 1010 metre

. The value of intensity of electric field produced on electrons due to proton will be

(A) 2.304 10–10

N/C (B) 14.4 V/m

(C) 16 V/m (D) 1.44 1011

N/C

24. Six charges, three positive and three negative of equal magnitude are to be placed at the vertices of a

regular hexagon such that the electric field at O is double the electric field when only one positive charge

of same magnitude is placed at R. Which of the following arrangements of charges is possible for P, Q,

R, S, T and U respectively?

(A) +, –, +, –, –, + (B) +, –, +, –, +, –

(C) +, +, –, +, –, – (D) –, +, +, –, +, –

25. A solid conducting sphere of radius a has a net positive charge Q2 . A conducting spherical shell of

inner radius b and outer radius c is concentric with the solid sphere and has a net charge Q . The

surface charge density on the inner and outer surfaces of the spherical shell will be

(A) 2 2

2,

4 4

Q Q

b c (B)

2 2,

4 4

Q Q

b c

(C) 2

0,4

Q

c (D) None of the above

26. A solid metallic sphere has a charge + 3Q. Concentric with this sphere is a conducting spherical shell

having charge – Q. The radius of the sphere is a and that of the spherical shell is b(b > a). What is the

electric field at a distance ( )R a R b from the centre

(A) 02

Q

R (B)

0

3

2

Q

R

(C) 2

0

3

4

Q

R (D)

2

0

4

4

Q

R

27. A non-conducting solid sphere of radius R is uniformly charged. The magnitude of the electric field due

to the sphere at a distance r from its centre

(A) Increases as r decreases for r < R (B) Decreases as r increases for 0 < r <

(C) Decreases as r increases for R < r < (D) In discontinuous at r = R

P Q

R U

T S

O

c

b


95

28. Two infinitely long parallel wires having linear charge densities 1 and 2 respectively are placed at a

distance of R metres. The force per unit length on either wire will be 0

1

4k

(A) 1 2

2

2k

R

(B)

1 22k

R

(C) 1 2

2k

R

(D)

1 2kR

29. A point charge of 40 stat coulomb is placed 2 cm in front of an earthed metallic plane plate of large size.

Then the force of attraction on the point charge is

(A) 100 dynes (B) 160 dynes

(C) 1600 dynes (D) 400 dynes

30. In the figure shown, if the linear charge density is , then the net electric field at O will be

(A) Zero (B) k

R

(C) 2k

R

(D)

2 k

R

31. A positively charged ball is supported on a rigid insulating stand. We wish to measure the electric field E

at a point in the some horizontal level as that of the hanging charge. To do so we put a positive test

charge q0 and measure F/q0 than E at that point

(A) > F/q0 (B) = F/q0

(C) < F/q0 (D) Cannot be estimated

32. 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)

33. An electric line of force in the xy plane is given by equation x2 + y

2 = 1. A particle with unit positive

charge, initially at rest at the point x = 1, y = 0 in the xy plane

(A) Not move at all

(B) Will move along straight line

(C) Will initially move along the circular line of force

(D) Information is insufficient to draw any conclusion

+ + + + + + + + + +

+ + + + + + + + + +

+

+

+ +

O

R

+


96

34. A wire is bent in the form of a regular hexagon of side a and a total charge Q is distributed uniformly

over it. One side of the hexagon is removed. The electric field due to the remaining sides at the centre of

the hexagon is

(A) 2

012 3

Q

a (B)

2

016 3

Q

a

(C) 2

08 2

Q

a (D)

2

08 2

Q

a

35. An electric field of strength 50 Vm–1

exists along the negative direction of Y–axis. If 1 C of positive

charge is shifted from a point A (1 m, –1 m) to B (1 m, 3 m), the work done by agent is

(A) 0 (B) – 0.2 mJ

(C) + 0.2 mJ (D) + 0.8 mJ

36. An electron moving with the speed 65 10 cm per sec is shooted parallel to the electric field of intensity

31 10 N/C . Field is responsible for the retardation of motion of electron. Now evaluate the distance

travelled by the electron before coming to rest for an instant (mass of 319 10 Kg,e charge

191.6 10 C)

(A) 7 m (B) 0.7 mm

(C) 7 cm (D) 0.7 cm

37. A small sphere carrying a charge ‘q’ is hanging in between two parallel plates by a string of length L.

Time period of pendulum is 0T . When parallel plates are charged, the time period changes to T. The ratio

0/T T is equal to

(A)

1/2qE

gm

g

(B)

1/2

g

qEg

m

(C)

1/2

g

qEg

m

(D) None of these

38. An electron of mass me initially at rest moves through a certain distance in a uniform electric field in time

t1. A proton of mass mp also initially at rest takes time t2 to move through an equal distance in this

uniform electric field. Neglecting the effect of gravity, the ratio of t2/t1 is nearly equal to

(A) 1 (B) (mp/me)1/2

(C) (me/mp)1/2

(D) 1836

m

+

–

+

–

+

–

+

–

+

–

+

–

+

–

+

–

+

–

L


97

39. Point charges + 4q, – q and + 4q are kept on the x-axis at points x = 0, x = a and x = 2a respectively, then

(A) Only – q is in stable equilibrium (B) None of the charges are in equilibrium

(C) All the charges are in unstable equilibrium (D) All the charges are in stable equilibrium

40. A mass m = 20 g has a charge q = 3.0 mC. It moves with a velocity of 20 m/s and enters a region of electric

field of 80 N/C in the same direction as the velocity of the mass. The velocity of the mass after 3 seconds in

this region is

(A) 80 m/s (B) 56 m/s

(C) 44 m/s (D) 40 m/s

41. An electron moves round a circular path of radius 0.1 m about an infinite linear charge of density

+1 C/m. The speed of the electron will be

(A) 5.6 103 m/s (B) 2.8 10

5 m/s

(C) 5.6 107 m/s (D) 2.8 10

7 m/s

42. An electron falls through a distance of 8 cm in a uniform electric field of 105 N/C. The time taken by the

electron in falling will be

(A) 3 10–6

s (B) 3 10–7

s

(C) 3 10–8

s (D) 3 10–9

s

43. A small ball of mass (36 ) gm has a charge of 10–8

C on it. It is suspended by a thread from a

vertical charged metal plate. In equilibrium the thread makes an angle of 45o with the plate. If g = 10

m/s2, then the charge density on the plate is

(A) 10–9

C/m2 (B) 10

–8 C/m

–2

(C) 10–7

C/m2 (D) 10

–6 C/m

2

44. 10 C charge is uniformly distributed over a thin ring of radius 1m. A particle (mass = 0.9 gram , charge

1 C) is placed on the axis of ring. It is displaced towards centre of ring, then time period of oscillations

of particle

(A) 0.6 sec (B) 0.2 sec

(C) 0.3 sec (D) 0.4 sec

45. A thin conducting ring of radius r has an electric charge + Q, if a point charge q is placed at the centre of

the ring, then tension of the wire of ring will be

(A) 2

08

Qq

r (B)

2

04

Qq

r

(C) 2 2

08

Qq

r (D)

2 2

04

Qq

r

46. A particle of specific charge (q/m) enters into uniform electric field E along the centre line, with velocity

v. After how much time it will collide with one of the plate (figure)

(A) d

V (B)

2

d

V

(C) md

qE (D)

2md

qE

d

E

+ Q

– Q l


98

47. A dust particle of radius 5 10–7

m lies in an electric field of 6.28 105 V/m. The surrounding medium is

air whose coefficient of viscosity is 1.6 10–5

N-s/m2. If the particle moves with a horizontal uniform

velocity of 0.02 m/s, the number of electrons on it is

(A) 10 (B) 20

(C) 30 (D) 40

48. Consider the charge configuration and a spherical Gaussian surface as shown in the figure. When

calculating the flux of the electric field over the spherical surface, the electric field will be due to

(A) q2 (B) Only the positive charges

(C) All the charges present (D) + q1 and – q1

49. Two electric dipoles of moment P and 64 P are placed in opposite direction on a line at a distance of 25 cm.

The electric field will be zero at point between the dipoles whose distance from the dipole of moment P is

(A) 5 cm (B) 25

9cm

(C) 10 cm (D) 4

13 cm

50. The electric dipole is situated in an electric field as shown in adjacent figure. The dipole and the electric

field are both in the plane of the paper. The dipole is rotated about an axis perpendicular the plane of the

paper about its axis at a point A in anti-clockwise direction. If the angle of rotation is measured with

respect to the direction of the electric field, then the torque for different values of the angle of rotation ‘’

will be represented in fig. given below by the

(A) Curve (1) (B) Curve (2)

(C) Curve (3) (D) Curve (4)

51. What will be the charge present inside a cube which produces electric field Ex = 600 x1/2

, Ey = 0, Ez = 0

(A) 60 10–12

C (B) 6 10–12

C

(C) 7 10–12

C (D) 70 10–12

C

q2 +q1

–q1

0.1 m

0.1 m

y

z

O


99

52. There exists a non-uniform electric field along x-axis as shown in figure. The field increases at a uniform

rate along positive x-axis. A dipole is placed inside the field as shown. For the dipole which one of the

following statement is correct

(A) Dipole moves along positive x-axis and undergoes a clockwise rotation

(B) Dipole moves along negative x-axis after undergoing a clockwise rotation

(C) Dipole moves along positive x-axis after undergoing an anticlockwise rotation

(D) Dipole moves along negative x-axis and undergoes an anticlockwise rotation

53. A point charge +q is at a distance d/2 from a square surface of side d and is directly above the centre of

the square as shown in fig. The electric flux through the square is

(A) q/0 (B) q/60

(C) q/0 (D) Zero

54. Eight field lines emerge from closed surface surrounding an isolated point charge. Would this fact change

if a second identical charge were brought to a point just outside the surface?

(A) The number of lines would change but the shape of the lines remains the same.

(B) The number of lines would remain the same but the shape of the lines change.

(C) The number of lines as well as the shape of the lines remains the same.

(D) The number of lines as well as the shape of the lines would change.

55. In Fig (a), a particle of charge Q produces an electric field of magnitude Epart at point P, at distance R

from the particle. In Fig (b), that same amount of charge is spread uniformly along a circular arc that has

radius R and subtends an angle . The charge on the arc produces an electric field of magnitude Earc at its

center of curvature P. For what value of does Earc = 0.500 Epart?

(A) 2 radian (B) 2 2 radian

(C) 2 3 radian (D) 4 3 radian

56. If a body gives out 109 electrons every second, how much time is required to get a total charge of 1C

from it?

(A) 1.6 1010

s (B) 6.25 109 s

(C) 1.6 109 s (D) 6.25 10

10 s

+q

– q

X-axis

d

d/2

q


100

57. A thin, metallic spherical shell contains a charge Q on it. A point charge q is placed at the centre of the

shell and another charge q1 is placed out side it as shown in figure. All the three charges are positive. The

force on the charge at the centre is

58. Towards left (B) towards right

(C) Upward (D) zero

59. Charge is distributed throughout a spherical region of space in such a manner that its volume charge

density is given by ρ = ar2, 0 ≤ r ≤ R

where a is constant. Find the total charge within the sphere.

(A) 34

3aR (B)

54

5aR

(C) 54

3aR (D)

34

5aR

60. In 1 gm of a solid, there are 5 1021

atoms. If one electron is removed from every one of 0.01 % atoms

of the solid, the charge gained by the solid is (given that electronic charge is 1.6 10–19

C)

(A) 8 10–2

C (B) 5 10–2

C

(C) 5 C (D) 8 C

61. Figure shows three pairs of identical spheres that are to be touched together and then separated. The

initial charges on them are indicated. Rank the pairs according to (a) the magnitude of the charge

transferred during touching and (b) the charge left on the positively charged sphere, greatest first.

(A) 1 > 2 > 3 (B) 3 > 2 > 1

(C) 2 > 1 > 3 (D) 3 > 1 > 2

62. If a neutral object made of substance A rubs a neutral object made of substance B, then A becomes

positively charged and B becomes negatively charged. If, however, a neutral object made of substance A

is rubbed against a neutral object made of substance C, then A becomes negatively charged. What will

happen if a neutral object made of substance B is rubbed against a neutral object made of substance C?

(A) B becomes positively charged and C becomes positively charged.

(B) B becomes positively charged and C becomes negatively charged.

(C) B becomes negatively charged and C becomes positively charged.

(D) B becomes negatively charged and C becomes negatively charged.


101

63. Two identical charges experience a force F. If half of the charge is transferred from one to another and

separation is reduced to half, what will be the new force F’ between them?

(A) F = 3F (B) 3

FF

(C) 3

16F F (D)

3

4F F

64. Identical isolated conducting spheres 1 and 2 have equal charges and are separated by a distance that is

large compared with their diameters (Fig. a). The electrostatic force acting on sphere 2 due to sphere 1 is

F. Suppose now that a third identical sphere 3, having an insulating handle and initially neutral, is

touched first to sphere 1 (Fig. b), then to sphere 2 (Fig. c), and finally removed (Fig. d). The electrostatic

force that now acts on sphere 2 has magnitude F’. What is the value of F’/F?

(A) 3

4 (B) 1

(C) 3

8 (D)

3

2

65. Two similar negative charges –q are situated at point (0, a) & (0, –a) along Y-axis. A positive charge Q is

left from point (2a, 0). Analyze the motion of Q.

(A) Motion is SHM having amplitude ‘2a’ (B) Motion is oscillatory but it will not be SHM

(C) Motion is translatory along +x-direction (D) Motion is translatory along –x-direction

66. Two positive charges q each are fixed at (–a, 0) and (a, 0) respectively. A particle free to move having

mass m and charge q0 is kept at the origin. Determine its time period along x axis.

(A)

3

0

2ma

kqq (B)

3

0

0

42

ma

qq

(C)

3

0

0

2ma

qq

(D) Motion is oscillation, not SHM.

67. Calculate the magnitude of electrostatic force on a charge placed at a vertex of a triangular pyramid (4

vertices, 4 faces), if 4 equal charges each q are placed at all four vertices of pyramid of side ‘a’.

(A)

2

2

3kq

a (B)

2

2

2 2kq

a

(C)

2

2

2 3kq

a (D)

2

2

6kq

a


102

68. A particle having a charge of 1mC and mass of 100 g is fixed at the bottom of a smooth inclined plane of

inclination 300. Where should another particle B, having same charge and mass should be placed so that

it may remain in equilibrium

(A) 30 10 m along incline plane from bottom (B) 30 20 m along incline plane from bottom

(C) 10 30 m along incline plane from bottom (D) 20 30 m along incline plane from bottom

69. In figure, a central particle of charge +q is surrounded by two circular rings of charged particles. What

are the magnitude and direction of the net electrostatic force on the central particle due to the other

particles?

(A) 2

2

2 ˆkqj

r (B)

2 2

2 2ˆ ˆkq kqi j

r r

(C) 2

2

2 ˆkqj

r (D)

2 2

2 2ˆ ˆkq kqi j

r r

70. Figure shows three situations involving a charged particle and a uniformly charged spherical shell. The

charges are given, and the radii of the shells are indicated. Rank the situations according to the magnitude

of the force on the particle due to the presence of the shell, greatest first.

(A) a > b = c (B) c > b > a

(C) b = c = a (D) b = c > a

71. Figure shows four arrangements of charged particles. Rank the arrangements according to the magnitude

of the net electrostatic force on the particle with charge Q, greatest first. [p denotes protons and e denotes

electrons]

(a)

(b)

(c)

(d)

(A) d > a > c > b (B) a > b = c > d

(C) d = c, a = b (D) a = d > b = c


103

72. In figure, a central particle of charge –2q is surrounded by a square array of charged particles, separated

by either distance d or d/2 along the perimeter of the square. What are the magnitude and direction of the

net electrostatic force on the central particle due to the other particles?

(A) 2

2 2

6 15ˆ ˆkq kqi j

d d (B)

2

2 2

6 15ˆ ˆkq kqi j

d d

(C) 2

15 ˆkqj

d (D)

2

2

6 ˆkqi

d

73. Two point charges (+Q) and (– 2Q) are fixed on the X-axis at positions a and 2a from origin respectively.

At what position on the axis, the resultant electric field is zero?

(A) (–a, 0) (B) 2 ,0a

(C) (0, 0) (D) 1 2 , 0a

74. A small plastic ball of mass m covered with a thin zinc coating, is suspended by means of an insulating

thread from a fixed point. There exists an electric field of magnitude E directed along horizontal. Now

ultraviolet light is made to incident on the ball due to which it acquires a positive charge. Acceleration

due to gravity is g. What is the origin of positive charge acquired by the ball?

(A) Excess of protons in plastic ball

(B) Deficiency of electrons in Zinc coating

(C) Deficiency of electrons in plastic ball

(D) Some positively charged particles given by ultraviolet light

75. In the above question, if the string makes an angle with vertical when in equilibrium, what is the

number of electrons lost by the ball?

(A) mg

eE (B)

sinmg

eE

(C) tanmg

eE

(D)

cotmg

eE

76. In the above question, what is the maximum angle by which the string gets deflected?

(A) 1tan

mg

qE

(B) 1 2

tanmg

qE

(C) 12 tan

qE

mg

(D) 1tan

qE

mg

77. For the given pair of charges, at what value of y will the electric field on y-axis will be maximum?


104

(A) 2

d (B)

2

d

(C) 2d (D) 2d

78. A small charged sphere of mass m is suspended on a string in a uniform field ˆ ˆ /E Ai Bj N C , where A

and B are positive numbers. The sphere is in equilibrium at the angle . Determine the tension in the string.

(A) cos

tan

AmgT

A B

(B)

cos

tan

AmgT

A B

(C) sec

tan

AmgT

A B

(D)

sec

tan

AmgT

A B

79. An inclined plane making an angle of 45o with the horizontal is placed in a uniform horizontal electric field of

100 Vm-1. A particle of mass 1kg and charge

1

30C is allowed to slide down from rest from a height of 1m. If

the coefficient of friction is 0.2, find the time it will take for the particle to reach the bottom.

(A) 2 sec (B) 1 sec

(C) 1

sec2

(D) 1

sec2 2

80. Four identical dipoles are placed in uniform electric field. Arrange the magnitude of torque on the dipoles

in decreasing order.

(A) 1 = 3 > 2 = 4 (B) 1 > 3 > 2 > 4

(C) 3 > 1 > 4 > 2 (D) 1 = 3 = 2 = 4

81. Arrange the magnitude of potential energy of dipoles in the above question in descending order.

(A) 1 = 2 = 3 = 4 (B) 3 = 2 > 1 = 4

(C) 1 > 2 > 4 > 3 (D) 1 = 3 > 2 = 4

82. A dipole having charges + q and – q is fixed on a rough surface as shown in the figure. Another charge Q

of mass m is placed at distance d from the dipole. Find the minimum value of d for which charge Q will

not move. Given a << d and coefficient of friction = 0.5)

(A)

1

3

0

4Qqa

mg

(B)

1

3

0

Qqa

mg

(C)

1

3

0

Qqa

mg

(D)

1

3

04

Qqa

mg


105

83. The electric field in a region of space0E E xi . What is the flux of electric field through a sphere of

radius r, centered at origin?

(A)

(B)

(C)

(D)

84. The drum of a photocopying machine has a length of 21 cm and a diameter of 12 cm. The electric field

just above the drum’s surface is 3 x 105 N/C. What is the total charge on the drum?

(A) 821 10 C (B)

921 10 C

(C) 0360 C (D) 0252 C

85. A solid metallic sphere has a charge + 3Q. Concentric with this sphere is a conducting spherical shell

having charge –Q. The radius of the sphere is a and that of the spherical shell is b (>a). What is the

electric field at a distance r(a < r < b) from the centre?

(A) 0

1

4

Q

r (B) zero

(C) 2

0

1 3

4

Q

r (D)

2

0

1

4

Q

r

86. As shown in the figure, charge Q is kept in the inner cavity and a charge 2Q and 3Q are imparted to the inner

and outermost shell. Find the charge on outer surface of outermost and outer surface of inner shell respectively.

(A) 3Q, –3Q (B) 6Q, –3Q

(C) 6Q, 3Q (D) 6Q, –6Q

87. A short dipole of dipole moment P is placed near a point charge Q as shown in figure. Find force on the

dipole due to the point charge.

(A) 3

KQP

r (towards right) (B)

3

KQP

r (towards left)

(C) 3

2KQP

r (towards right) (D)

3

2KQP

r (towards left)

88. A dipole is placed in a constant electric field as shown in the figure. If it is released from the rest from

this position, find the kinetic energy gained when it is parallel to electric field vector. (Assume gravity

free space and that the dipole is small)

(A) pE 1 cos (B) pE cos 1

(C) pE 1 cos (D) zero

89. Five styrofoam balls are suspended from insulating threads. Several experiments are performed on the

balls and the following observations are made :


106

(i) Ball A repels C and attracts B.

(ii) Ball D attracts B and has no effect on E.

(iii) A negatively charged rod attracts both A and E.

An electrically neutral styrofoam ball gets attracted if placed nearby a charged body due to induced

charge. What are the charges, if any, on each ball?

A B C D E A B C D E

(A) + – + 0 + (B) + – + + 0

(C) + – + 0 0 (D) – + – 0 0

90. The diagram shows the arrangement of three small uniformly charged spheres A, B and C. The arrows

indicate the direction of the electrostatic forces acting between the spheres (for example, the left arrow on

sphere A indicates the electrostatic force on sphere A due to sphere B). At least two of the spheres are

positively charged. Which sphere, if any, could be negatively charged?

(A) sphere A (B) sphere B

(C) sphere C (D) no sphere

91. Two identical small balls each have a mass m and charge q. When placed in a hemispherical bowl of

radius R with frictionless, nonconductive walls, the beads move, and at equilibrium the line joining the

balls is horizontal and the distance between them is R (figure). Neglect any induced charge on the

hemispherical bowl. Then the charge on each bead is: (here K = 0

1

4 )

(A)

1/2

3

mgq R

K

(B)

1/2

3

mgq R

K

(C)

1/2

3 mgq R

K

(D)

1/2

3 mgq R

K

92. A simple pendulum has a length l, mass of bob m. The bob is given a charge q coulomb. The pendulum is

suspended in a uniform horizontal electric field of strength E as shown in figure, then calculate the time

period of oscillation when the bob is slightly displace from its mean position is :

A B C

D E

A

CB


107

(A) 2g

(B) 2qE

gm

(C) 2qE

gm

(D) 2

2

2qE

gm

93. In the diagram shown P is a point negative charge. It’s weight is balanced by the electric force due to the

fixed very long wire. The equilibrium of the particle is

(A) stable, for vertical displacements

(B) neutral for vertical displacements

(C) stable for horizontal displacements (parallel to the wire)

(D) neutral for horizontal displacements (parallel to the wire)

94. A particle of charge –q & mass m moves in a circle of radius r around an infinitely long line charge on

linear charge density + . Then time period will be:

(A) 22

mT r

k q

(B)

22 34

2

mT r

k q

(C) 1 2

2

k qT

r m

(D)

1

2 2

mT

r k q

95. Consider two thin uniformly charged concentric shells of radii r and 2r having charges Q and –Q respectively,

as shown. Three points A, B and C are marked at distances 3

,2 2

r r and

5

2

rrespectively from their common

centre. If EA, EB and EC are magnitudes of the electric fields at points A, B and C respectively then

(A) EA > EB > EC (B) EC > EB > EA

(C) EB > EA = EC (D) EB > EA > EC

96. Consider a solid uniformly charged sphere. There are two points A (inside) and B (outside) where the

electric fields are same. The ratio of distance of A to the distance of B from the surface is:

(A) 1: 1 (B) 2: 1

(C) 1: 2 (D) having many values

97. The maximum electric field intensity on the axis of a uniformly charged ring of charge q and radius R will be:

(A) 2

0

1

4 3 3

q

R (B) 2

0

1 2

4 3

q

R

(C) 2

0

1 2

4 3 3

q

R (D)

20

1 3

4 2 3

q

R

98. Two concentric rings, one of radius R and total charge +Q and the second of radius 2R and total charge

Q, lie in x-y plane (i.e., z = 0 plane). The common centre of rings lies at origin

and the common axis coincides with z-axis. The charge is uniformly distributed

E

q m1

-Q

Q

r

2r

A B C


108

on both rings. At what distance from origin is the net electric field on z-axis zero.

(A) 2

R (B) 0

(C) 2 2

R (D) 2 R

99. Two positively charged particles of charges q1 and q2 have mass m each. A uniform electric field having

magnitude E exists in positive x direction as shown in figure. The given two charged particles are

released from rest at t = 0 as shown in figure. If position of q1 at t = 2 sec. is given by coordinate (+2a, 0)

then the x-coordinate of q2 at t = 2 sec is (neglect gravitational interaction between the particles) -

(A) 1 2 2q q

E am

(B) 1 2q q

E am

(C) 1 22 2q q

E am

(D) 1 22

q qE a

m

100. Charge 2Q and –Q are placed as shown in figure. The point at which electric field intensity is zero will be:

(A) Somewhere between –Q and 2Q

(B) Somewhere on the left of –Q

(C) Somewhere on the right of 2Q

(D) Somewhere on the right bisector of line joining –Q and 2Q

101. If two balls of given masses and charges are released, which of the following is incorrect arrangement in

equilibrium?

(A) (B)

(C) (D)

+q

m m

+3q

+q

+2q

2m

m

1

2

2 > 1


109

ANSWER KEY

Questions Answers Questions Answers Questions Answers

1 C 35 C 69 D

2 D 36 C 70 D

3 B 37 C 71 D

4 C 38 B 72 B

5 A 39 C 73 B

6 C 40 B 74 C

7 A 41 C 75 C

8 D 42 D 76 B

9 B 43 A 77 C

10 C 44 A 78 B

11 C 45 C 79 D

12 B 46 C 80 A

13 A 47 C 81 C

14 C 48 C 82 C

15 B 49 A 83 B

16 B 50 B 84 C

17 C 51 C 85 C

18 D 52 D 86 D

19 D 53 B 87 C

20 C 54 B 88 C

21 B 55 C 89 A

22 B 56 B 90 A

23 D 57 D 91 D

24 D 58 B 92 D

25 A 59 A 93 A

26 C 60 D 94 C

27 C 61 C 95 D

28 B 62 A 96 C

29 A 63 C 97 B

30 A 64 B 98 C

31 A 65 C 99 B

32 C 66 D 100 AB

33 C 67 B

34 A 68 A

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