Topper’s Package Physics - XII Permutation and ... · 8/8/2020 · Topper’s Package Physics -...

Topper’s Package Physics - XII Permutation and CombinationsElectrostatics

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1. CHARGES AND ITS PROPERTIES1. If an object of mass 1 kg contains 4 1020

atoms. If one electron is removed from everyatom of the solid, the charge gained by thesolid in 1 g is(a) 2.8 C (b) 6.4 10–2 C(c) 3.67 10–3 C (d) 1.67 1022 C

2. A coin is made up of Al and weighs 0.75 g.It has a square shape and its diagonalmeasures 17 mm. It is electrically neutraland contains equal amounts of positive andnegative charges. The magnitude of thesecharges is (Atomic mass of Al = 26.68g)(a) 3.47 104 C (b) 3.47 102 C(c) 1.67 1020 C (d) 1.67 1022 C

3. A conducting sphere is negatively charged.Which of the following statements is true?(a) The charge is uniformly distributed

throughout the entire volume(b) The charge is located at the center of

the sphere(c) The charge is located at the bottom of

the sphere(d) The charge is uniformly distributed on

the surface of the sphere

4. The number of electrons that must be removedfrom an electrically neutral silver dollar togive it a charge of +2.4 C(a) 2.5 1019 (b) 1.5 1019 C(c) 1.5 10–19 (d) 2.5 10–19

2. COULOMBS LAW5. Point charges + 4q, – q and + 4q are placed at

the points x = 0, x = a and x = 2a on the x-axisrespectively then(a) Only charge – q is in stable equilibrium(b) No charge is in equilibrium(c) All the charges are in unstable equilibrium(d) All the charges are in stable equilibrium

6. Three charges each of value + Q, are placed at

the corners of an equilateral triangle. A fourthcharges q is placed at the centre of the triangle,for what value of q all the charges remainstationary

(a) 3Q

(b) 3Q

(c) Q3 (d) Q3

7. A point charge q is situated at a distance d fromone end of a thin nonconduction rod of lengthL having charge Q (uniformly distributed alongits length) as shown in figure. Then themagnitude of electric force between the two is

q

d L

Q

(a) )Ld(d2qQ

π41

0 (b) )Ld(dqQ2

π41

0

(c) )Ld(d3qQ

π41

0 (d) )Ld(dqQ

π41

0

8. An electric charge q exerts a force F on asimilar electric charge q separated by adistance r. A third charge q/4 is placed midwaybetween the two charges. Now, the force F will....(a) become F/3 (b) become F/9(c) become F/27 (d) remain F

9. Two identical balls having like charges andplaced at a certain distance apart repel eachother with a certain force. They are broughtin contact and then moved apart to a distanceequal to half their initial separation. The forceof repulsion between them increases 4.5 timesin comparison with the initial value. The ratioof the initial value. The ratio of the initialcharges of the balls is

ELECTROSTATICS Unit 1


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(a) 2 (b) 3(c) 4 (d) 6

10. Two point charges placed at distance of 20 cmin air repel each other with a certain force.When a dielectric slab of thickness 8 cm anddielectric constant K is introduced betweenthese point charges, force of interactionbecomes half of its previous value. Then K isapproximately(a) 2 (b) 4(c) 2 (d) 1

11. A certain charge Q is divided at first into twoparts q and (Q – q). Later on the charges areplaced at a certain distance. If the force ofinteraction between two charges is maximum,then

(a) 14

qQ (b) 1

2qQ

(c) 13

qQ (d) 3

1qQ

12. Two similar charged spheres are suspendedby strings of equal length when they aresuspended in air then the angle between thestring is 30°. The angle remains the samewhen they are suspended in liquid of density

30.8 /g cm . Calculate the dielectric constantof the liquid if density of the material of thesphere is 31.6 /g cm(a) 1 (b) 2(c) 3 (d) 4

13. Four charges equal to Q are placed at thefour corners of a square and a charge q is atits centre. If the system is in equilibrium, thenthe value of q is

(a) (1 2 2)4Q

(b) (1 2 2)4Q

(c) (1 2 2)2Q

(d) (1 2 2)2Q

14. Two small conducting spheres S1 and S2 hangby light nonconducting threads from fixed pointP1 and P2 and are at same level. S1 has mass3m and carries charge 3q while S2 has a mass2m and carries charge 2q. The repulsionbetween them causes the thread to make smallangles 1 and 2 with the vertical. What is theapproximate value of the ratio 1/2?(a) 3 : 2 (b) 2 : 3(c) 3 : 4 (d) 4 : 3

3. ELECTRIC FIELD

15. A charge particle (Q = –16 nc) enterstransversely in uniform E

(10 1Vm ) with

initial velocity 10 m/s. If length of plates is1m then after how much time particle exitsfrom E

(M = 1 mg)

++ + + +++ + + +

(a) 0.1 sec (b) 10 ns(c) 10 µs (d) None of these

16. Two charged particle of masses m and 2m havecharges + 2q and +q respectively. They are keptin a uniform electric field far away from eachother and then allowed to move for the sametime. The ratio of their kinetic energies is(a) 4 : 2 (b) 3 : 1(c) 8 : 1 (d) 5 : 7

17. A rod of length L having charge Q is framed in

semicircular arc then E

at centre is

(a)2

0 L2Q

(b) 20 LQ

(c)2

0 LQ2

(d) None of these

18. All the surfaces in given fig. are frictionless.An object of charge Q is placed ‘d’ distance awayfrom a wall. Now an electric field is switchedon. If object collides with wall elastically andreturn to initial position. If this processcontinues then time period of this oscillationis

E+Q

M

d

Wall

(a) QEmd8

(b) QEmd2

(c)MdQE

(d)MdQE8


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19. Three small spheres, each carrying a positivecharge Q, are placed on the circumference ofa circle of radius ‘r’ to form an equilateraltriangle. The electric field intensity at thecentre of the circle will be

(a)3Qr (b)

32Q

r

(c)12 2Qr (d) zero

20. The figure shows some of the electric field linescorresponding to an electric field. The figuresuggests

C A

B

(a) A B CE E E (b) A B CE E E (c) A C BE E E (d) A C BE E E

21. A metallic solid sphere is placed in a uniformelectric field. The lines of force follow the path(s)shown in figure as(a) 1(b) 2

(c) 3

1

2

3

4

1

2

3

4

(d) 422. A hollow dielectric sphere as shown in the

diagram has ‘a’ and ‘b’ as its inner and outerradii. The total charge carried by the sphereis + Q, which is uniformly distributedthroughout the dielectric sphere between ‘a’and ‘b’. The electric field for a < r < b is givenby ( r – relative permittivity of dielectricmaterial)

(a) a4Q

r0

(b) 2r0 b4

Q

a b

(c) 2r0 a4

Q

(d)

332r0

33

abr4arQ

23. The electric field strength due to a ring ofradius R at a distance x from its centre on theaxis of ring having charge Q is given by

3/22 20

1 QxE ,4 R x

. At what distance

from the centre will electric field be maximum(a) x R (b) /2x R(c) / 2x R (d) 2x R

24. An insulated sphere of radius R has a uniformvolume charge density . The electric field ata point P inside the sphere and distant r fromthe centre is

(a)0

.3R

(b)03

r

(c) zero (d)0

23

r

25. A ring of charge with radius 0.5m has 0.02 mgap. If the ring carries a charge of +1C, theelectric field at the centre is

(a) 42.31 10 /N C (b) 82.31 10 /N C(c) 41.6 10 /N C (d) 81.6 10 /N C

26. Two point charges 8q and 2q are locatedat x O and x L respectively. The locationof a point on the axis at which the net electricfield due to these two point charges is zero is(a) 8L (b) 4L(c) 2L (d) /4L

27. A non-conducting solid sphere of radius R isuniform charged. The magnitude of theelectric field due to the sphere at a distance rfrom its centre(a) Increases as r increaeses for r R(b) Decreases as r increases for 0 r (c) Decreases as r increases as r increasesfor R r (d) Is discontinuous at r R

28. Three positive charges of equal value q areplaced at the vertices of an equilateral triangle.The resulting lines of force should be sketchedas in


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(a) (b)

(c) (d)

29. A metallic shell has a point charge ‘q’ keptinside its cavity. Which one of the followingdiagrams correctly represents the electric linesof forces.

(a) (b)

(c) (d)

30. Six charges, three positive and three negativeof equal magnitude are to be placed at thevertices of a regular hexagon such that theelectric field at O is double the electric fieldwhen only one positive charge of samemagnitude is placed at R. Which of the followingarrangements of charges is possible forP.Q,R,S,T and U respectively

(a) , , , , ,

(b) , , , , ,

(c) , , , , ,

P Q

ST

U RO

(d) , , , , ,

31. A spherical portion has been removed from asolid sphere having a charge distributeduniformly in its volume in the figure. Theelectric field inside the emptied space is

(a) Zero everywhere(b) Non-zero and uniform(c) Non-uniform(d) Zero only at its center

32. A conducting sphere of radius R is charged toa potential of V volts. Then the electric field ata distance ( )r R from the centre of the spherewould be

(a)Vr

(b)2R Vr

(c) 2RVr

(d) 2r VR

33. Two identical point charges are placed at aseparation of l. P is a point on the line joiningthe charges, at a distance x from any onecharge. The field at P is E. E is plotted againstx for values of x from close to zero to slightlyless than l. Which of the following bestrepresents the resulting curve ?

(a)E

lxO(b)

E

lxO

(c)

E

lxO (d)

E

lxO

34. Six charges are placed at the vertices of aregular hexagon as shown in the figure. Theelectric field on the line passing through pointO and perpendicular to the plane of the figureat a distance of ( )x a from O is

(a) 30

Q ax

(b) 30

2Q ax

O

+Q

+Q

+Q

–Q

–Q

–Q

a

(c) 30

3Q ax (d) zero

35. A long cylindrical shell carries positive surfacecharge in the upper half and negative


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surface charge – in the lower half. Theelectric field lines around the cylinder willlook like figure given in (Figures areschematic and not drawn to scale)

(a) (b)

(c) (d)

36. A slab infinite in the x-y direction and ofthickness L in the z-direction, carries aunifrom positive charge density, i.e. (t) = 0.Sketch the electric field a function of positionboth outside and inside the slab

(a) (b)

(c) (d)

37. A semi-infinite insulating rod has linearcharge density . The electric field at the pointP as shown in figure

(a)2

20

2(4 )r

at 45° with AB

(b)2

0

24 r

at 45° with AB

(c)0

24 r

at 45° with AB

(d)0

24 r

at 135° with AB

38. Figure shows some of the electric lines offorce due to three point charges Q1, Q2 andQ3 of equal magnitude. Comment on the signsof charge Q2:

(a) negative(b) positive(c) cannot say(d) may positive or may negative

39. Two blocks of mass 1kg (A) and 2kg (B) areplaced as shown figure and connected by aspring of spring constant k. Coefficient offriction between blocks is m and ground issmooth. A charge q is given to block B andan uniform electric field is switched on thesystem. If block A and B does not slip overeach other and blocks motion is simpleharmonic motion. Find amplitude and timeperiod of the motion.

(a) 1 2, 2m mEqA T

k k

(b) 22 , 2mEqA T

k k

(c) 1 23 , 2m mEqA T

k k

(d) 1 22 , 2m mEqA T

k k

4. ELECTRIC FLUX

40. If ia

xEE 0

then flux through the shaded area

is

(a) 20E a

y

xz

(a, 0)

(b) zero

(c) 30E a

(d) 30E a


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41. A cylinder of radius R and length L is placedin a uniform electric field E parallel to thecylinder axis. The total flux for the curvedsurface of the cylinder is given by(a) 22 R E (b) 2 2R LE

(c)2 2R REL

(d) zero

42. If there are only one type of charge in theuniverse, then

(a) 0s

E ds

(b) 0

sE ds

if the charge is outside the

surface

(c)0s

qE ds

if charges of magnitude q

were inside the surface(d) both (b) and (c) are correct

43. If 0s

E ds

over a surface, then

(a) the electric field inside the surface andon it is zero

(b) the electric field inside the surface isnecessarily uniform

(c) all charges must necessarily be outsidethe surface

(d) all of these44. A large plate sheet of charge having surface

charge density 5.0 10–16 cm–2 lies int hex-y plane. The electric flux through a circulararea of radius 0.1 m is if the normal to thecircular area makes an angle of 60° with thez-axis(a) 4.4 10–6 Nm–2C–1

(b) 2.2 10–7 Nm–2C–1

(c) 4.4 10–7 Nm–2C–1

(d) 2.2 10–6 Nm–2C–1

5. ELECTRIC DIPOLE

45. A dipole of dipole moment P is placedperpendicular to an electric field E, the workdone in turning it by 180° is(a) Zero (b) PE

(c)2

PE(d) 2 PE

46. A point particle of mass M is attached to oneend of a massless rigid non-conducting rode oflength L. Another point particle of same massis attached to the other end of the rod. Two

particles carry charges + q and – q respectively.This arrangement is held in a region ofuniform electric field E such that the rodmakes a small angle (< 5°) with the fielddirection the minimum time needed for therod to become parallel to the field after it is setfree.

(a)qE2

MLπ2 (b)qE2

MLπ

(c)qE2

ML2π

(d)qE2

MLπ4

47. Electric field on the axis of a small electricdipole at a distance r is 1E

and 2E

at a distance

of 2r on a line of perpendicular bisector. Then

(a) 2 1/8E E

(b) 2 1/16E E

(c) 2 1/4E E

(d) 2 1/8E E

48. An electric dipole has a fixed dipole momentp ,which makes with respect to x-axis. Whensubjected to an electric field

1E = ˆEi , it

experience a torque

1 ˆT k .When subjectedto another electric field

2 1

ˆE 3E j it

experiences a torque

2 1T T . The angle is(a) 30° (b) 45°(c) 60° (d) 90°

49. In a certain region of space, electric field isalong the z-direction throughout. Themagnitude of electric field is however notconstant, but increases uniformly along thepositive z-direction at the rate of 105 NC–1m–1. The force experienced by the system havinga total diple moment equal to 10–7 cm in thenegative z-direction is(a) –10–2 N (b) 10–2 N(c) 10–4 N (d) –10–4 N

50. In the above question, torque experineced bythe system is(a) 102 N (b) 10–2 N(c) zero (d) 103 N

51. Find the net force on the electric dipole fora electrostatic charge system shown in figure,if q1 = q2 = q3 = q;


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(a) 3kpqa

(b) 3 32.kpq kqp

a a(c) zero (d) None of these

52. Charges –q, –q, +2q are placed at the cornersof equilateral triangle of side l, the magnitudeof resultant electric dipole moment will be

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

53. A dipole consists of two point charge +q and–q separated by a distance d. It is at adistance of R from the surface semi-infinitepefect conductors as indicated in figure. Findthe force acing on the dipole as a functionof R:

(a)2

40

3( )32

qdR

(b)

2

40

16( )44

qdR

(c)2 2

40

q dR

(d)2 2

40

269

q dR

54. An electric dipole is placed inside a hollowsphere. Find the electric flux passing throughthe sphere:

(a) zero (b)0

q

(c)02q (d)

0

2q

6. GAUSS LAW

55. A charge Q is placed at corner of a cube thenflux through shaded area is

Q

(a)024

Q (b)

03Q

(c)08

Q (d)

06Q

56. A small sphere whose mass is 10 mg. carriesa charge q = 8.85 nC. It hangs in the earth’sgravitational field from a silk thread that makesan angle = 45° with a large uniformly chargednon-conducting sheet as in figure. The chargedensity on the sheet is

(a) 298 /nC m

(b) 2196 /nC m

(c) 249 /nC m

+

m, q

+++++

(d) 2392 /nC m

57. Two conducting plates X and Y, each havinglarge surface are A (on one side) are placedparallel to each other. The plate X is given acharge Q whereas the other is neutral. Theelectric field at a point in between the platesis given by

(a)A2

Q

(b)A2

Q

0 towards left

X

P

Y

(c)0A2

Q

towards right

(d)02

Q

towards right

58. A charge Q is distributed uniformly on a ringof radius R. A sphere of equal radius R isconstructed with its centre at the periphery ofthe ring as shown in the figure. The flux of the


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electric field through the surface of the sphereis(a) 0/Q

(b) 0/2Q

(c) 0/3Q

O1 O2 R

Ring Sphere

(d) 0/4Q 59. A hollow hemispherical surface of radius R is

placed with its cross section perpendicular toa uniform electric field E as shown in figure.Electric flux linked with its surface is(a) 0

(b) 2R E

(c) 22 R E

E

R (d) 0/2E

60. Due to charge inside a cube, the electric fieldis 1/2600 , 0, 0n y zE x E E . The chargeinside the cube is

(a) 600 µC

(b) 60 µC

(c) 7 µC

O X

Y 0.1 m

0.1 m

(d) 8 µC61. Three identical plates with large surface areas

are kept parallel to each other as shown. Theplate X is given a charge Q and the plate Z acharge –2Q and the middle plate Y is neutral.The charge appearing on the outer surface ofplate Z is

(a) /2Q

(b) Q

(c) Q

YX Z(d) /2Q62. A long cylindrical volume contains a uniformly

distributed charge density . The electric fieldat a point P inside the cylindrical volume at adistance x from its axis is

xP

(a)02

x (b)

0

x

(c)0

23

x (d)

03x

63. In a region of space the electric field is givenby ˆ ˆ ˆ8 4 3E i j k

. The electric flux througha surface of area of 100 units in x-y plane is(a) 800 units (b) 300 units(c) 400 units (d) 1500 units

64. Three infinitely long charge sheets are placedas shown in figure. The electric field at a pointP is

–2

–

Pz = a

z = 3a

xz = –a

z

(a)0

2 k (b)

0

4 k

(c)0

2 k

(d)0

4 k

65. According to figure, a hemispherical objectis placed in an electric field, find the outwardflux through its curved surface(a) ER2

(b)2

2E R

(c) E2R(d) E(R)

66. The electric field at the centre of ahemispherical surface having uniform surfacecharge density is

(a)0

(b)02

(c)04

(d)08

67. Choose the correct graph of electric field dueto infinite line of charge at a point P, which


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is at a perpendicular distance from the linein any direction.

(a) (b)

(c) (d)

68. Five charges q1, q2, q3, q4 and q5 are fixedat their positions as shown in figure. S isGaussian surface. The Gauss’s law is given

by 0

S

qE ds

. Which of the following

statements is correct?

(a) E

on the LHS of the above equation willhave a contribution from q1, q5 and q3will q on the RHS will have a contributionfrom q2 and q4 only.

(b) E

on the LHS of the above equation willhave a contribution from all chargeswihile q on the RHS will have acontribution from q2 and q4 only.

(c) E

on the RHS of the above equation willhave a contribution from all charges whileq on the RHS will have a contributionfrom q1, q3 and q5 only

(d) Both E

on the LHS and q on the RHSwill have a contributions from q2 and q4only.

7. POTENTIAL

69. Along the positive direction of x-axis thereexists a constant electric field 0E

. If electric

potential at 0x is zero then its value atx x will be

(a) 0( )V x xE (b) 0( )V x xE (c) 2

0( )V x x E (d) 20( )V x x E

70. Potential at common centre of two concentric

rings is zero if 1

2

equals to (b > a)

(a)ab

(b)ba

(c) 1

(- )2

1

Oa

b×

×

×××

×

×××

×

××

(d)a bb a

71 An electric field )j30i20(E

N/C exists inthe space. If the potential at origin is taken tobe zero, the potential at (2m, 2m) point is(a) – 50 V (b) 100 V(c) – 100 V (d) 200 V

72. A and B are two concentric spheres. If A is givena charge Q while B is earthed as shown infigure. Then :

A

B+ +

+

++

++++

+

(a) The charge density of A and B are same(b) The field inside and outside A is zero(c) The field between A and B is not zero(d) The field inside and outside B is zero

73. The electric potential V at any point x, y, z (allin metre) in space is given by 24V x volt.The electric field at the point (1m, 0m, 2m) in

1V m is(a) 8 V along negative x-axis(b) 8 V along positive x-axis(c) 16 V along negative x-axis(d) 16 V along positive x-axis

74. Water from a tap maintained at a potential ofV is allowed to fall by drops of radius r througha small hole into a hollow conducting sphereof radius R standing on an insulating standuntil it fills the entire sphere. Then thepotential of the hollow conductor is


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(a)R Vr

(b)r VR

(c)2

2r VR

(d)2

2R Vr

75. A hollow metal sphere of radius 5 cm is chargedsuch that the potential on its surface is 10V.The potential at the centre of the sphere is(a) 0 V(b) 10 V(c) same as at point 5 cm away from the

surface(d) same as at point 25 cm away from the

surface76. n small drops of the same size are charged to V

volt each. If they coalesce to form a single largedrop, then its potential will be(a) /V n (b) Vn(c) 1/3Vn (d) 2/3Vn

77. An infinite nonconducting sheet has a surfacecharge density 20.30 /µC m on one side.How far apart are equipotential surfaceswhose potentials differ by 100V ?(a) 3.9 mm (b) 4.9 mm(c) 5.9 mm (d) 1.9 mm

78. Two concentric, thin, metallic spheres of radii

1R and 2 1 2( )R R R bear charges 1Q and 2Qrespectively. Then the potential at radius r

between 1R and 2R will be 04

1

times

(a)r

QQ 21 (b) rQ

RQ 2

1

1

(c)2

2

1

1RQ

RQ

(d)1

2

2

1RQ

RQ

79. A charge Q is distributed over two concentrichollow spheres of radii r and R (> r) such thatthe surface densities are equal. The potentialat the common centre is

(a)

rR4rRQ

0

22

(b)rR

Q

(c) 0 (d) 22

0 rR4rRQ

80. The figure below shows two equipotential linesin XY plane for an electric field. The scales aremarked. The X-component, Ex and Y-component, Ey of the electric field in the space

between these equipotential lines arerespectively

Y

X 0

1

2

3

2 4 6 8

y (c

m)

2 volt

4 volt

x (cm) (a) 1 1100 , 200V m V m (b) 1 1100 , 200V m V m (c) 1 1200 , 100V m V m (d) 1 1200 , 100V m V m

81. A charge + q is fixed at each of the points0 0 0, 3 , 5x x x x x x .... up to and a

charge – q is fixed at each of the points0 0 02 , 4 , 6x x x x x x .... upto . Here 0x

is a positive constant. Take the electricpotential at a point due to a charge + Q at a

distance r from it to be r4Q

0. Then, the

potential at the origin due to the above systemof charges is

(a) 0 (b) 0 0

q8 x ln2

(c) (d) 0 0

q ln24 x

82. The electric field E

, between two points isconstant in both magnitude and direction.Consider a path of length d at angle 60 with respect to field lines as shown in thefigure. The potential difference betweenpoints 1 and 2 is

2

60°d

1

(a) cos60E

d (b) cos60E d

(c)cos60

Ed

(d) cos60Ed

83. The figure shows the variation of electricintensity E versus distance r. What is thepotential difference between the points

2r m and 6r m


14

(V/m)

E

0 2 4 6 r(m)

10

(a) 30V (b) 30V(c) 40V (d) 60V

84. Three concentric metal shells A, B and C haveradii a, b and c respectively. The shells A & Care given charges q and – q respectively andthe middle shell B is earthed. The chargesappearing on the inner and outer surfaces ofB are

(a) q and /bq c

(b) q and qA

CB

(c) /bq c and q

(d) q and /bq c

85. Two concentric hollow metal spheres haveradii 1R and 2R . The outer sphere is given apositive charge Q and the inner sphere isearthed. What is the charge on the innersphere ?(a) zero

(b) Q(c) 1 1 2/( )R Q R R

R1

R2

(d) 1 2( / )R Q R

86. An electric charge 310 µC is placed at theorigin (0, 0) of x-y coordinate system. Twopoints A and B are situated at ( 2, 2) and(2, 0) respectively. The potential differencebetween the points A and B will be(a) 4.5 volt (b) 9 volt(c) zero (d) 2 volt

87. A point charge q is placed inside a conductingspherical shell of inner radius 2R and outerradius 3R at a distance of R from the centreof the shell. The electric potential at the

centre of shell will be 0

14 times

(a) 2qR (b)

43

qR

(c)56

qR (d)

23

qR

8. POTENTIAL ENERGY & WORK DONE

88. A free proton and a free -particle initially atseparation of 1Å are released, the kineticenergy of proton and that - particle when atinfinite separation bear a ratio :–(a) 1 : 1 (b) 1 : 2(c) 1 : 4 (d) 4 : 1

89. Fig. shows two parallel equipotential surfacesA and B kept at a small distance r from eachother in an electric field E. A point charge of– q coulomb is taken from the surface A to B.The amount of work done is equal to

A B r

(a)0

q4 r

(b)

0

q4 r

(c) zero (d) q E r90. Two identical rings P and Q of radius 0.1 m are

mounted coaxially at a distance 0.5 m apart.The charges on the two rings are 2µC and4µC respectively. The work done in transferringa charge of 5µC from the centre of P to that ofQ is(a) 1.28 J (b) 0.72 J(c) 0.144 J (d) 2.24 J

91. Two identical thin rings, each of radius Rmetres, are coaxially placed at a distance Rmetres apart. If 1Q coulomb and 2Q coulombare respectively, the charges uniformly spreadon the two rings, the work done in moving acharge q from rings, the work done in movinga charge q from the centre of one ring to thatof the other is

R

A B

q

R

R 2 1

Q1 Q2

(a) zero

(b)1 2

0

( )( 2 1)24

q Q QR


15

(c) 1 2

0

2( )4

q Q QR

(d) 1 2

0

( )( 2 1)24

q Q QR

92. Point charge q moves from point P to pointS along the path PQRS (figure) in a uniformelectric field E pointing parallel to thepositive direction of the x-axis. Thecoordinates of the points P, Q, R and S are(a, b, 0), (2a, 0, 0), (a, – b, 0) and (0, 0, 0)respectively. The work done by the field inthe above process is given by expression

(a) qEa

(b) qEa

(c) 2qEa

Y

S

R

Q

P

E

(d) 2 2(2 )qE a b

93. The potential energy of a system of threeidentical point charges of 3.3 µC each, locatedat the vertices of an equilateral triangle witha side of 1m is(a) 0.5 J (b) 0.4 J(c) 0.3 J (d) 3.3 J

94. A charge q and having mass m placed at adistance a from d fixed from a fixed charge Q,is related. Its speed at infinite distance is

Q q

mfixed

d

(a) (b) 2kQqmd

(c) zero (d)2kQqmd

95. A particle of mass 2g and charge 1C is held ata distance of 1m from a fixed charged of 1 mc.If the particle is released, it will be repelled.The speed of the particle when it is at adistance of 10m from the fixed charge is(a) 100 m/sec (b) 90 m/sec(c) 60 m/sec (d) 45 m/sec

96. Three charges Q, +q and +q are placed at thevertices of a right angled isosceles triangle asshown. The net electrostatic energy of theconfiguration is zero if Q is equal to

(a) 1 2q

(b)

21 2

qa

a

Q

+q+q(c) 2q

(d) q97. A charged particle q is shot towards another

charged particle Q which is fixed, with a speedv. It approaches Q upto a closest distance r andthen returns. If q were given a speed 2v , thenthe closest distance of approach would be(a) r (b) 2r(c) r/2 (d) r/4

98. Positive and negative point charges of equal

magnitude are kept at 0, 0,2a

and

0, 0,2a

respectively. The work done by the

electric field when another positive point

charge is moved from (–a, 0, 0) to (0, a, 0) is

(a) positive(b) negative(c) zero(d) depends on the path connecting the initial

and final positions99. Two equal point charges are fixed at x = –a

and x = +a on the x-axis. Another point chargeQ is placed at the origin. The change in theelectrical potential energy of Q. when it isdisplaced by a small distance x along the x-axis, is approximately proportional to(a) x (b) x2

(c) x3 (d) 1/x100. Four equal charges of magnitude q each are

placed at four corners of a square with itscentre at origin and lying in y-z plane. A fifthcharge +Q is moved along x-axis. Theelectrostatic potential energy (U) varies on x-axis as

(a)–x xO

U

(b)–x xO

U


16

(c)–x xO

U

(d)–x xO

U

101. The work done in carrying a charge q onceround a circle of radius a with a charge Qat is centre is

(a)04

qQa

(b)2

04qQ

a

(c)04

qa

(d) zero

102. A hollow conducting sphere is placed in anelectric field produced by a point charge placedat P as shown in figure. Let VA, VB, VC bethe potential at point A, B and C respectively,then

(a) VC > VB (b) VA > VB(c) VB > VC (d) VA = VC

9. MISCELLANEOUS103. Three charges are placed on X-axis as shown

in figure. Charge –Q at origin will oscillate if itis displaced along (no gravity)(a) X-axis(b) Y-axis(c) Z-axis

(d) both (b) and (c)

y

Q - Qa x

z

Qa

104. Five balls numbered 1 to 5 are suspended usingseparate threads. Pairs (1, 2), (2, 4) while pairs(2, 3), (4, 5) show repulsion. Therefore ball 1must be(a) neutral(b) made of metal(c) positively charged(d) negatively charged

105. A charge q is placed at the centre of the openend of cylindrical vessel. The electric flux ofelectric field of charge q through the surfaceof the vessel is(a) 0/q (b) 0/2q

(c) 0/4q (d) 0

106. The electron of mass em , initially at rest,moves through a distance in a uniform electricfield in time 1t . A proton of mass pm alsoinitially at rest takes time 2t to move throughan equal distance in this uniform electric field.Neglecting effect of gravity, the ratio 2 1/t t isnearly

(a) 1 (b)p

e

mm

(c)e

p

mm (d) 1836

107. A Charge + q is carried from a point A (r, 135°)to point B (r, 45°) following a path which is aquadrant of circle of radius r. If the dipolemoment is p, the work done by the externalagent is

– +

A B

p

r r 45° 45°

(a) 0 (b) 20 r4pq

(c) 20 r

pq24

1 (d) r

pq4

1

108. The electric potential V as a function ofdistance x (in metre) is given by

2(5 10 9)V x x volt . The value ofelectric field at 1x m would be

(a) 20 /volt m (b) 6 /volt m(c) 20 /volt m (d) 11 /volt m

109. The variation of potential with distance R froma fixed point is as shown in the figure. Theelectric field at 5R m is

(Volt)V

0 1 5R (m)

1

2

3

4

5

2 43 6


17

(a) 2.5 /V m (b) 2.5 /V m

(c)2 /5

V m (d)2 /5

V m

110. The potential at a point x (measured in µm)due to some charges situated on the x-axis isgiven by

220( )

4V x volt

x

The electric field E at x = 4 m is given by

(a)10 /9

volt µm

and in the +ve x-direction

(b) 5 /3

volt µm

and in the –ve x-direction

(c)5 /3

volt µm

and in the +ve x-direction

(d)10 /9

volt µm

and in the –ve x-direction

111. An ellipsodial cavity is carved within a perfectconductor. A positive charge q is placed at thecentre of the cavity. The points A and B are onthe cavity surface as shown in the figure. Then

q BA

(a) Electric field near A in the cavity = Electricfield 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 surface

of the cavity is 0/q

112. A positively charged thin metal ring of radiusR is fixed in the xy-plane with its centre atthe O. A negatively charged particle P isreleased from rest at the point 0(0,0 )z , where

0 0z . Then the motion of P is(a) Periodic for all values of 0z satisfying

00 z (b) Simple harmonic for all values of satisfying

00 z R (c) Approximately simple harmonic provided

0z R(d) Such that P crosses O and continues to

move along the negative z-axis towardsz

113. A non-conducting ring of radius 0.5 m carriesa total charge of 101.11 10 C districbutednon-uniformly on its circumference producingan electric field E

everywhere in space. The

value of the line integral 0

. ( 0ll

E dl l

being

centre of the ring) on volt is(a) + 2 (b) –1(c) –2 (d) Zero

114. Figure shows three spherical and equipotentialsurfaces 1, 2 and 3 round a point charge q. Thepotential difference 1 2 2 3V V V V . If 1t and

2t be the distance between them. Then(a) 1 2t t

(b) 1 2t t q1

23

t2

t1(c) 1 2t t

(d) 1 2t t

115. A spherical charged conductor has surfacecharged density . The electric field on itssurface is E and electric potential of conductoris V. Now the radius of the sphere is halvedkeeping the charge to be constant. The newvalues of electric field and potential would be(a) 2 ,2E V (b) 4 ,2E V(c) 4 ,4E V (d) 2 ,4E V

116. Two identical particles of charge q each areconnected by a massless spring of forceconstant k. They are placed over a smoothhorizontal surface. They are released when theseparation between them is r and spring isunstretched. If maximum extension of thespring is r, the value of k is : (Neglectgravitational effect)

qk

q

(a)

2

0

14q

r r (b)2

02 1

rqr

(c)

2

0

2 1qr r (d)

2

0

1qr r

117. The energy stored in the electric field producedby a metal sphere is 4.5 J. If the spherecontains 4C charge, its radius will be

9 2 2

0

1: 9 10 /4

Take Nm C

(a) 32 mm (b) 20 mm(c) 16 mm (d) 28 mm


18

118. Four closed surfaces and corresponding chargedistributions are shown below.

Let the respective electric fluxes through thesurfaces be 1 2 3 4, , and . Then(a) 1 2 3 4= (b) 1 3 2 4;(c) 1 2 3 4 (d) 1 2 3 4

119. The region between two concentric spheres ofradii ‘a’ and ‘b’, respectively (see figure), has

volume charge density ,Ar

where A is aconstant and r is the distance from the centre.At the centre of the spheres is a point chargeQ. The value of A such that the electric field inthe region between the spheres will beconstant, is :

Qa

b

(a) 22Qa

(b) 2 22 ( )Q

b a

(c) 2 22

(a )Q

b (d) 22aQ

120. The potential (in volts) of a charge distributionis given by

V(z)= 30 – 5z2 for |z| 1mV(z)= 35 – 10|z|for |z| 1mV(z) does not depend on x and y. If this potnetialis generated by a constant charge per unitvolume 0 (in units of 0 ) which is spread overa certain region, then choose the correctstatement.(a)

0 020 in entire region(b)

0 010 for |z| 1m and 0

0elsewhere

(c) 0 020 for |z| 1m and

00

elsewhere(d)

0 040 in the entire region

121. A thin disc of radius b = 2a has a concentrichole of radius a in it (see figure). It carriesuniform surface charge on it. If the electricfield on its axis at height h(h << a) from itscentre is given as E then values of E is

(a)0a (b)

02a

(c)04a (d)

08a

122. Determine the ratio 1

2

qq

, as lines of forces

of two points charges as shown in figure

=8q =4q

(a)1

2

12

qq (b)

1

24

qq

(c) 1

22

qq (d) 1

21

qq

123. A small block of mass m and charge +q iskept on smooth inclined plane of angle 60°,placed in a elevator going upward withacceleration ‘a0’. Electric field E existsbetween the vertical sides of the wall of theelevator. The time taken by the block to cometo the lowest point of inclined plane is

(a)

0

2

( ) 3

htqEg a m


19

(b)0

223 ( ) 3

hmtm g a qE

(c)qEtm

(d) None of these

124. A charged particle of mass m and charge q,initial at rest x = 0, is forced to move byan external electric field 0

ˆ( )E E x j ,where is a positive constant and x is thedisplacement of the particle in time t alongx-axis. Find the distance moved by thecharged particle when it again is brought torest.

(a)

02E(b)

0E

(c)

03E(d) 2E0

125. In two cases (a) and (b) a particle of massm is executing SHM shown in figure. Indiagram (b) particle is moving a charge q sothat Eq = mg. If their velocities are sameat mean position, mark the correct optionif A1 and A2 be their amplitudes of T1 andT2 are their time periods

T1 T =m2 1

(a) A1 = A2, T1 = T2(b) A2 > A1, T1 = T2(c) A1 = A2, T2 > T1(d) A1 > A2, T2 > T1

126. If electric field in a region is2 2ˆ ˆ2 ( ) jE axy i a x y

where a is a constant,

then find the potential as function of (x, y)

(a) 3

223

ayax (b)3

02 –3

ayV

(c)3

20 –

3ayV ax y (d)

2 3

0 2 3axy ayV

127. The figure shows the potential of two equaland oppsote point charges. The dotted curvesare the individual potential function whereas solid curve the total potential function, thewould be encountered when the two chargesare brought closer:

(a) (b)

(c) (d)

128. A point charge q is placed inside anelectrically neutral shell whose outer surfacehas spherical shape. Find the potential V atthe point P lying outside the shell at adistance r from the centre O of the outersurface

(a)0

14

qVr

(b)0

18

qVr

(c)0

24

qVr

(d)2

0

14

qVr

129. A thin wire ring of radius r has an electriccharge q. A point charge q0 is placed at therings centre. The increment of the forcestretching the wire is

(a) 02 2

08

qq

r (b) 0

2 204

qq

r

(c) 02 2

02

qq

r (d) 0

2 20

qq

r

130. If the charge density of a spherical chargedistribution is given by

0 for( )

0 for

qr r a

ar

r a

, then the total

charge on the distribution is

(a) 30

23

a (b) 30

13

a

(c) 30 0q a (d) 2 a3 0


20

131. The electric potential at a point (x, y, z) isgiven V = – x2y – xz3 + 4. The electric field

E

at the point is

(a) 3 2 3ˆ ˆ ˆ(2 ) 3E i xy z j x k xz

(b) 2 2 2ˆ ˆ ˆ2 ( ) (3 )E i xy j x y k xz y

(c) 3 2ˆ ˆ ˆE i z j xyz k z

(d) 3 2 2ˆ ˆ ˆ(2 ) 3E i xy z j xy k z x

132. Two point charges placed at a certain distancer in air exert a force F on each other. Thenthe distance r at which these charges willexert the same force in a medium of dielectricconstant k is given by

(a) r (b) rk

(c)rk (d) r k

133. Two point charge –Q and 2Q are placed ata distance r apart, where should be a thirdcharge q be placed so that the system is inequilibrium

( – )r x

2Qq

–Q

r

x

(a)( 2 1)

rx

(b)( 2 1)

rx

(c) ( 2)3

rx (d)3rx

10. INTEGER TYPE QUESTIONS

134. Minimum value of a charge on a body can be4n × 10–20 C. The value of n is

135. Electric field intensity due to a source chargeQ at distance r varies as E r–n. Then the valueof n is

136. Electric field intensity due to electric dipole ata point of distance r from its centre varies as

1E .nr

Find the suitable value of n which is

satisfies given condition.137. Electric flux through a closed surface in free

space enclosing a charge q is 0.nq Find the

value of n.138. The linear charge density of an infinite line

charge producing an electric field of 9 × 104 NC–1 at a distance of 2 cm is a × 10–7 C/m. Findthe value of a.

139. The acceleration 1.6 × 109n m/s2 produced inan electron placed in electric field of intensity9.1 × 106 N C–1. The value of n which is satisfiedgiven condition. (mass of electron = 9.1 × 10–31

kg, e = 1.6 × 10–19 C).140. A charged particle of mass 3 mg is held

stationary in space by placing it in an electricfield of 6 × 104 N C–1 directed upward. Themagnitude of the charge is 5 × 10–2n. Find thevalue of n.

141. Two point charges separated by a distance drepel each other with a force of 9 N. If theseparation between them becomes 3d, the forceof repulsion will be

142. In a hydrogen atom, the distance between theelectron and proton is 2.5 × 10–11 m. Theelectrical force of attraction between them willbe 3.7 × 10–n. Then the value of n is

143. Four charges as shown in figure are placed atthe corners of a square of side a. If the ratio ofQ/q is 2x . Where Fnet on Q is zero. Thenfind the vaue of x.

q

q

Q

Q

a a


21

1. CHARGES AND ITS PROPERTIES1. b 2. a 3. d 4. b

2. COLOUMB LAW5. c 6. d 7. d 8. d 9. a10. b 11. b 12. a 13. b 14. b

3. ELECTRIC FIELD15. a 16. c 17. a 18. a 19. d20. c 21. d 22. d 23. c 24. b25. b 26. c 27. c 28. c 29. c30. d 31. b 32. c 33. d 34. a35. c 36. a 37. b 38. a 39. a

4. ELECTRIC FLUX40. a 41. d 42. d 43. c 44. c

5. ELECTRIC DIPOLE45. a 46. c 47. b 48. c 49. b50. c 51. c 52. c 53 a 54. a

6. GAUSS LAW55. a 56. a 57. c 58. c 59. a60. c 61. a 62. b 63. b 64. c65 a 66 c 67 c 68. a

7. POTENTIAL69. b 70. c 71. b 72. c 73. a74. d 75. b 76. d 77. c 78. a79. d 80. b 81. d 82. b 83. b84. a 85 d 86. c 87. c

8. POTENTIAL ENERGY AND WORK DONE88. d 89. c 90. b 91. b 92 b93. c 94. d 95. b 96. b 97. d98. c 99. b 100. b 101. d 102. d

9. MISCELLANEOUS103. d 104. a 105. b 106. b 107. c108. a 109. a 110. c, d 111. d 112. a113. c 114. a 115. b 116. d 117. a118. a 119. a 120. b 121. c 122. c123. a 124. a 125. c 126. a 127. a128. a 129. a 130. c 131. d 132. c133. b

10. INTEGER TYPE QUESTIONS134. 4 135. 2 136. 3 137. 1 138. 1139. 2 140. 2 141. 1 142. 7 143. 2

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