Electrostatics Solved QBpdf

7/30/2019 Electrostatics Solved QBpdf

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ELECTROSTATICS Question Bank

EASY QUESTIONSE

1. In the circuit shown, a potential difference of 60Vis applied across AB. The potential difference

between the pointsMandNis

(a) 10 V (b) 15 V

(c) 20 V (d) 30 V

A

B

M

N

2 C

CC

2 C

60 V

Sol.: Charge on capacitorCbetweenMNis

2

60C

C30

V3030

C

CV

MN

(d)

A

B

M

N

2 C

CC

2 C

60 V

E

2. A positively charged thin metal ring of radiusR is fixed inxy plane with its centre at theorigin O. A negatively charged particle P is released from rest at the point (0, 0, Z0). Then

the motion ofP is(a) periodic for all values ofZ0

(b) SHM for all values ofZ0 satisfying 0 R

(d) cant be said

Sol.: (a)

E

3. A capacitor of capacitance C is connected with a

battery of emf as shown. After full charging adielectric of same size of capacitor and dielectricconstant k is inserted then choose correct statements.(capacitor is always connected to battery)

C

(a) electric field between plates of capacitor remain same

(b) charge on capacitor is C

(c) energy on capacitor decreased

(d) electric field between plates of capacitor increased.

Sol.: P.D. same and electric field same (a)E


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4. Shown in the figure is a distribution of charges. Theflux of electric field due to these charges through thesurface is(a) 3 q / 0 (b) 2 q / 0(c) q / 0 (d) zero

+q q

q

Sol.: (d)

E

5. Two spherical conductorsA andB of radii 1 mm and 2 mm are separated by a distance of5 cm and are uniformly charged. If the spheres are connected by a conducting wire then inequilibrium condition, the ratio of the magnitude of the electric fields at the surface ofspheresA andB is

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

Sol.:1

2

A

B

B

A

r

r

E

E

(d)

E

6. A point charge + q is fixed at point B. Another pointcharge + q atA of mass m vertically aboveB at height his dropped from rest. Choose the correct statement

(a) It will collide withB(b) It will execute S.H.M

(c) It will go down only if0

2

4q

< mgh2

h

A

B

+q

+q

(d) go down up to a point and then come up.

Sol.: For charge + q atA to come down, Fe < mg

mg4 20

2

hq

(c)

E

7. The electric field intensity at a point at a distance 2 m from a charge q isE. The amount ofwork done in bringing a charge of 2 coulomb from infinity to this point will be

(a) 2Ejoules (b) 4Ejoules (c)2

Ejoules (d)

4

Ejoules

Sol.: Potential at this point, ErEr

qV 2

4 0

Work done = qV= 4Ejoules.

(b)

E


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8. A simple pendulum of length l has a bob of mass m, with a charge q on it. A vertical sheetof charge, with surface charge density passes through the point of suspension. Atequilibrium, the string makes an angle with the vertical, then

(a)mg

q

02tan

(b)mg

q

0

tan

(c)

mg

q

02cot

(d)mg

q

0

cot

Sol.:mg

qE

mg

Fe tan

mg

q

mg

q

0

0

2

2/tan

(a)B

T

O

Sheet of charge

E

A

C

+

+

++

++

++

+++

E

9. A charged particle of mass m and charge q is released from rest in an electric field of constantmagnitudeE. The kinetic energy of the particle after time twill be

(a)qm

tE222

(b)2

2

2 t

mqE(c)

m

tqE

2

222

(d)t

mqE

2

Sol.: (c)

E

10. If a positively charged pendulum is oscillating in a uniformfield as shown, then its time period as compared to that whenit was uncharged will

(a) increase (b) decrease

(c) not change (d) none of these

+

+ + + + + + + + + + +

Sol.: (a)

E

11. A andB are two concentric metallic hollow spheres. IfA isgiven a charge q whileB is earthed as shown in figure, then

(a) charge density ofA andB are same

(b) field inside and outsideA is zero

(c) field betweenA andB is not zero

(d) field inside and outsideB is zero

q B+ +

++

++++

++

+A

Sol.: (c)


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E

12. A table tennis ball which has been covered with a conducting paint is suspended by a silk

thread so that it hangs between two metal plates. One plate is earthed. When the other plateis connected to a high voltage generator, the ball

(a) is attracted to the high voltage plate and stays there

(b) hangs without moving

(c) swings backward and forward hitting each plate in turn

(d) is repelled to the earthed plate and stays thereSol.: (c)

E

13. A spring block system undergoes vertical oscillations above a large horizontal metal sheetwith uniform positive charge. The time period of the oscillation is T. If the block is given acharge Q, its time period of oscillation

(a) remains same

(b) increases

(c) decreases

(d) increases ifQ is positive and decreases ifQ is negativeSol.: (a)

E

14. There is an electric fieldEinX-direction. If work done in moving a charge 0.2 Cthrough adistance of 2 m along a line making an angle of 60 withX-axis is 4.0 joule. The value ofEis

(a) 3 N / C (b) 4 N / C (c) 5 N / C (d) 20 N / C.

Sol.: As coscos dsqEdsFW N/C.20,60cos22.04 EE

(d)

E

15. In electrolysis, the amount of mass deposited or liberated at an electrode is directlyproportional to

(a) amount of charge (b) square of current

(c) concentration of electrolyte (d) square of electric charge

Sol.: (a)

E

16. The ratio of the forces between two small spheres with same charges when they are in air towhen they are in a medium of dielectric constant Kis

(a) 1 : K (b)K: 1 (c) 1 : K2 (d) K2 : 1


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Sol.: In air2

2

0

14

1

r

qF

In medium (k)2

2

0

24

1r

q

kF

12

1 k

F

F

(b)

E

17. A charge Q is divided into two parts of magnitude q and Q q. If the coulomb repulsion

between them when they are separated at some distance is to be maximum, the ratio ofq

Q

should be

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

Sol.:

204

1

r

qQqF

For maximum repulsion force 02 qQdq

dF

21

2

q

Q

(a)

E18. There are two charges +1 C and +5 C. The ratio of the forces acting on them will be

(a) 1 : 5 (b)1 : 1 (c) 5 : 1 (d) 1 : 25

Sol.: 2112 FF then1

1

21

12 F

F

(b)

E

19. The electric potential Vis given as a function of distancex (metre) by V = (5x2+10x 9)volt.

Magnitude of electric field atx = 1 is(a) 20 V/m (b)6 V/m (c) 11 V/m (d) 23 V/m

Sol.: V/m2010101

x

xdx

dVE

(a)

E

20. If specific resistance of a wire is , its volume is 3m3 and its resistance is 3 omhs, then itslength will be

(a) 1

(b) 3 (c) 31

(d) 31


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Sol.: Volume =Al = 3 l

A3

NowAlR 9

2l 3l

(b)

E

21. Figure shows the electric lines of force emerging from acharged body. If the electric field atA andB areEA andEBrespectively and if the displacement betweenA andB is rthen

(a)BA

EE (b)BA

EE

(c)r

EE B

A (d)

2r

EE B

A

A Br

Sol.:

n

dg

n

gg 1' ,

n

nRd

1

(b)

E

22. The magnitude of electric field intensityEis such that, an electron of mass m and charge e

placed in it would experience an electrical force equal to its weight is given by

(a) mge (b)e

mg(c)

mg

e(d) g

m

e2

2

Sol.: eE= mg

e

mgE

(b)

E

23. Figure shows three points A, B and C in a region ofuniform electric fieldE

. The line AB is perpendicular andBC is parallel to the field lines. Then which of thefollowing holds good. Where VA, VB andVC represent theelectric potential at pointsA,B and C respectively

(a)CBA

VVV (b)CBA

VVV

(c)CBA

VVV (d)CBA

VVV

A

B C

Sol.: (b)


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E

24. ABCis an equilateral triangle. Charges +q are placed at eachcorner. The electric field intensity at centroidO will be

(a)2

02

1

r

q

(b)

20

3

2

1

r

q

(c)2

0

3

2

1

r

q

(d) zero

O

+q

A

B C+q+q

r

Sol.: Electric field due each charge have same magnitude and makes an angle of 1200 with eachother.

(d)

E

25. A charged particle of mass m and charge q is released from rest in an electric field ofconstant magnitudeE. The kinetic energy of the particle after a time tis

(a)m

tqE222

(b)m

tqE2222

(c)m

tqE

2

222

(d)m

tqE2224

Sol.: atuv , u = 0

tm

qEv

m

tEqmv

22

1 2222

(c)

E

26. Three charges Q, +q and +q are placed at the verticesof a right angle triangle (isosceles triangle) as shown.The net electrostic energy of the configuration is zero,ifQ is equal to

(a)21

q(b)

22

2

q

(c) 2q (d) +q a

+q +q

Q

Sol.: 02

2

a

kQq

a

kq

a

Qqk ,

222

qQ

(b)

E


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27. A spherical conductorA of radius r is placed concentrically inside a conducting shellB ofradius R(R > r). A charge Q is given to A, and thenA is joined to B by a metal wire. Thecharge flowing fromA toB will be

(a) Q

rR

R(b)

rRr

Q (c) Q (d) zero

Sol.: When the two are joined by a metal wire, they become a single conductor. As charge canreside only on the outer surface of a conductor, the entire charge Q must flow to the outersphere.

(c)

E

28. An electron moves in a circular orbit at a distance from a proton with kinetic energy E. Toescape to infinity, the energy which must be supplied to the electron is

(a)E (b) 2E (c) 0.5E (d) 2E

Sol.: Total energy = kinetic energy = -E

So energyEshould be supplied

(a)

E

29. A capacitor is connected to a battery. The force of attraction between the plates when the

separation between them is halved(a) remains the same (b) becomes eight times

(c) becomes four times (d) becomes two times

Sol.: Distance between plates halved capacitance becomes doubled also charge becomes doubled,

Force of attraction Q2

Force becomes four time.

(c)

E

30. The electric E

is given by jbiaE

(where a andb is constant and ji , are unit vector

alongx andy axis respectively), the flux passing through a square area of side l and paralleltoy-z plane is

(a) bl2 (b) al2 (c) 222 lba (d) 222 lba

Sol.: Area vector ilA 2

2. alAE

(b)


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E

31. Four charge particle of charges q, q, q and 3q

are placed at the vertices of a square of side a asshown. The magnitude of dipole moment of thearrangement is

(a) aq22 (b) aq

(c) 3 qa (d) qa22

q 3q

q q

Sol.: pnet = 22 qa

(a)q q,q,q

q q

qap

21 qap

qap

E

32. A cylinder of radius R and length L is placed in a uniform electric field Eparallel to theaxis of cylinder. The total flux through the curved surface of the cylinder is given by

(a) 2 R2E (b) 2 R2 /E (c)E2RL (d) zero

Sol.: (d)

E

33. An uniform electric field in positivex-direction exists in a region. LetA be the origin,B bethe point on the x-axis at x = +1 cm and Cbe the point on the y-axis at y = +1 cm. The

potential at the pointsA,B andCare VA, VB andVCrespectively, then

(a)BA VV (b) BA VV (c) CA VV (d) CA VV

Sol.: In the direction of electric field potential decreases and perpendicular to electric field it

remain same, henceBCA

VVV

(b)

E

34. The electric field at the origin is along the positive X-axis. A small circle is drawn with thecentre at the origin cutting the axes at pointsA,B, CandD having coordinates (a, 0) (0, a),(a, 0), 0, a) respectively. Out of the points on the periphery of the circle, the potential isminimum at(a)A (b)B (c) C (d)D

Sol.: Clearly potential decreases along the direction of electric field

Vmin is atA (a, 0)

(a)


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E

35. Charge Q is given a displacement jbiar

in an electric field jEiEE 21

. The work

done is(a) Q(E1a +E2b) (b)

22

21 )()( bEaEQ

(c) Q(E1 +E2)22 ba (d) 2222

21 ) baEEQ

Sol.: dw = QE .

rd = Q ( ) 21 jEiE . ( ) idyixd

= Q a b

dyQExdE0 0

21 = Q (E1a +E2b)

(a)

E

36. In the circuit shown, the equivalent capacitance betweenthe pointsA andB is

(a)3

10F (b)

4

15F

(c)5

12F (d)

6

25F

A B

3 F

2 F 4 F

6 F5 F

Sol.: Since4

6

2

3 The circuit is treated as wheatstone bridge.

Ceq=4242

6363

= 2 +6

20

6

8 =

3

10F

(a)

E

37. A non-conducting ring of radiusR has charge Q distributed uniformly over it. If it rotateswith an angular velocity , the equivalent current will be

(a) zero (b) Q (c)

2

Q (d)R

Q

2

Sol.: With each rotation, charge Q crosses any fixed point P near the ring. Number of rotationsper second = /2.

Charge crossing P per second current =

2

Q

(c)

E


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38. A battery consists of a variable numbern of identical cells having internal resistance reach.They are connected in series. The terminal of the battery are joined by a conducting wire

and the current i is measured. Which of the graphs as shown in figure gives correctrelationship between i andn?

(a)

X

Y

O

i

n

(b)

X

Y

O

i

n

(c)

X

Y

O

i

n

(d)

X

Y

O

i

n

E

39. A half ring of radiusR has a charge of per unit length. The potential at the center of thehalf ring is

(a)R

k

(b)R

k

(c)R

k

(d) k

Sol.: dV=R

Rdk

R

kdQ

00

dkdvv

= k (d)

E

40. If electric field is given by i

x

E 1

2

V/m, the magnitude of potential difference between

pointsx = 10 cm andx = 20 cm is(a) 1 V (b) 2V (c) 5V (d) 10 V

Sol.: dV= 2.0

1.0

25

1. dx

xdxE V

(c)E

41. A cube of side b has a charge q at each of its vertices. The electric potential at the centre ofthe cube is

(a)b

q

034

(b)b

q

0

3

(c)b

q

0

2

(d) zero


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Sol.:b

q

b

qV

3

48

2

3.

4

1

0

(a)E

42. Four equal charges Q are placed at the four corners of a square of side a. The work done inremoving a charge Q from the centre of the square to infinity is

(a) zero (b)a

Q

0

2

4

2

(c)

a

Q

0

22

(d)

a

Q

0

2

2

Sol.: iif VQVVQVQW 0 , W=a

Q

a

QQ

224

2.

4

1.

(c)

E

43. In a regular polygon of n sides, each corner is at a distance r from the center. Identicalcharges of magnitude Q are placed at (n 1) corners. The field at the center is

(a)2

r

Qk (b)

2)1(

r

Qkn (c)

21 r

Qk

n

n

(d)

2

1

r

Qk

n

n

Sol.: From symmetry electric field at the centre is2r

Qk

(a)

E

44. Seven point charges each of charge q is placed at the seven corners of a cube of side a (onecorner is empty). Find the magnitude of electric field at centre of cube.

(a) zero (b)2

04

1

a

q

(c)

2

03

1

a

q

(d)

2

0

7

4

1

a

q

Sol.:2

0

2

34

1

a

qE

2

03

1

a

q

(c)

E

45. A charged sphere of diameter 4 cm has a charge density of 10 -4 coulombs/cm2. The workdone in joules when a charge of 40 nano-coulombs is moved from infinity to a point which isat a distance of 2 cm from the surface of the sphere, is

(a) 14.4 (b) 28.8 (c) 144 (d) 288


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Sol.:2

410

cm

CAQ

16 cm2 = 16 10-4 C

rQV

04 Work done W= qV=

rqQ

04

(a)

E

46. The magnitude of electric intensity at a distancex from a charge q isE. An identical charge isplaced at a distance 2x from it. Then the magnitude of the force it experience is

(a) qE (b) 2 qE (c)2

qE(d)

4

qE

Sol.: GivenE=2

04 xq

.

Hence the magnitude of the electric intensity at a distance 2x from charge q is

44

1

4)2(4'

20

20

E

x

q

x

qE

Therefore, the force experienced by a similar charge q at a distance 2x is

4'

qEqEF

(d)

E

47. A conductor of resistance 3 is stretched uniformly till its length is doubled. The wire is nowbent in the form of an equilateral triangle. The effective resistance between the ends of anyside of the triangle in ohms is

(a)2

9(b)

3

8(c) 2 (d)1

Sol.:R =

VlA

l

A

l2

l2, RAB = 8/3

(b)

4 4

4A B

E

48. Eight dipoles of charges of magnitude e are placed inside a cube. The total flux coming out ofthe cube equals to

(a)e8

(b)0

16

e

(c)0

e(d) zero

Sol.: Net charge inside the cube is zero (d)


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E

49. Four point charges q1, q2, q3 andq4 are placed at the corners of the squareof side a, as shown in figure. The potential at the centre of the square is

(Given : q1 = 1 108 C, q2 = 2 10

8 C, C103 83q ,

C102 84q , a = 1 m)

(a) 507 V (b) 607 V

(c) 550 V (d) 650 V

a

a a

a

P

q1 q2

q3q4

Sol.:

r

q

r

q

r

q

r

qV 4321

04

1= 507 V

(a)

E

50. If there are n capacitors in parallel connected to V volt source, then total energy stored isequal to

(a) CV (b) 22

1nCV (c) 2CV (d) 2

2

1CV

n

Sol.: Energy Stored= 22net2

1)(

2

1nCVVC

(b)

E

51. There is an air-filled 1 pF parallel plate capacitor. When the plate separation is doubled andthe space is filled with wax, the capacitance increases to 2pF. The dielectric constant of waxis

(a) 2 (b) 4 (c) 6 (d) 8Sol.: (b)

E

52. For the circuit shown in the adjoining figure, the charge on 4 Fcapacitor is(a) 30 C (b) 40 C

(c) 24 C (d) 54 C

1F

5F

4F

3F 10V

Sol.: 1064

11 qq

C241 q (c)

4F

3F 10V

q1

6Fq2

q1

E


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53. Two conducting spheres of radii r1 andr2 are at the same potential. The ratio of their chargesis

(a)

2

2

2

1

rr (b)

2

1

2

2

rr (c)

2

1

rr (d)

1

2

rr

Sol.: Potential (V) =r

q

04

1

2

1

2

1

r

r

q

q

(c)

E

54. Six point charges are arranged at the vertices of

regular hexagon of side length a (shown in figure).The magnitude of electric field at the centre ofregular hexagon is

(a)2

04 a

q

(b) zero

(c)2

02 a

q

(d) none of these

+q

+qq

+q

+q +q

O

Sol.: Resultant field =2

0

04

22

a

qE

(c)

E

55. In the given figure, find the equivalent capacitancebetweenA andB.

(a)3

2C(b)

4

5C

(c)2

3C(d)

5

4C

A B

C C

CC

C C

CC

Sol.: Reduced circuit is

CCeq

2

3

(c)

C C

CC

CC


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E

56. Two large plate separated by a distance d in vertical plane

and connected to battery as shown. An electron of charge eand mass m is at rest between the plates. Find the value ofpotential difference of battery.

(a)d

mge(b)

d

mge2

(c)e

mgd(d)

e

mgd2

electron d

Sol.: eEmg d

Vemg ,

e

mgdV

(c)

E

57. Two plates are 2 cm apart. A potential difference of 10V is applied between them, theelectric field between the plates is

(a) 20 N/C (b) 500 N/C (c) 5N/C (d) 250N/C

Sol.: d= 2cm = 2 102 m, V= 10 volt ,

2102

10

d

VE 500 N/C

(b)

E

58. Suppose the electrostatic potential at some points in space are given by xxV 22 . Theelectrostatic field strength atx = 1 is(a) zero (b) -2 (c) 2 (d) 4

Sol.: dx

dvEx , xEx 22 , atx = 1 E(x=1) = 0

(a)

E

59. A slab of copper of thickness b is inserted in betweenthe plates of parallel plate capacitor as shown in figure.

The separation between the plates is d if2

db , then

the ratio of capacities of capacitors after and beforeinserting the slab will be

d

b

(a) 1:2 (b) 2 : 1 (c) 1 : 1 (d) 1 : 2


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Sol.:d

AC 01

,

tdA

C

02 ,

2

dbt given

1

2

1

2 C

C

(b)E

60. The equivalent capacity of the combinationshown in figure is(a) C (b) 2C(c) 3/2C (d) C/2

C

C

C

BA

Sol.: One single capacitor is in short circuit and the remaining two capacitors are in parallel.

(b)E

61. An electric dipole is placed at an angle of 300 to a non-uniform electric field. The dipolewill experience

(a) a translational force only in the direction of the field

(b) a translational force only in a direction normal to the direction of the field

(c) a torque as well as a translational force

(d) a torque only

Sol.: (c)

E

62.Coulombs law is applicable to(a) point charges (b) spherical charges (c) like charges (d) all of these

Sol.: (a)

E

63. A point charge q and a charge q are placed atx = -a andx = +a respectively. Which of thefollowing represents a part ofE-x graph?

x

E

a +aO(a) x

E

a

O(b)

x

E

+aO(c)

(d) all of these

Sol.: (d)

E

64. The charge on any one of the 2Fcapacitors and 1F capacitor will be givenrespectively (in C) as

(a) 1 , 2 (b)2 , 1

(c) 1, 1 (d) 2,2

2F 2F

1F

2V


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Sol.: Potential difference across the boththe line is same i.e. 2V.Hence charge flowing line 2

C222

2

Q

So charge on each capacitor in line(2) is 2 C (d)

Line (2)

2F 2F

1F

2V

Line (1)

E

65. The electric potential V (in volt) varies with x (in metre) according to the relation245 xV . The force experienced by a negative charge of 2 106 C located atx = 0.5 m

is

(a) 2 106 N (b) 4 106 N (c) 6 106 N (d) 8 106 N

Sol.: Electric field xxdx

d

dx

dVE 845 2

Force on charge qxqEq 8

Atx = 0.5 m, force = 8 2 106 0.5 = 8 106 N

(d)

E

66. A charge q is placed at the centre of the line joining two equal charges Q. The system of thethree charges will be in equilibrium ifq is equal to

(a) (Q/4) (b) (Q/2) (c) (Q/2) (d) (Q/4)

Sol.: Net force on any charge = 0. Force on any charge Q at end

04 22

2

x

KqQ

x

QKF . Hence,

4

Qq

(a)

E

67. The electric potential at a point situated at a distance ron the axis of a short electric dipoleof momentp will be 1/4 (0) times

(a)p/r3 (b)p/r2 (c)p/r (d) none of the above

Sol.: Potential at axial point2

04

1

r

PV

(b)


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E

68. The charge per unit length for a very long straight wire is . The electric field at points near

the wire (but outside it) and far from the ends varies with distance ras(a) r (b) 1/r (c) 1/r2 (d) 1/r3

Sol.:r

E02

. Hence

rE

1

(b)E

69. A body has a charge of one coulomb. The number of excess (or lesser) electrons on it fromits normal state will be

(a) (b) 1.6 1019 (c) 1.6 1019 (d) 6.25 1018

Sol.: Q = ne, 1819

1025.6106.1

1

n

(d)E

70. The net charge on a condenser is

(a) Infinity (b) q/2 (c) 2q (d) zero

Sol.: Net charge 0 QQ (d)

E

71. A conducting hollow sphere of radius 0.1 m is given a charge of 10 C. The electricpotential on the surface of sphere will be

(a) zero (b) 3 105 V (c) 9 105 V (d) 9 109 V

Sol.: Vsurface= V10910

1010109

4

1 51

69

0

r

Q

(c)E

72. The effective capacitance between the pointsxandy in the will be

(a) 1 F (b) 1.5 F

(c) 2 F (d) 4 F

1F

1F

1F

x

y

Sol.:

11

111Ce 1.5 F

(b)


20/75


E

73. The equivalent capacitance between the points

XandYin the figure will be(a) 2C/3 (b) C/3

(c) 3C/2 (d) 3C

CX

C/2

Y

+

Sol.: Capacitors in series,321

21 C

CC

CCCe

(b)

E

74. A charged ball hangs from a silk thread of length l. Itmakes an angle with a large charged conducting sheet Pas shown in the figure. The surface charge density of thesheet is proportional to

(a) cos (b) cot

(c) sin (d) tan

S

++++++

Sol.:02

sin

qT , MgT cos ,

tan

(d) Tsin

Tcos

Mg

02.

q

E

75. A charge q is placed at a distance a/2 above the centre of a

horizontal square surface of edge a as shown in figure. Theelectric flux through the square surface is

(a) Q/20 (b) Q/0

(c) Q/60 (d) Q/80

q

aa/2

a

Sol.: Complete the cube, adding other five faces.

0

qcube

,06

q

face

(c)


21/75


E

76. In the figure shown (circuit), the capacitance between the

pointsA andB will be

(a) 1F (b) 2F

(c) 3F (d) 4F

A

B

2F

2F1F1F

2F

Sol.: Ceff= 2 FSimplifying the circuit)

(b)

E

77. Two equal positive charges +q each are fixed a certain distance apart. A third equal positivecharge +q is placed exactly mid-way between them. Then the third charge will

(a) move at an angle of 450 to the line joining the two charges

(b) move at an angle of 900 to the line joining the two charges

(c) move along the line joining the two charges

(d) stay at rest

Sol.: Mid point will be neutral point, hence third charge will experience no force and will stay atrest.

(d)E

79. Two equal negative charges q are fixed at points (0, a) and (0, a) on they-axis. A positivecharge Q is released from rest at a point (2a, 0) on thex-axis. The charge Q will

(a) execute simple harmonic motion about the origin

(b) move to the origin and remain at rest there

(c) move to infinity

(d) execute oscillatory but not simple harmonic motion

Sol.: Resultant force on Q will be always towards origin. It will undergo oscillatory motion, butnot SHM (amplitude being comparable to other dimension and not small).

(d)

E

80. Two point charges +4q and +q are placed 30 cm apart. At what point on the line joiningthem is the electric field zero?

(a) 15 cm from charge 4q (b) 20 cm from charge 4q

(c) 7.5 cm from charge q (d) 5 cm from charge q


22/75


Sol.:

22

21

4

r

qK

r

qK

22

1 rr and 3021 rr

Hence, r1 = 20 cm

(b)E

81. The effective capacitance of two capacitors of capacitances C1 and C2 (with C2>C1)

connected in parallel is6

25times the effective capacitance when they are connected in

series. The ratio C2/C1 is

(a)2

3(b)

3

4(c)

3

5(d)

6

25

Sol.: Cparallel = C1 + C2, Cseries =21

21

CC

CC

Given Cseries6

25 Cparallel andC2 > C1

Solving2

3

1

2 C

C

(a)E

82. A capacitor of capacitance 4 F is charged to 80 V and another capacitor of capacitance6 F is charged to 30 V. When they are connected together, the energy lost by the 4 Fcapacitor is(a) 7.8 mJ (b) 4.6 mJ (c) 3.2 mJ (d) 2.5 mJ

Sol.: Vcommon VCC

VCVC50

21

2211

For 4 F capacitor2

12

12

1,2

1Cf VCEVCEi

Energy loss 222

1Cfi

VVCEE 7.8 103 J

(a)E

83. Two concentric spheres are of radii r1 and r2. The outersphere is given a charge q. The charge 'q on the inner

sphere will be (inner sphere is grounded) r2r1'q

(a) q (b) q (c)2

1

rrq (d) zero


23/75


Sol.: 0'

21

r

q

r

q

(d)E

84. The equivalent capacitance between pointsMandNis

(a) 011

10C (b) 2C0

(c) C0 (d) none of these

C0

C0

C0

C0M N

C0

C0

Sol.:

00 5

3

2

11

CCCe

011

10CC

e

(a)

2C0 (5/3)C0

M N

E

85. As shown in the figure. If value of 'Q is2

Qthen what is

the value of dielectric constant kis

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

Q Q

Metal plate Dielectric

Sol.: We know

k

QQ1

1' ,

k

QQ 1

12

k= 2

(c)

E86. In the given circuit diagram, initially battery was connected.

Find the work done by battery if capacitor is completelyfilled with a dielectric of dielectric constant k= 3.

(a) 22

1CV (b) 2CV

(c) 22CV (d) 22

3CV

C

V

Sol.: CVCVkCVkCVQ 2)1()( , W= 22CVQV

(c)


24/75


E

87. A parallel plate capacitor of capacitance Cis connected to a battery of emfV. If a dielectric

slab is completely inserted between the plates of the capacitor and battery remainsconnected, then electric field between plates

(a) decreases (b) increases

(c) remains constant (d) may be increase or may be decrease

Sol.: (c)

E

88. A uniform electric field )(0 jiEE exists in the region. The potential difference

PQ VV between point P(0, 0) andQ (a, 0) is

(a) aE0 (b) aE 20 (c) aE0 (d) aE 20

Sol.: aEiajiEVV PQ 00 )()( .

(a)

E

89. A long string with a charge of per unit length passes through an imaginary cube of edge

a. The maximum flux of the electric field through the cube will be

(a) 0/a (b)0

2

a

(c)0

26

a

(d)0

3

a

Sol.: The maximum length of the string which can fit into the cube is a3 , equal to its body

diagonal. The maximum charge inside the cube is a3 , and hence the maximum flux

through the cube is0

3

a

(d)E

90. The electric potential Vat any pointx,y,z (all in metres) in space is given by V= 4x2 volts.The electric field (in V/m) at the point (1 m, 0, 2 m)

(a) i8 (b) i8 (c) i16 (d) i58

Sol.: xx

VEx 8

0 zy EE as Vis independent ofy andz.

Forx = 1, iE 8

(a)


25/75


E

91. In a parallel-plate capacitor of capacitance C, a metal sheet is inserted between the plates,

parallel to them. The thickness of the sheet is half of the separation between the plate. Thecapacitance now becomes

(a) 4C (b) 2C (c) C/2 (d) C/4

Sol.:

d

d/4

A A

d/4d/2

C

d/4 d/4

C

=

Before the metal sheet is inserted, C=d

A0

After the sheet is inserted, the system is equivalent to two capacitors in series, each of

capacitance Cd

AC 4

)4/(0

.

The equivalent capacity is now 2C.

(b)

E92. Which one of the following statement is incorrect?

(a) A moving charged particle produced electric and magnetic field both.

(b) Equipotential surface is always perpendicular to electric field.

(c) Kirchhoffs junction law follows conservation of charge.

(d) electric field inside the conductor is always zero.

Sol.: (d)

E

93. Two capacitors of capacitance 3 Fand 6 F are charged to a potential of 12 V each. Theyare now connected to each other, with the positive plate of one to the negative plate of theother. Then

(a) the potential difference across 3 Fis zero

(b) the potential difference across 3 Fis 4 V

(c) the charge on 3 Fis zero

(d) the charge on 3 Fis 10 C

Sol.: (d)


26/75


E

94. Four charges +2q, 2q, 3q and +3q are kept inthe corners of a square of side a. The total fieldat the centre O is,

(a) zero (b)2

04

22

a

q

(c)2

04

2

a

q

(d)

204

210

a

q

O

+2q 2q

+3q 3qa

Sol.: qqqq EEEEE 3322

qq EEE 232

2

02

4

52

a

qE

O

+2q 2q

+3q 3qa

qE 2

qE 3

qE3

qE 2

204

210

a

qE

(d)E

95. Figure shows some of the electric field lines

corresponding to an electric field. The figuresuggests that (E= electric field, V= potential)

(a) VA = VB (b)EA =EB

(c) VAVB (d) VAVB

A B

Sol.: Potential decreases in the direction of electric field.

VAVB (d)

E

96. Two spheres of radii randR carry charges q andQ respectively. When they are connected

by a wire, there will be no loss of energy of the system if

(a) qr= QR (b) qR = Qr (c) qr2 = QR2 (d) qR2 = Qr2

Sol.: There will be no loss of energy if the potential of the spheres is the same i.e. if

R

Q

r

qV

00 44

or

R

Q

r

q

(b)E

97. If three moles of monatomic gas is mixed with 1 moles diatomic gas, the resultant value of for the mixture is

(a) 1.66 (b) 1.50 (c) 1.40 (d) 1.57


27/75


Sol.: 57.1)5(1)3(3

)25(1)23(3

21

21

2

21

vv

pp

CnnC

CnCn

(d)E

98. Capacitance of a capacitor becomes3

4times its original value if a dielectric slab of

thickness t = d/2 is inserted between the plates (d = separation between the plates). Thedielectric constant of the slab is(a) 2 (b) 4 (c) 6 (d) 8

Sol.:d

AC 0

,

k

ddd

AC

22

3

4 0,

k

dd

d

22

3

4

, d

k

dd 3

22 , k= 2

(a)E

99. In the figure shown, conducting shells A andBhave charges Q and 2Q distributed uniformly over

A andB .Value ofVA VB is

(a)R

Q

04(b)

R

Q

08

(c)R

Q

04

3

(d)

R

Q

08

3

A

Q

R

2R

2QB

Sol.:R

Q

R

Q

R

QVA

2

4

1

2

2

4

1

00

R

QVB

2

3

4

1

0 ,

R

QVV BA

08

(b)E

100. Three point charges q, 2q and 2q are placed at the vertices of an equilateral triangle of

side a. The work done by some external force to slowly increase their separation to 2a willbe

(a)a

q 2

0

2.

4

1

(b)

a

q

0

2

4(c)

R

q

3

3.

4

1 2

0(d) zero

Sol.:

a

qqqqqqUi

04

2222

= 0

024

2222

0

a

qqqqqqU

f

Wext = U= 0

(d)


28/75


E

101. Two identical charges are placed at the two corners of an equilateral triangle. The potential

energy of the system is U. The work done in bringing an identical charge from infinity tothe third vertex is

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

Sol.: UUUUW if 3 2U

(b)E

102. A unit positive charge has to be brought from infinity to a midpoint between two charges20C and 10C separated by a distance of 50 m. How much work will be required?(a) 10.8 104 J (b) 10.8 103 J (c) 1.08 106 J (d) 0.54 105 J

Sol.: Workdone in taking unit positive charge from infinity to that point = potential at that point

J

25

1010

25

1020109

669 J108.10 3

(b)E

103. The electric potential at a point (x,y) is given by: V= Kxy. The electric field intensity at adistance rfrom the origin varies as

(a) r2 (b) r (c) 2r (d) 2r2

Sol.: jxiyKjy

Vi

x

VE

2222 )()( KxKyEEE yx = Kr

i.e., rE (b)

E

104. The inward and outward electric flux for a closed surface in units of N-m2/coulomb arerespectively 8 103 and 4 103. Then the total charge inside the surface is

(a) 4 103 coulomb (b) 4 103 coulomb

(c)

0

3104

coulomb (d) (4 103 )0 coulomb

Sol.:33 108104 = 4 103N-m2/coulomb

According to Gausss law, q = (4 103)0 coulomb (d)

E

105. In the circuit shown in the figure, C = 6F. Thecharge stored in the capacitor of capacity Cis

(a) zero (b) 90 C(c) 40 C (d) 60 C

C 2C 10V


29/75


Sol.: Both the capacitors are in series.

Therefore, charge stored on them will be same.

Net capacity CCC

CC32

2)2(

6

32 F = 4 F

Potential difference = 10 V q = CV= 40 C

(c)E

106. Two small spheres each having the charge +Q are suspended by insulating threads of lengthL from a hook. This arrangement is taken in space where there is no gravitational effect,then the angle between the two thread and the tension in each will be

(a)2

2

0 )2(4

1,180

L

Q

(b)

2

2

04

1,90

L

Q

(c)2

2

0 24

1,180

L

Q

(d)

2

2

04

1,180

L

Q

Sol.: The position of the balls in no gravity space will beas shown

= 180 and Force =2

2

0 )2(4

1

L

Q

(a)

L L180

E

107. A solid conducting sphere of radius 5 cm is charged so that the potential on its surface is10V. The potential at the centre of the sphere is

(a) 5 V (b) 10 V (c) 15 V (d) zero

Sol.: Charge resides on the outer surface of a conducting sphere

Therefore, potential at the centre will be same as that on the surface.

(b)E

108. The distance between the plates of an isolated parallel plate condenser is 4mm and potentialdifference is 60 volts. If the distance between the plates is increased to 12mm, then

(a) The potential difference of the condenser will become 180 volts.

(b) The P.D. will become 20 volts.

(c) The P.D. will remain unchanged.

(d) The charge on condenser will reduce to one third

Sol.: For capacitor Vd

VVV

d

d

V

V180

4

1260

1

212

2

1

2

1

(a)


30/75


E

109. Four condensers each of capacity 4F are connected as

shown in figure. QP VV 15 volts. The energy stored inthe system is

(a) 2400 ergs (b) 1800 ergs

(c) 3600 ergs (d) 5400 ergs

4F

4F

4F4F

P Q

Sol.: Total capacitance of given system F5

8

eqC

JVCU eq662 1018022510

5

8

2

1

2

1 erg1800erg1010180 76

(b)E

110. Three charges 2q, q, q are located at the vertices of an equilateral triangle. At the centreof the triangle

(a) The field is zero but potential is non-zero

(b) The field is non-zero but potential is zero

(c) Both field and potential are zero

(d) Both field and potential are non-zero

Sol.: Obviously, from charge configuration, at the centreelectric field is non-zero. Potential at the centre due to

2q charge r

qV q

22 .

and potential due to q charge

r

qV q (r= distance of centre point)

Total potential 02 qq VVqVV

(b)

2q

qq

r

r rEq EqE2q

E

111. The charge on 4F capacitor in the given circuit is(a) 12 C (b) 24 C(c) 36 C (d) 32 C

10V

3F 5F

1F4F

Sol.: Equivalent capacity between A andB

F

4.210

46

Hence charge across 4F(Since in seriescombination charge remains constant)

or 24104.26 F C

(b)

1F4F

A B

3F

10V

5F

6F

4FA B

3F

10V

6F


31/75


E

112. The electric potential Vat any point P (x, y,z) in space is given by V= 4x2 (where Vis in

volt andx

in meter). The electric field at the point (1m, 2m) in volt/metre is(a) 8 along negativex-axis (b) 8 along positivex-axis

(c) 16 along negativex-axis (d) 16 along positivez-axis

Sol.: The electric potential 24),,( xzyxV ,

ixix

VE 8

iE 8)2,1(

(a)E

113.A particle A has charge +q and a particle B has charge +4q with each of them having thesame mass m. When allowed to fall from rest through the same electric potential difference,

the ratio of their speedB

A

v

vwill become

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

Sol.: Using2

1

4

2

q

q

Q

Q

v

vQv

m

QVv

B

A

B

A

(b)E

114. Two infinitely long parallel conducting plates having surface charge densities + and respectively, are separated by a small distance. The medium between the plates is vacuum.If0 is the dielectric permittivity of vacuum, then the electric field in the region between the

plates is

(a) zero (b)02

volts/meter

(c)0

volts/meter (d)

0

2

volts/meter

Sol.: Electric field between the plates is

00 2)(2

0

volt/meter

(c)

E E


32/75


E

115. Two identical capacitors, have the same capacitance C. One of them is charged to potentialV1 and the other to V2. The negative ends of the capacitors are connected together. When the

positive ends are also connected, the decrease in energy of the combined system is

(a) 22214

1VVC (b) 2221

4

1VVC

(c) 2214

1VVC (d) 221 )(

4

1VVC

Sol.: Initial energy of the system2

2

2

12

1

2

1CVCVU

i

When the capacitors are joined, common potential

22

2121 VV

C

CVCVV

Final energy of the system

221

2

212 )(4

1

22

2

1)2(

2

1VVC

VVCVCUf

Decreased in energy 221 )(4

1VVCUU fi

(c)

E

116. If an insulated non-conducting sphere of radiusR has charge density . The electric field ata distance rfrom the centre of sphere (r


33/75


MODERATE QUESTIONSM

118. A point charge q is placed at a height a from vertex of squareof side a as shown. The electric flux through the square is

(a)0

q(b) zero

(c)06

q(d)

024q

a

a

a

a

a

q

Sol.: (d)

M

119. In the given circuit, find the heat generated if switchSis closed.

(a) 22

3CV (b) 2

2

1CV

(c) 2CV (d) 23

1CV

CC

C

SV

Sol.: Ceq= CSo, work done by battery = CV2

Heat generated = 22

1CV

(b)

M120. If net electric fieldE due to dipole at point P

makes an angle 30 with the line OP as shown,

then find the value of angle .

(a)

2

1tan 1 (b) 2tan 1

(c)

3

2tan 1 (d)

2

3tan 1

E

P

30

q

O q

Sol.: tan 30 = tan2

1, tan =

3

2

(c)


34/75


M

121. Let VandEbe the potential and the field respectively at a point. Which of the following

assertion is correct?(a) IfV= 0,Emust be zero (b) IfV 0,Ecannot be zero

(c) IfE 0, Vcannot be zero (d) none of these

Sol.: (d)

M

122. A charge q is placed at the axis of a charged ring

of radius r at a distance of r22 as shown in

figure. If ring is fixed and carrying a charge Q, thekinetic energy of charge q when it is released andreaches the centre of ring will be,

(a)r

qQ

04(b)

r

qQ

012

(c)r

qQ

06(d)

r

qQ

02

Q

r+

++ +

+

++

+

++

+++

+

+r22

q

Sol.: K.E. of q at O = PO VVq

=

220

0 )22(44 rr

Q

r

Qq

=r

qQ

r

qQ

00 643

2

(c)

Q r++

+ +

+++

+

++

+++

+

+r22

qO P

M

123. Figure shown in five capacitors connected across a12 V power supply. What is the potential dropacross the 2F capacitor?

(a) 2 V (b) 4 V

(c) 8 V (d) 10 V

6F

1F 2F 3F

6F

12V

Sol.: 1 F, 2 F and 3F are in parallel and theirequivalent capacitance is 6F.

Hence, each 6 F capacitor has potential differenceof 4V.

6F 6F 6F

12V

(b)


35/75


M

124. A parallel plate capacitor is maintained at a certain potential difference. When a dielectric

slab of thickness 3 mm is introduced between the plates, the plate separation had to beincreased by 2 mm in order to maintain the same potential difference between the plates.The dielectric constant of the slab is

(a) 2 (b) 3 (c) 4 (d) 5

Sol.:A

KtdQ

C

QV

01

11'

'

,A

Qd

C

QV

0

Now, VV '

K

tdd1

1

mm2' dd , mm3t

K1132 K=3

(b)M

125. A point charge q is placed inside a conducting spherical shell of inner radius 2R and outerradius 3R at a distance ofR from the centre of the shell. The electric potential at the centre

of shell will be04

1

times (potential at infinity is zero)

(a)R

q

2(b)

R

q

3

4(c)

R

q

6

5(d)

R

q

3

2

Sol.: VC=

R

q

R

q

R

q

324

1

0

=

R

q

6

5

4

1

0

(c)

M

126. Two conducting platesXandY, each having large surface areaA(on one side) are placed parallel to each other. The plate X isgiven a charge Q whereas the other is neutral. The electric field at

a point in between the plates is given by

(a)A

Q

2(b)

02 A

Qtowards left

(c)02 A

Qtowards right (d)

02

Qtowards right

Q

Sol.: Charge on inner face, q =22

0 QQ

Electric field =0

2 A

Q

(c)


36/75


M

127. Two concentric conducting shellsA andB are of radiiR and 2R. A charge q is placed at the

centre of shells. ShellB is earthed and a charge q is given to shell A. If charges on outersurface ofA andB are QA andQB respectively, then

(a) QA = q, QB = 0 (b) QA = 2q, QB = q

(c) QA = 2q, QB = 0 (d) QA = q, QB = q

Sol.: (c)

M

128. A solid hemispherical uniform charged bodyhaving charge Q is kept symmetrically along the

y-axis as shown in figure. The electric potential at

a distance d from the origin along the x-axis atpoint P will be

y

(0,0,0) (d,0,0)xP

(a)d

Q

04

1

(b) less than

d

Q

04

1

(c) more thand

Q

04

1

and less than

d

Q

04

2

(d) more than

d

Q

04

2

Sol.: Assuming sphere is complete then charge on it = 2Q

So potential at point P due to this spherical charge =

d

Q2

4

1

0

Hence potential due to hemisphere =d

Q

04

1

(a)M

129. Two large conducting parallel plates having equalcharge Q are placed very close to each other anddistance between the plates is d. Find the work done

by external agent to increase the separation betweenplates by d(area of plate isA)

Q Q

d

(a)0

2

2 AdQ

(b)0

2

2

A

dQ(c)

0

2

2

3

A

dQ(d)

0

2

A

dQ

Sol.: Force on first plate due to second plate QA

Q

02

Wext = Welectric field0

2

2

A

dQ

(b)

Q Q

d


37/75


M

130. A capacitor of capacitance Chaving initial charge2Q0, is connected to a battery of potential

differenceC

QV 0 as shown, then work done by the

battery is

(a)C

Q

2

20 (b)

C

Q

2

3 20

(c)C

Q203 (d)

C

Q

3

2 20

++++

2Q0

V

S

Sol.: Charge through the battery 000 32 QQQ . Work done by battery

C

QQ 003

(c)

M

131. Two point charges +8q and -2q are located atx = 0 andx =L respectively. The location of apoint on thex-axis at which the net electric field due to these two point charges is zero, is

(a) 2L (b)4

L(c) 8L (d) 4L

Sol.:

0

4

8

4

22

0

2

0

x

q

Lx

q orx = 2L

(a)

M

132. Four conducting plates are placed parallel to eachother. Separation between them is d and area ofeach plate is A. Plate number 1 and 3 areconnected to each other and plate number 2 and 4are connected to a battery of emf . Chargeflowing through the battery is

1

2

3

4

(a) dA0 (b)

dA0

23 (c)

dA02 (d)

dA0

32

Sol.: There are three capacitors C1 2 , C2 3, C3 4

equivalent capacitance isd

A0

3

2 .

So charge flown through battery isd

A0

3

2

(d)

21 2 3 3 4


38/75


M133. In the given circuit the value of charge across

capacitorAB as a function of time is

(a)

RC

t

eCE 21 (b)

RC

t

eCE 212

(c)

RC

t

eCE

2

12/ (d)

RC

t

eCE

2

12

A

E

B

C

CC

D

R

Sol.: Charge flow through battery as a function of time , )1(2 2CRt

eCEQ

(b)

M

134. Two identical conducting spheres having unequal charges q1 andq2 separated by distance r.If they are made to touch each other and then separated again to the same distance. Theelectrostatic force between the spheres in this case will be (neglect induction of charges)

(a) less than before (b) same as before (c) more than before (d) zero

Sol.: Since the two spheres are identical, the final charges on each of the sphere after they are

made to touch will be

221 qq

Change in electrostatic force between them

2

21

2

2

21

12

2

r

qKq

r

qq

KFF

212212 44 qqqqrK

04

2

212 qq

r

K

12 FF

(c)M

135. A small ball of mass m and charge +q tied with aninsulating string of length l, is rotating on a verticalcircular path under gravity and in a uniform horizontal

electric fieldEas shown. The tension in the string will beminimum for

E

m,q

(a)

mg

qE1tan (b)

(c)

mg

qE1tan2

(d)

mg

qE1tan


39/75


Sol.: The geffective will be directed along the resultant force of mg andqE. The angle made by the direction of geff with

vertical

mgqE1tan .

The tension in the string will be minimum when the bob is justopposite to the direction ofgeff.

qE

geffmg

Hence the required angle

mg

qE1tan

(d)M

136. A dipole of dipole moment p is kept at the centre of a ring of radius R and charge q. Thedipole moment has direction along the axis of the ring. The resultant force on the ring due tothe dipole is

(a) zero (b)3

04 R

pq

(c)3

02 R

pq

(d)

304 R

pq

only if the charge is uniformly distributed on the ring.

Sol.: The electric field due to the dipole on the circumference of the ring3

04 R

pE

and it is

directed normal to the plane of charged ring.

Hence force on the charged ring3

04 R

pqqEF

(b)M

137. An electric field given by jyiE )2(34 2

pierces Gaussian cube of side 1m placed at

origin such that its three sides representsx, y and z axes. The net charge enclosed within the

cube is(a) 04 (b) 03 (c) 05 (d) zero

Sol.: Net flux in x-direction = 0Net flux in y-direction

]2)0(3[]2)1(3[ 2 AA

Aq

30

00 33 Aq , (as )12

mA

(b)

x

y

z


40/75


M

138. A parallel plate capacitor of capacitance C is charged with a battery of potential V. Thebattery is then disconnected and electromagnetic waves are incident on negative plate of thecapacitor. As a result the negative plate starts emitting electrons towards the positive plate.The current which flows between the plates remains constant till time t1 and then startsdecreasing. The potential difference between the plates at time t1 is (Assume plates ofcapacitor are close to each other)(a) V (b) V/2 (c) 2V (d) zero

Sol.: The current starts decreasing when the potential difference between the plates becomeszero. (d)

M

139. n identical charge particle are placed on the vertices of a regular polygon ofn sides of sidelength a. One of the charge particle is released from polygon. When this particle reaches afar of distance, another particle adjacent to the first particle is released. The difference ofkinetic energies of both the particles at infinity is k. Magnitude of charge is

(a) ak04 (b)a

k

04(c)

a

k(d) ka

Sol.: ka

q

0

2

4

(a)M

140. A dielectric slab of thickness dis inserted in a parallel plate capacitor whose negative plateis at x = 0 and positive plate is at x = 3d. The slab is equidistant from the plates. Thecapacitor is given some charge. Asx goes from 0 to 3d.

(a) the magnitude of the electric field remains the same

(b) the direction of the electric field changes continuously

(c) the electric potential increases continuously

(d) the electric potential increases at first, then decreases and again increasesSol.: (c)

M

141. A circular ring carries a uniformly distributed positive charge and lies in XYplane withcentre at origin of co-ordinate system. If at a point (0, 0, z), the electric field is E, thenwhich of the following graphs is correct?

(a)

OZ

Y

E

z(b)

OZ

Y

E

z

(c)

O Z

Y

E

z (d)

OZ

Y

E

z

Sol.: (c)


41/75


M

142. Four metallic plates, each with surface area of one sideA, are placed at a distance dfrom each other. The platesare connected as shown in figure. Then the capacitanceof the system between P andQ is

1

2

3

4

P(+)

Q()

(a)d

A03 (b)d

A02 (c)d

A

3

2 0 (d)d

A

2

3 0

Sol.:d

AC

CC

CCCPQ

3

2

3

2

2

2 0

(c)

P(+)

2 3

3 4 Q()2 1

M

143. A semi-circular arc of radius a is charged uniformly and the charge per unit length is . Theelectric field at its centre is

(a)a04

(b)

a04

(c)a02

(d)

a02

Sol.: (d)

M

144. Two identical parallel plate capacitors are placed in series and connected to a constant voltagesource ofV0 volt. If one of the capacitors is completely immersed in a liquid with dielectricconstant K, the potential difference between the plates of the other capacitor will change to

(a) 01

VK

K(b) 0

1V

K

K

(c) 0

2

1V

K

K(d) 0

1

2V

K

K

Sol.: (b)

M

145. The equivalent capacitance of the network (with allcapacitors having the same capacitance C) is

(a) (b) zero(c)

2

13C (d)

2

13C

A

B

Upto

Sol.:)(

23211

CCC

CC

CCCC

022 22 CCCC

2

31CC

(c)


42/75


M

146. A hollow conducting sphere is placed in an electric fieldproduced by a point charge placed at P as shown in figure.Let VA, VB, VC be the potentials at points A, B and Crespectively. Then

(a) BC VV (b) CB VV

(c)BA VV (d) CA VV

A C P

B

Sol.: (a)

M

147. A current Iis passing through a wire having two sections P andQ of uniform diameters dandd/2respectively. If the mean drift velocity of electrons at P andQ is denoted by vp and

vQ respectively, then

(a) Qp vv (b) Qp vv2

1 (c)

Qpvv

4

1 (d) Qp vv 2

Sol.: Drift velocityneA

ivd

Avd

1 or

2

1

dvd

Then22

2/

d

d

d

d

v

v

P

Q

Q

P QP vv

4

1

(c)

M

148. Three large thin sheets with surface chargedensity , 2 and are placed as shown infigure. Electric field intensity at the point P is

(a) k4

0

(b) k4

0

(c) k2

0

(d) k2

0

2

P

k

z 3a

z a

z 0

Sol.:

kkEP

222

2

2 0000

(c)

M

149. Two charges, each of magnitude q = 2 C are placedat the vertices Q andR of the triangle as shown inthe figure. The sum of the sides PQ andPR is 12 cmand their product is 32 cm2. The potential at point Pwould be

P

Q R

(a) 6.00 105

V (b) 6.25 105

V (c) 6.50 105

V (d) 6.75 105

V


43/75


Sol.: 12yx , 32xy

xy

yxkq

y

kq

x

kqVp

= 6.25 105

(b)

M

150. A particle carrying a charge q is moving with aspeedv towards a fixed particle carrying a charge Qat large distance. It approaches Q up to a certaindistance rand then returns as shown in the figure. Ifcharge q were moving with a speed 2v at largedistance , the distance of the closest approach would

be

q Qv

r

(a) r (b) 2r (c)2

r(d)

4

r

Sol.:r

KqQmv 2

2

1

1

22

2

1

r

KqQvm

41 rr

(d)

M151. Three infinitely long charge sheets are placed as

shown in figure. The electric field at point P is

(a) k0

(b) k

2

0

(c) k4

0

(d) k4

0

z

2

x

Z=3aZ=0

Z=a

P

Sol.: kkkEp 2

2

22 000

, kEp 0

(a)M

152. Three concentric conducting spherical shells haveradii r, 2r and 3r and charges q1, q2 and q3respectively appeared on the shells when innermostand outermost shells are earthed as shown in thefigure. Then

(a) 231 qqq (b)4

21

qq

(c) 31

3 q

q(d)

3

1

2

3 q

q

r

2r

3r

q1q2q3


44/75


Sol.:

r

kq

r

qqk

33321 voltage of outersurface. Which is connected to the earth

r

kqr

qqk33

321 0 0321 qqq

(a)M

153. The electric field in a region is given by jiE 4

N/kg. Work done by this field is zero

when a particle is moved along the line

(a) y + 4x = 2 (b) 4y +x = 6 (c)x +y = 5 (d)x y = 5

Sol.: Work done will be zero when displacement is perpendicular to the field. The field makes anangle

4

1tan 11 with positivex-axis

while the liney + 4x = 2 makes an angle

4tan 12 with positive x-axis

021 90

i.e. the liney + 4x = 2 is perpendicular to E

.

(a)M

154. A charge +q is fixed at each of the points x =x0, x = 3x0,x = 5x0 .. on thex-axis and acharge q is fixed at each of the pointsx = 2x0,x = 4x0,x = 6x0 . Here,x0 is a positiveconstant. Take the electric potential at a point due to charge Q at a distance r from it to beQ/40r. Then the potential at the origin due to the above system of charges is

(a) zero (b)2ln8 00x

q

(c) (d)

004

2ln

x

q

Sol.: ...............432 0000

x

kq

x

kq

x

kq

x

kqV ,

004

2ln

x

qV

(d)M

155. Figure shows three spherical and equipotential surfaces1, 2 and 3 round a point charge q. The potentialdifference V1 V2 = V2 V3. Ift1 andt2 be the distance

between them. Then

(a) t1 = t2 (b) t1 > t2

(c) t1 < t2 (d) t1t2

3

21

qt1

t2


45/75


Sol.:

21

12

21

21

11

rr

rrKq

rrKqVV

so, 2112 rrrr [ potential difference is constant]

t2 > t1 (c)

M

156. If the capacitance of each capacitor is C, then effectivecapacitance of the shown network across any two

junctions is

(a) 2C (b) C(c) C/2 (d) 5C

Sol.: The given network is a balanced wheatstone bridge with one capacitor in parallel with thisbridge.

(a)

M

157. For the given diagram which of the followingstatement is true? (V1 and V2 are the potentialdifference across capacitorC1 andC2 respectively)

(a) with S1 closed, V1 = 15V, V2 = 20V

(b) with S3 closed, V1 = V2 = 25V

(c) with S1 andS2 closed, V1 = V2 = 0

(d) with S1 andS3 closed, V1 = 20 V, V2 = 20V

Sol.: (d)

S2S1

V1=20V V2=20V

C2=3pFC1=2pFS3

M158. A part of the circuit is shown in the figure. All the

capacitors have capacitance of 2F. Then

(a) charge on capacitorC1 is zero.

(b) charge on capacitorC2 is zero.

(c) charge on capacitorC3 is zero.

(d) charge on capacitors cannot be determined.

2V 3V

2V

2VC1

C2

C3


46/75


Sol.: 03222222 XXX

186 X

V3X

Potential difference across C3 is zero.

2V 3V

2V

X

(X2)

2VC1

C2

C3

Hence charge on C3 is zero.

(c)

M

159. A parallel plate capacitor has two layers of dielectricsas shown in figure. This capacitor is connected acrossa battery, then the ratio of potential difference acrossthe dielectric layers is

(a) 4/3 (b) 1/2

(c) 1/3 (d) 3/2

K1=2 K2=6

d 2d

Sol.: Electric field in dielectrics areE1 andE2

2

3

22

1

2

1

dE

dE

V

V

3

1

2

2

1

K

K

E

E

(d)

K1=2 K2=6

d 2d

E2E1

M

160. An air capacitor consists of two parallel plates A andB asshown in the figure. Plate A is given a charge Q and plateBis given a charge 3Q. P is the median plane of the capacitor.IfC0 is the capacitance of the capacitor, then

(VP, VA andVB are potential at P,A andB respectively)

(a)04C

Q

VV AP (b) 02CQ

VV AP

(c)0C

QVV AP (d)

04C

QVV BP

A P B

Q 3Q

Sol.:0C

QVV AB

02C

QVV PB

02C

QVV AP A B

Q 3Q

Q 2Q2Q

Q

P

(b)


47/75


M

161. An electric field is given by N/C jxiyE

. The work done by electric field in moving a

1C charge from position vector m22 jirA

to m4 jirB

is

(a) + 4 J (b) 4 J (c) + 8 J (d) zero

Sol.: Welectric field= kdzjdyidxEq .

0

1,4

2,2

1,4

2,2

1,4

2,2

xyxydxdydxy

(d)M

162. A ball of mass 2 kg having charge 1 C is dropped from the top of a high tower. In spaceelectric field exist in horizontal direction away from tower which varies as

61025 xE V/m (where x-is horizontal distance from tower), the maximumhorizontal distance ball can go from the tower is

(a) 5m (b) 2.5m (c) 10m (d) 15m

Sol.: Fx xx 251025101 66

2

25,

2

25 x

dx

dvv

xa x

xx

dxxdvvX

xx252

max

0

0

0

05 2maxmax XX

M

163. The maximum electric field intensity on the axis of a uniformly charged ring of charge qand radiusR will be

(a)2

0 334

1

R

q

(b)

20 3

2

4

1

R

q

(c)

20 33

2

4

1

R

q

(d)

20 22

2

4

1

R

q

Sol.: Eat axis of ring

23

22 xR

Kqx

ForEmax, 0dx

dE,

2

Rx

Emaximum2

02

32

20 33

2

4

1

2

2/

4

1

R

qR

RR

Rq

(c)


48/75


M

164. Two capacitors of capacitances 3 Fand 6 Fare charged to a potential of 12 V each. Theyare now connected to each other, with the positive plate of each joined to the negative plateof the other. The potential difference across each will be(a) zero (b) 3 V (c) 4 V (d) 6 V

Sol.: Charge stored in capacitor 3F = 36 Ccharge stored on capacitor 6 F = 72 C

6

72

3

36 QQ

i.e., 72 + 2Q = 72 Q

3Q = 2 72

Q = 48

Vcommon = 33648 = 4 V

(c)

+++++

+++++

72

36

M

165. Two identical metal plates are given positive charges Q1 andQ2 (< Q1) respectively. If theyare brought close together to form a parallel plate capacitor with capacitance C, the potentialdifference between them is

(a)C

QQ

221 (b)

C

QQ 21 (c)C

QQ 21 (d)C

QQ

221

Sol.: Within the plates electric fields due to charges Q1 andQ2 are

A

QEand

A

QE

0

22

0

11

22

)(2

121

0

21 QQA

EEE

V=Ed=C

QQQQ

A

d

2)(

221

21

0

(d)M

166. Two identical thin rings, each of radiusR are coaxially placed at a distance R apart. IfQ1 andQ2 are the charges uniformly spread on the two rings, the work done by the electric field inmoving a charge q from the centre of first ring to the centre of the second ring is

(a) zero (b) )12)((24

21

0

QQR

q

(c)R

q

04

2

(Q1+Q2) (d)

R

QQq

0

21

42

)()12(


49/75


Sol.:V1 =

R

Q

R

Q

24

1 21

0

, V2 =

R

Q

R

Q

24

1 12

0

Work done = q (V1 V2) =

R

Q

R

Q

R

Q

R

Qq

2241221

0

=R

q

24 0(Q1 Q2) )12(

(b)

M

167. Two equal point charges are fixed atx = -a andx = + a on thex-axis. Another point charge Qis placed at the origin. The change in the electrical potential energy of system, when it isdisplaced by a small distancex along thex-axis, is approximately proportional to

(a)x (b)x2 (c)x3 (d) 1/x

Sol.: Potential energy of the system when charge Q is at O isa

qQ

a

qQ

a

qQU

20

When charge Q is shifted to position O, the potential energy will be1

2

2

221

2

)(

)2(

)()(

a

x

a

qQ

xa

aqQ

xa

qQ

xa

qQU

=

2

2

12ax

aqQ )( ax

U = U U0 = )(22

12 2

32

2

xa

qQ

a

qQ

a

x

a

qQ

Hence U 2xU .

(b)

M

168. A charge q is placed at the midpoint of the line joining two equal charges Q. The system ofthree charges will be in equilibrium when q has the value(a) Q/4 (b) Q/2 (c) Q/4 (d) Q/2

Sol.: Net force on a charge placed atA is zero

04

4

4 202

0

2

d

Qq

d

Q

4

Qq

(c)

AB

CQ Qq

d


50/75


M

169. A fully charged capacitor has a capacitance C. It is discharged through a small coil ofresistance wire embedded in a thermally insulated block of specific heat capacity s and massm. If the temperature of the block is raised by T, the initial potential difference Vacross thecapacitance is

(a)s

TmC2(b)

s

TmC(c)

C

Tms(d)

C

Tms2

Sol.: Energy Stored= Loss of Heat , TmsCV 22

1,

C

TmsV

2

(d)M

170. Three large conducting parallel plates are separated by a

small distance. A charge 1.0 C is given to middle plate.Find the charge on outer surface of the upper plate.

(a) 1 C (b) C2

1

(c) C3

1(d) C

6

1

Sol.: (b)

M171. Two concentric spherical shell of radius R and 2R having

initial charges Q and 2Q respectively as shown. On closingthe switch Scharge flow from outer sphere to earth is

(a) Q (b) Q

(c) 3Q (d) 3Q

2RQ

R

2Q

S

Sol.: On closing the switch potential of outer shell is zero

022

1 R

KQ

R

KQ, Q1 = Q charge flow = 3Q

(d)

M

172. Three unchanged capacitor of capacitance 1F,2F and 3F are connected as shown in figure.If potentials at point P, Q andR are 1V, 2V, 3Vrespectively. Then potential at O is

(a)11

18V (b)

18

11V

(c) 5 V (d) none of these

1 F

P

2 F3 F

Q

R

O


51/75


Sol.: 0332211 vvv

6

7v V

(d)1 F

P

2 F3 F

QR

1V

O

2V3V

M

173. A positively charged ball hangs from a silk thread. We put a positive test charge q0 at a

point and measure0q

F, then it can be predicted that the electric field strengthEbecomes

(a) greater than0q

F (b) Equal to0q

F

(c) less than0q

F(d) cannot be estimated

Sol.: (a)

M

174. Two point charges +4e ande are kept at distancex apart. At what distance a charge q mustbe placed from charge +e, so that q is in equilibrium

(a)2x (b)

32x (c)

3x (d)

6x

Sol.:

224

y

Kqe

yx

qeK

,

3

xy

(c)M

175. Consider two concentric metal spheres. The outer sphere isgiven a charge Q > 0, then(a) the inner sphere will be polarized due to field of the

charge Q.(b) the electrons will flow from inner sphere to the earth ifSis shorted.(c) the shorting ofSwill produce a charge of Qb/a on theinner sphere(d) none of the above

A

B

b

a

S

Sol.: When Sis open, spheres A and B have same +ve potential.

When Sis closed, potential of B becomes zero.

So, the potential ofB decreases.

This decreases of potential takes place due to flow of electrons from earth to inner sphereB.

(c)


52/75


M

176. In the given diagram, the potential

difference betweenA andB is V1, whenswitch is open. The potential difference

betweenA andB when switch is closedis V2. Then

S

Q0

A

C

++++

B

Q0

2C

++++

(a)C

QV

20

1 ,C

QV 02 (b) 1V zero , 2V zero

(c)C

QV

20

1 , 2V zero (d)C

QV

20

1 ,C

QV

20

2

Sol.: Charge flow is zero after closing the switch,so,

C

QVV

2

021

(d)

M

177. Two concentric hollow spherical shell of radius Rand 2R having charges Q and 2Q as shown. Findthe total electric potential energy of arrangement.

(a)R

KQ2

2

5(b)

R

KQ2

(c)RKQ

2

3 (d)RKQ

2

2

R

2R

2Q

Q

Sol.: Self energy R

KQ

R

QK

R

KQ222

2

3

22

2

2

Interaction energy

R

KQ

R

QKQ2

2

2

TotalR

KQ2

2

5

(a)

M

178. The dielectric strength of air is 3.0 106 NC1. The largest charge that a 0.30 cm radiusmetal sphere can hold without sparking is

(a) 9 nC (b) 8.2 nC (c) 6 nC (d) 3 nC

Sol.: ||E

on the surface, should be less than 3 106 N/C

Hence, 62

103.

r

QK, 6

6

9 103109

109

Q

9

103

Q , nCQ 3max

(d)


53/75


M

179. If each capacitor has capacitance C then find

CAB(a) C (b) C/2

(c) 3C/2 (d) none of these

A B

Sol.: Effective circuit

2

3CC

eff

(c)

A B

=A B

CC

CC

CC

C C

M

180. Two insulating plates are both uniformly charged insuch a way that the potential difference between themis V2 V1 = 20 V. (i,e, plate 2 is at a higher potential).The plates are separated by d= 0.1m and can be treatedas infinitely large. An electron is released from rest onthe inner surface of plate 1. What is its speed when ithits plate 2? ( e = 1.6 1019 C, m0 = 9.11 10

31 kg)

(a) 2.65 106 m/s (b) 7.02 1012 m/s

(c) 1.87 106 m/s (d) 32 1019 m/s

0.1m

Y

X

1 2

Sol.: VeVm 202

1,

61065.2 V m/s

(a)M

181. A condenser of capacitance C1 is charged to V0 volt. The energy stored in it is U0. It isconnected in parallel to another uncharged condenser of capacitance C2. The energy loss inthe process is

(a) 21

021

2 CC

UCC

(b) 0

2

21

21 UCC

CC

(c)21

01

CC

UC

(d)

21

02

CC

UC

Sol.: Cfinal = C1 + C2, Vcommon

21

01

CC

VC

Efinal 2

21

0121

2

1

CC

VCCC

2101

21

20

21

2 CC

UC

CC

VC

02

01

2

1UVCE

initial , Eloss =Einitial -Efinal =

21

02

CC

UC

(d)


54/75


M

182. In the adjoining figure. A section of a complicated circuit

is shown in whichE= 10 volt, C1 = 2F, C2 = 3F and(VB VA) = 10 volt. The potential on C1 will be

(a) 0 volt (b) 4 volt

(c) 12 volt (d) 16 volt

A B

C1 C210V

+

Sol.:5

203

21

21

CC

VCV net =12 Volt

(Vnet = V1 + V2 = 20 V)

A B

V1 V210V

+ C1

10VC2

(c)

M

183. Ifn drops, each of capacitance Cand charged to a potential V, coalesce to form a big drop,the ratio of the energy stored in the big drop to that in each small drop will be

(a) n : 1 (b) n4/3: 1 (c) n5/3: 1 (d) n2: 1

Sol.: Charge on big drop = n (CV) (charge conservation)

Radius of big drop rnR 3/1 (volume conservation)

Energy of small drop r

qEs

0

2

42

1

Energy of big drop3/1

0

22

42

1

n

qnEb

1

3/5n

E

E

s

b

(c)M

184. Two concentric spheres of radii r1 andr2 carry charges q1 andq2 respectively. If the surfacecharge density () is the same for both spheres, the electric potential at the common centrewill be

(a)2

1

0

.r

r

(b)1

2

0

.r

r

(c) 210

rr

(d) 210

rr

Sol.: Vcommon20

2

10

1

44 r

q

r

q

2

2

2

2

1

1

44 r

q

r

q


55/75


Vcommon = 210

22

22

21

11

0 44

1rr

r

rq

r

rq

(d)

M

185. A solid conducting sphere having a charge Q is surrounded by an uncharged concentricconducting hollow spherical shell. The potential difference between the surface of solidsphere and the outer surface of the hollow shell is V. If the shell is now given a charge of

3Q , the new potential difference between the same two surfaces is

(a) V (b) 2 V (c) 4 V (d) 2 V

Sol.: In the given situation potential difference is independent of charge on outer shell. (a)

M

186. Two parallel plate capacitors of capacitances C and 2C are connected in parallel andcharged to a voltage Vwith the help of a battery. The battery is then disconnected and thespace between the plates of the first capacitor is filled with a dielectric of dielectric constantk. The voltage across the combination now will be

(a) V (b)k

V

3(c)

1

3

k

V(d)

2

3

k

V

Sol.: Total charge CVCVCV 32

Final capacitance 22 KCCKC

Common voltage across combination 2

3

2

3

K

V

KC

CVV

C

(d)M

187. Consider the situation shown in the figure. ThecapacitorA has a charge q on it whereas B is uncharged. The charge appearing on the capacitorB along time after the switch is closed is

(a) zero (b)2

q

(c) q (d) 2q

+

+

+

+

+

+

+

BA

q

Sol.: When switched is closed, inner plates of two capacitor get connected with each other. Butouter plates are not connected. It means circuit is not completed. Therefore, no current willflow or no charge will appear onB.

(a)


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M

188. A thin, metallic spherical shell contains a charge Q on it.

A point charge q is placed at the centre of the shellanother charge q1 is placed out side as shown. All threecharges are positive. The electrostatic force on the chargeat the centre is

q

Q

q1

(a) towards left (b) towards right (c) upward (d) zero

Sol.: (d)

M

189. Four positive charges of same magnitude Q are placed at

the four corners of a rigid square frame as shown in thefigure. The plane of the frame is perpendicular to z-axis. Ifa negative charge q is placed at a distance z away fromthe centre above frame (z


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M

191. Two thin wire rings each having a radius R are placed at a distance dapart with their axis

coinciding. The charges on the two rings are +Q and Q. The potential difference betweenthe centres of the two rings is

(a) zero (b)

220

11

4 dRR

Q

(c)2

04 d

QR

(d)

220

11

2 dRR

Q

Sol.:22

00 44 dR

Q

R

QVA

2200 4

4 dR

Q

R

QV

B

220

11

2 dRR

QVV BA

(d)

A BA

R Rd

Q -Q

M

192. Two concentric spheresA andB having radii a andb respectively are

having a potential difference ofV, when the switch S is open. Thepotential difference when switch is closed

(a) is less than V (b) is greater than V

(c) is equal to V (d) cannot be determined.

ab

S

Sol.: (c)

M

193. A parallel plate condenser with a dielectric of dielectric constant Kbetween the plates has acapacity Cand is charged to a potential Vvolt. The dielectric slab is slowly removed from

between the plates and then reinserted. The net work done by the system in the process is

(a) 21 CVK (b) zero (c) 212

1CVK (d)

K

KCV

12

Sol.: (c)

M

194. 8 drops of equal radius coalesce to form a bigger drop. By what factor the charge andpotential change?

(a) 8, 4 (b) 8, 8 (c) 6, 8 (d) 8, 10


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Sol.: Charge on each drop = q

88

q

q

q

qf,

33

3

4

3

48 Rr rR 2 ,

r

qV

04

,

r

qV

24

8'

0

, 4'

V

V

(a)M

195. A andB are similarly charged bodies which repel with force F. Another uncharged sphere Cof same size and material is touched withB and removed. It is kept at mid-point of distance

betweenA andB. Force on Cis

(a)2

F(b) 2F (c) F (d) F

3

2

Sol.:2

0

2

4 rQ

F

Fr

Q

r

Q

r

QFC

2

0

2

2

0

2

2

0

2

4

24

4/

24

2/

(c)

A B

Q Qr

A B

Q

r/2 r/2

Q/2Q/2

C

M

196. A unit positive charge moves in an electric fieldEalong the path PQR. The potential difference between

pointsR andP will be

(a) zero (b)E. r

(c)2

.rE(d) 2.rE

R

V

PE

Q

EE

450

r

Sol.:2

.r

EVVPR

(c)

M

197. The distance between plates of a parallel platecapacitor is 5d. The positively charged plates is at x =0 and negatively charged plate is at x = 5d. Two slabsone of conductor and the other of a dielectric of samethickness dare inserted between the plates as shown infigure. Potential (V) versus distancex graph will be

CONDUCTOR

DIELECTRIC

+q q

O d 3d2d 4d 5dx


59/75


V

O d 3d2d 4d 5dx

(a)

V

O d 3d2d 4d 5dx

(b)

V

O d 3d2d 4d 5dx

(c)

V

O d 3d2d 4d 5dx

(d)

Sol.:E= slope ofV-x graph

Einside a conductor = 0

slope ofV-x graph betweenx = dtox = 2dshould be zero andEin air >Ein dielectric

|slope in air| > | slope in dielectric| (b)

M

198. For circuit the equivalent capacitancebetween points P andQ is(a) 6C (b) 4C(c) 3C/2 (d) 3C/4

P Q

C C C C C C

Sol.:CCC

eff

1

3

11

4

3CCeff

(d)

M

199. Seven capacitors, a switch Sand a source of e.m.f.are connected as shown in the figure. Initially, S isopen and all capacitors are uncharged. After S isclosed and steady state is attained, the potentialdifference in volt across the plates of the capacitor

A is

21F7F28F

59V

4F

1F2F

3FA

(a) 12 (b) 15 (c) 17 (d) 19


60/75


Sol.: The equivalent circuit is

Ifq be the charge on each capacitor, then

597328721

qqqqq

or q = 84 C Potential difference acrossA

127

84

7

qvolt.

(a)

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