Topper’s Pacakge Physics- XII Permutation and CombinationsMagnetic Effect of Current, Magnetism

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1. CHARGES IN MAGNETIC FIELD1. An ionised gas contains both positive and

negative ions. If it is subjected simultaneouslyto electric field along positive x-direction and amagnetic field along positive z-direction, then(a) positive ions deflect towards +y direction

and negative ions towards –y directions(b) all ions deflect towards –y direction(c) all ions deflect towards +y direction(d) positive ions deflect towards – y direction

and negative ions towards + y direction2. A beam consisting or protons and electrons

moving at the same speed goes through a thinregion in which there is a magnetic fieldperpendicular to the beam. The protons and theelectrons(a) will go undeviated(b) will be deviated by the same angle and will

not separate(c) electron will be deviated less as compared

to proton(d) electrons will be deviated more as

compared to protons3. A charged particle goes undeflected in a region

containing electric and magnetic fields. It ispossible that(a)

E is parallel to

B and v is parallel to

E

(b)E and

B are in same direction

(c) v is parallel to B but

E is not parallel or

antiparallel to B(d)

E is parallel to

B but v is not parallel or

antiparallel to E

4. A charged particle moves in a gravity-free spacewithout change in speed. Which of the followingare possible?(a) E = 0, B = 0 (b) E = 0, B 0(c) E 0, B 0 (d) all of these

5. A proton is released from rest in a regioncontaining uniform E and B (magnetic field)parallel to each other. Its path is :–

(a) Straight line (b) Circular(c) Parabolic (d) Remains rest

6. An electron is revolving in a circular orbit ofradius r in a hydrogen atom. The angualrmomentum of the elctron is l. The dipolemoment associated with it is:(a) (e/m)l (b) (e/2m)l(c) (m/e)l (d) (2m/e)

7. A charged particle moves through a magneticfield perpendicular to its direction. Then(a) kinetic energy changes but the

momentum is constant(b) the momentum changes but the kinetic

energy is constant(c) both momentum and kinetic energy of the

particle are constant(d) both momentum and kinetic energy of the

particle are constant8. A charge particle with charge q enters a region

of constant, uniform and mutually orthogonalfields E and B , and comes out without anychange in magnitude or direction of v . Then.(a)

2v B E/E (b) 2v E B/B

(c) 2v B E/B (d)

2v E B/E9. A particle of mass m and charge q moves with a

constant velocity v along the positive x-direction.It enters a region containing a uniformmagnetic field B directed along the negative z-direction, extending from x = a to x = b. Theminimum value of v required so that the particlecan just enter the region x > b is

(a)qbBm

(b) q b B

m

(c)q aBm

(d) q (b )B

2m10. For a positiviely charged particle moving in a x-

y plane initially along the x-axis, there issudden change in its path due to the presenceof electric and /or magnetic fields beyond P. Thecurved path is shown in the x-y plane and isfound to be non-circular

MAGNETIC EFFECT OF CURRENT,MAGNETISM

Unit 4

Topper’s Pacakge Physics- XII Permutation and CombinationsMagnetic Effect of Current, Magnetism

45

Which one of the following combinations ispossible?

(a) ˆ ˆE 0;B bj ck (b)

ˆ ˆ ˆE ai ;B ck ai

(c) ˆ ˆE 0;B cj bk (d)

ˆ ˆ ˆE aj ;B ck bj11. An electron moving with a speed u along the

positive x-axis at y = 0 enters a region of uniform

magnetic fleld

0ˆB –B k which exists to the

right of y-axis. The electron exits from theregion after sometimes with the speed v atcoordinate y, then

(a) v > u, y < 0 (b) v = u, y > 0(c) v < u, y > 0 (d) v = u, y < 0

12. An experimenter’s diary reads as follows “acharged particle is projected in a magnetic fieldof 3ˆ ˆ7i 3 j 10 T . The acceleration of

particleis found to be 6 2ˆ ˆai 7 j 10 m/s ’’. Thevalue of a is(a) 4 (b) 3(c) 6 (d) 10

13. A magentic field

0ˆB –B jexists in the region a

< x < 2a and

0ˆB –B j , in the region 2a < x <

3a, where B0 is a positive point charge moving

with a velocity

0ˆV V i , where V0 is a positive

constant, enter the magnetic field at x = a. Thetrajectory of the charge in this region can belike.

(a) (b)

(c) (d)

14. Two identical particles having the same massm and charges +q and –q separated by a distancedenter in a uniform magnetic field B directedperpendicular to paper inwards with speeds v1and v2 as shown in figure. The particles will notcollide if : (Ignore electrostatic force)

(a) 1 2md v vBq (b) 1 2

md v vBq

(c) 1 22md v vBq (d) v1 = v2

15. A charged particle is projected with velocity v0along positive x-axis. The magnetic field B isdirected along negative z-axis between x =0 andx = L . The particle emerges out (at x = L ) at anangle of 60° with the direction of projection. Findthe velocity with which the same particle isprojected (at x = 0 ) along positive x-axis so thatwhen it emerges out (at x = L ), the angle madeby it is 30° with the direction of projection

(a) 02v (b) 0v2

(c) 0v3 (d) 0v 3

16. A particle of charge per unit mass is releasedfrom origin with velocity

0ˆv v i in a magnetic

field

0ˆB –B k for

0

0

v3x2 B and

B 0 for

0

0

v3x2 B . The x-coordinates of the particle

at time 0

t3B would be

Topper’s Pacakge Physics- XII Permutation and CombinationsMagnetic Effect of Current, Magnetism

46

(a)

0

00 0

v3 3 v t2 B 2 B

(b)

0

00 0

v3 v t2 B 3B

(c)

0 0

0 0

v v3 t2 B 2 3B

(d)

0 0

0

v v t32 B 2

17. A charged particle of specific charge (charge/mass) is released from origin at time t = 0with velocity

0

ˆ ˆv v i j in uniform magneticfield

0ˆB B i . Coordinate of the particle at time

t = 0B are

(a)

0 0 0

0 0 0

v 2v v, ,

2B B B (b)

0

0

v ,0,02B

(c)0 0

0 0

2v v0, ,B 3B

(d)0 0

0 0

v 2v,0,B B

18. A particle having charge q enters a region ofuniform magnetic field B

(directed inwards) andis deflected as shown. The magnitude of themomentum of the particle is

(a)qBy

2 (b)qBy

x

(c)2qB y x

2 x

(d)2qBy

2x19. A particle of mass m and charge q enters a

region of magnetic field with a uniform velcoityV as shown in figure. Find the angle subtendedby the circular described by it in the magneticfield.

V

(a) 90 2 (b) 180

(c) 180 2 (d) 90

20. An electron and proton having equalmomentum enter an uniform magnetic fieldnormal to the lines of force. If the radii ofcurvature of circular path be re and rprespectively then:

(a)e e

p p

r mr m

(b)e e

p p

r mr m

(c)pe

p e

mrr m

(d)e

p

r 1r 1

21. Kinetic energy of each electron in a beam oftelevision tube is 'K'. The electrons are emittedhorizontally from geomagnetic south togeomagnetic North. The vertical component'sof earth magnetic field points down and has amagnitude B. In which direction will theelectrons deflect.(a) towards east (b) towards north(c) towards south (d) towards west

22. An electron beam is moving horizontallytowards east. If this beam passes through auniform magnetic field direction upwards, thenin which direction will the beam be deflected ?(a) towards north (b) toward south(c) toward west (d) can't say

23. An electron enters the region between theplanes of a parallel plate capacitor at a pointequidistant from either plate. The capacitorplates one 'd' apart and 'l' long. A potentialdifference of V0 is kept across the plates.Assuming that the initial velocity of the electronis parallel to the capacitor plates, calculates thelonger value of the velocity of the electrons sothat they do not fly out of the capacitor at theother end.

(a) 0eVV l2mgy

(b) 0eVV l

2my

(c)20eV d

V l2my

(d) 0eV dV l

my

Topper’s Pacakge Physics- XII Permutation and CombinationsMagnetic Effect of Current, Magnetism

47

24. In a region an uniform magnetic field 'B'occupies a space of thickness 'd'. A particle ofmass 'm' and charge 'q' is accelerated by apotential difference V0 flies through transversemagnetic field 'B' as shown. Find the angle ''through which the particle deviates from theinitial direction of its motion.

(a)1

0

qsin dB2V m

(b)1

0

qsin 2dBV m

(c)1

0

dB qcos2 V m

(d) none

2. FORCE ON CURRENT CARRYING CONDUCTOR

25. A wire is situated in the east-west direction andthe current flowing through it is 0.5 ampere.The wire is held perpendicular to magnetic field

of 0.2 × 10 -4 T . The force acting on the wirewill be

(a) 0.0 (b) 1 × 10–6 N

(c) 1 × 10–5 N (d) 4 × 10–5 N26. A conductor ABCDEF, with each side of length

L, is bent as shown. It is carrying a current I ina uniform magnetic induction B, parallel to thepositive y direction. The force experienced bythe wire is

(a) BIL in the positive y-direction(b) BIL in the positive z-direction(c) 3BIL in the positive y-direction(d) Zero

27. A conductor PQ of length L, carries a current I.PQ is placed perpendicular to a long straightconductor XY carrying a current i as shown. Theforce acting on PQ is F.

(a) 0µ IiF ln2;upwards

2

(b) 0µ IiF ln2;downwards

2

(c) 0µ IiF ln3;upwards

2

(d) 0µ IiF ln3;downwards

2

28. Two long conductors, separated by a distance dcarry current I1 and I2 in the same direction.They exert a force F on each other. Now thecurrent in one of them is increased to two timesand its direction is reversed. The distance isalso increased to 3d . The new value of the forcebetween them(a) –2F (b) F /3(c) –2F /3 (d) –F /3

29. A wire carrying a current i, is kept in the x-y

plane along the curve y A sin 2 2 x

. A

magnetic field exists in the z-direction. Themagnitude of force on the portion of the wirebetween x = 0 to x = is(a) Bi (b) 2Bi(c) zero (d) none of these

30. Some current i=2A is flowing in a write frameas shown in figure. The frame is a combination

Topper’s Pacakge Physics- XII Permutation and CombinationsMagnetic Effect of Current, Magnetism

48

of two equilateral triangles ACD and CDE of side1m. It is placed in uniform magnetic field B=4Tacting perpendicular to the plane of frame. Themagnitude of magnetic force acting on theframe is

(a) 24 N (b) zero(c) 16 N (d) 8 N

31. A flexible conducting wire loop of length ‘l’ liesin a magnetic rield ‘B’ perpendicular to the planeof the loop. When current i is passed throughthe loop, it opens into a circle. Find the tensiondeveloped in the wire.

(a)BilT

(b)BilT2

(c)BilT3

(d) none

32. A wire of length l carries a current I along X-axis. A magnetic field exists given by

0ˆ ˆ ˆB B i j k T. The magnitude of the

magnetic force acting on the wire is:

(a) I l B0 (b) 03I Bl

(c) 2I l B0 (d) 02 I Bl

33. A long straight wire carrying current of 30 Arests on a table. Another wire AB of length 1 m,mass 3 g carries the same current but in theopposite direction, the wire AB is free to slideup and down. The height upto which AB willriese is(a) 0.6 cm (b) 0.7 cm(c) 0.4 cm (d) 0.5 cm

34 A wire of length ‘l’ and mass ‘m’ is suspended bya pair of flexible leads in a magnetic field ofinduction B. What is the magnitude of currentrequired to remove the tension in the supportingleads?

(a)mgilB

(b)2mgilB

(c)mgi2lB

(d) 0

35. A metal rod of mass ‘m’ and length ‘l’ issuspended on two springs as shown. The springsare extended by X0. When current i passes ththrough the rod, it wires by x. Find the magneticfield.

(a)0

0

mg(x x)B

i l x

(b)0

0

mg(x x)B

2i l x

(c)0

0

mg xB

2i l x (d)

20mg x

B2xi l

36. A constant current i flows through a mertal rodof length I and mass m tat slides of frictionlesscoil as shown if the initial speed of the rod is‘v0’ and a magnetic field ‘B’ acts vertically up.Find the total distance moved by the rod beforecoming to stop.

(a)20mv

S2Bi l

(b)20mv

SBi l

(c)202mv

SBi l

(d)20mv2S

3 Bi l

37. A long horizontal wire P carries a current of i1.It is rigidly fixed. Another fine wire Q is placeddirectly above and parallel to P. The weight ofthe wire Q is ‘W’. Find the portion of the wire Q

Topper’s Pacakge Physics- XII Permutation and CombinationsMagnetic Effect of Current, Magnetism

49

from the wire P so that Q remains suspendeddue to the magnetic repulsion.

(a)2

0 1 2µ i ir

2 mg

(b)0 1 2µ i i

r3 mg

(c)0 1 2µ i i

rmg

(d)

0 1 2µ i ir

2 mg

38. A pair of parallel horizontal conducting rails ofnegla resistance shorted at one end is fixed ona tab c distance between the rails is L. Aconducting mass i rod of resistance R can slideon the rails friction. The rod is tied to a massless string which passes " pulley fixed to theedge of the table. A block of mas tied to the otherend of the string, hang verticil constantmagnetic field B exists perpendicular to thetable. If the system is released from rest, findthe terminal velocity achieved by the rod.

(a) rmgVBLR

(b) r 2 2

2mgRVB L

(c) r 2 2

mgRV2B L

(d) None

39. A square frame carrying a current 1 is locatedin the same plane as a long straight wirecarrying a current 10. The frame side has alength a. The axis of the frame passing throughthe mid-points of the opposite sides is parallelto the wire and is separated from it by thedistance which is a( 1) . Find the ampereforce acting on the frame.

(a)0 0

2

2µ (I I )f

(4 1)

(b)0 0

2

2µ IIf

3 (4 1)

(c)0 0

2

2µ IIf

( 1)

(d)0 0

2

µ IIf

( 1)

40. A constant current i flows through a metal rodof length ‘l’ and mass in that sides on frictionlessrails as shown in fig. If the initial speed of therod is 'V0' and a magnetic field 'B' acts verticallyup. Find the speed of the rod as a function oftime

(a)BilV tm

(b) V = V0

(c) 0BilV V tm

(d)BilV t2m

3. BIOT SAVART’S + AMPERE CIRCUTAL LAW

41. A straight section PO of a circuit lies along thex-axis from x = – a/2 to x = a/2 and carries asteady current I. The magnitude of magneticfield due to the section PO at a point y = + a willbe(a) proportional to a (b) proportional to a2

(c) proportional to a–1 (d) equal to zero

42. A long, straight wire of radius R carries acurrent distributed uniformly over its cross-section. The magnitude of the magnetic field is(a) maximum at the axis of the wire(b) minimum at the axis of the wire(c) minimum at the surface of the wire(d) none of these

43. Two straight long conductors AOB and COD areperpendicular to each other and carry currentsI1 and I2 . The magnitude of magnetic inductionat point P at a distance ‘a’ from O in a directionperpendicular to the plane ABCD is

(a) 1/22 201 2

µI I

2 a

(b)

1 20

1 2

I Iµ.

2 a I I

(c) 0 1 2µ I I2 a

(d) 01 2

µI I

2 a

Topper’s Pacakge Physics- XII Permutation and CombinationsMagnetic Effect of Current, Magnetism

50

44. A point charge q is in motion with velocity v

relative to an inertial axis “A”. Theinstantaneous location of q with respect to afixed observation point P is r as shown . B

, themagnetic field at point P is given by

(a) 03

µ q (r v)B4 r

(b) 0

3

µ q (v r)B2 r

(c) 03

µ q (v r)B4 r

(d) zero

45. Currents I1 and I2 flow in the wires shown infigure. The field is zero at distance x to the rightof I. Then.

(a)1

2

IX aI

(b)2

1

IX a

I

(c)1 2

1 2

I IX a

I I

(d)

1 2

1 2

I IX a

I I

46. A circular coll of radius 20 cm and 20 turns ofwire is mounted vertically with its plane inmagnetic meridian. A small magnetic needle isplaced at the centre of the coil and it is deflectedthrough 45°, when a current is passed throughthe coil. When horizontal component of earth’sfield is 0.34 × 10–4 T, the current in coil is(a) 0.6 A(b) 6A(c) 6 × 10–3 A(d) 0.06 A

47. For c = 2a, and a < b < c, the magnetic field atpoint P will be zero when

(a) a = 2b (b) a = 35 b

(c) a= 53 b (d) a =

13 b

48. Two long parallel wires are at a distance 2dapart. They carry steady equal currents flowingout of the plane of the paper as shown. Thevariation of the magnetic field B along the lineXX’ is given by

(a) (b)

(c) (d)

49. A long, straight metal rod has a long hole ofradius a drilled parallel to the rod axis with cross-sectional view shown below. If the rod carriesa current I, the value of the magnetic field onthe axis of the rod is

(a) 2

02 2

µ IaB

2 c b a

(b) 0µ I

B2 c

(c)

20

2 2

µ IaB

4 c b a

(d) B = zero

50. A non-planar loop of con ducting wire carryinga current I is placed as shown in the figure.Each of the straight sections of the loop is of

Topper’s Pacakge Physics- XII Permutation and CombinationsMagnetic Effect of Current, Magnetism

51

length 2a. The magnetic moment due to thisloop at the point P (a, 0, a) points in the direction

(a) 1 ˆ ˆ– j k2

(b) 1 ˆ ˆ ˆ–i j k3

(c) 1 ˆ ˆ ˆi j k3

(d) 1 ˆ ˆi k2

51. A long straight wire long the z-axis carries acurrent I in the negative z direction. themagnetic vector field B

at a point havingcoordinates (x, y) in the z = 0 plane is

(a)0

2 2

ˆ ˆµ I yi xj2 x y

(b)

02 2

ˆ ˆµ I xi yj2 x y

(c)0

2 2

ˆ ˆµ I xj yi2 x y

(d)

02 2

ˆ ˆµ I xi yj2 x y

52. A long wire carries a steady current. It is bentinto a circle of one turn and the magnetic fieldat the centre of the coil is B. It is then bent intoa circular loop of n turns. The magnetic field atthe centre of the coil will be(a) nB (b) n2B(c) 2nB (d) 2n2B

53. Net magnetic field at the centre of the circle Odue to a current carrying loop as shown in figureis 180º

(a) zero(b) perpendicular to paper inwards(c) perpendicular to paper outwards(d) is perpendicular to paper inwards if 90º

and perpendicular to paper outwards if90º 180º

54. Equal currents i =1A are flowing through thewires parallel to y-axis located at x = +1m, x =2m, x = + 4 m etc. but in opposite directions asshown. The magnetic field at origin (in tesla)would be

(a) 7 ˆ–1.33 10 k (b) 7 ˆ1.33 10 k

(c) 7 ˆ2.67 10 k (d) 7 ˆ2.67 10 k 55. Same current i is flowing in three infinitely long

wires along positive x, y and z directions. Themagnetic field at a point (0, 0, a) would be

(a) 0µ i ˆ ˆj i4 a

(b) 0µ i ˆ ˆi j2 a

(c) 0µ i ˆ ˆi j2 a

(d) 0µ i ˆ ˆ ˆi j k2 a

56. Two wires AO and OC carry equal currents i asshown in figure. One end of both the wireextends to infinity. Angle AOC is . Themagnitude of magnetic field at a point P on thebisector of these two wires at a distance r frompoint O is

(a) 0µ i cot2 r 2

(b) 0µ i cot4 r 2

(c)0

1 cosµ i 24 r sin

2

(d) 0µ i sin4 r 2

57. A wire carrying current I is tied between pointsP and Q and is in the shape of a cirular arch ofradius R due to a uniform magnetic field B(perpendiculawr to the plane of the paper, shwonby xxx) in the vicinity of the wire. If the wiresubtends an angle 02 at the entre of the circle

Topper’s Pacakge Physics- XII Permutation and CombinationsMagnetic Effect of Current, Magnetism

52

(of which if forms an arch) then the tension inthe wire is

(a) IBR (b)0

IBRsin

(c)0

IBR2sin (d)

0

0

IBRsin

58. Current I flows through a long conducting wirebent at right angles as shown in figure. Themagnetic field at a point P on the right bisectorof the angle XOY at a distance r from O is

r

O

(a) 0µ Ir (b) 02µ I

r

(c) 0µ I2 1

4 r

(d) 0µ 2I 2 1

4 r

59. A long wire is first bent into a circular coil ofone turn and then into a circular coil of smallerradius having n turns. If the same currentpasses in both the case. Find ratio of magneticfield produced by circular wire of one turn andmagnetic field due to circular wire of n turns(a) n (b) n2

(c)1n

(d) 2

1n

60. A coil having N turns is wound tightly in theform of a spiral with inner and outer radii a andb respectively. When a curent F passes throughthe coil, the magnetic field at the center is:

(a) 0µ NIb (b) 02µ NI

a

(c)0µ NI blog

2(b a) a (d)0µ IN blog

2(b a) a

61. An electric current i is flowing through aninfinitely long conductor bent into a loop of theshape shown. Find the magnetic field at thecentre o of the circular part of the loop

(a) 00

µ 2iB (1 )

4 r

(outward direction)

(b) 00

µ 2iB (1 )

4 r

(inward direction)

(c) 00

µ iB (1 )

4 r

(outward direction)

(d) 00

µ iB (1 )

4 r

(inward direction)

62. A square frame of side length 'd' carries acurrent i produces a field B at its centre. Thesame current is passed through a circular coilhaving same perimeter as the square. The field

at the centre of circular coil is B0. Find 0

BB

(a)2

8 2

(b) 2

8 2

(c) 2

28

(d)22

5

63. Two identical coils each of radius r and havingnumber of turns 'n' are lying in perpendicularplanes, such that they have common centre.Find the magnetic field at the centre of the coils,

if they carry current equal to i and i3

respectively

(a) 0µ niB

r (b) 02µ ni

Br

(c) 0µ niB

2r (d) none

64. Find the magnitude of the magnetic fieldinduction at the origin 0 due to a very long

Topper’s Pacakge Physics- XII Permutation and CombinationsMagnetic Effect of Current, Magnetism

53

conductor carrying current i of the shape asshown.

(a) 0µ i ˆ ˆi k4 r 2

(b) 0µ i ˆ ˆi k4 r 2

(c) 0r i ˆ ˆi kr 2

(d) None

65. Find the magnetic induction at the point O, ifthe wire carrying a current I has a shape shownin fig. The radius of the curved part of the wireis 'R'. And the linear part of the wire are verylong

(a) 20µ i1 ( 1)

4 r

(b) 20µ i1

4 r

(c) 20µ i1

4 r

(d) 0µ i (1)4 r (1 )

66. Two insulating infinitely long wires lyingmutually perpendicular to each other as shown.If the two wires carry currents i, and \v findthe locus of the point, where the magnetic fielddue to two wires is zero.

(a)2

1

iy x

i (b) 1 2y i , i x

(c)1

2

iy xi

(d)1 2

xyi i

67. A current of ‘i’ ampere is flowing in the sides ofan equilateral triangle of side ‘l’. Find themagnetic field at the centroid of the triangle.

(a)9 i4 l

(b)9 i2 l

(c)9 i7 l

(d) none

68. A wire of length T and mass 'm' is suspended bya pair of flexible leads in a magnetic field ofinduction B. What is the magnitude of currentrequired to remove the tension in the supportingleads

(a)mgilB

(b)2mgilB

(c)mgi2lB

(d) i = 0

4. MAGNETIC MOMENT & TORQUE ON COIL69. A current carrying loop is placed in a uniform

magnetic field in four different orientations I,II, III and IV. Arrange them in the decreasingorder of potential energy

(I) (II)

III IV

(a) I > III > II > IV (b) I > II > III > IV(c) I > IV > II > III (d) III > IV > I > II

70. Two insulated rings one of slightly smallerdiameter than the other, are suspended alongtheir common diameter as shown in the figure.Initially the planes of the rings are mutuallyperpendicular. When a steady current is setupin each of them

Topper’s Pacakge Physics- XII Permutation and CombinationsMagnetic Effect of Current, Magnetism

54

(a) The two rings rotate into a common plane(b) The inner ring oscillates about its initial

position(c) The inner ring stays stationary while the

outer one moves into the plane of the innerring

(d) The outer ring stays stationary while theinner one moves into the plane of the outerring

71. An infinite current carrying wire passes throughpoint O and in perpendicular to the planecontaining a current carrying loop ABCD asshown in the figure. Choose the correct option(s)

(a) Net force on the loop is zero(b) Net torque on the loop is zero(c) As seen from O, the loop rotates clockwise(d) As seen from O, the loop rotates anti

clockwise

72. A metallic wire is folded to form a square loop ofside a. It carries a current i and is keptperpendicular to a uniform magnetic field. If theshape of the loop is changed from square to acircle without changing the length of the wireand current, the amount of work done in doingso is(a) 2iBa ( 2) (b) 2iBa ( 2)

(c)2 4iBa 1

(d)2 4iBa 1

73. A rigid circular loop of radius r and mass m liesin the x-y plane on a flat table and has a currenti flowing in it. At this particular place, the

earth’s magnetic field is x zˆ ˆB B i B k

. The

value of i so that one edge of the loop lifts fromthe table is

(a) 2 2r z

mg

r B B (b)z

mgrB

(c)x

mgrB (d)

x z

mgr B B

74. In the figure shown a coil of single turn is woundon a sphere of radius R and mass m. The planeof the coil is parallel to the plane and lies in theequatorial plane of the sphere. Current in thecoil is i. The value of B if the sphere is inequilibrium is

(a)mg cos

iR

(b)

mgiR

(c)mg tan

iR

(d)

mg siniR

75. A magnetic needle of magnetic moment 6.7 ×10–2 A m2 and moment of inertia 7.5 × 10–6 kgm2 is performing simple harmonic oscillationsin a magnetic field of 0.01 . T. Time taken for10 complete oscillations is(a) 6.65 s (b) 8.89 s(c) 6.98 s (d) 8.76 s

76. A uniform magnetic field B of 0.3 T is along thepositive Z - direction. A rectangular loop (abcd)of sides 10 cm × 5 cm carries a current I of 12A. Out of the following different orientationswhich one corresponds to stable equilibrium?

(a) (b)

(c) (d)

77. A magnetic dipole is acted upon by two magenticfields which are inclined to each other at angleor 75° . One of the fields has a magnitude of 15mT. The dipole attains stable equilibrium atangle of 30° with this field. The magnitude ofthe other field (in mT) close to(a) 1 (b) 11(c) 36 (d) 1060

78. A wire of length L meter carrying a current i am-pere is bent in the form of a circle. The magni-tude of magnetic moment is

Topper’s Pacakge Physics- XII Permutation and CombinationsMagnetic Effect of Current, Magnetism

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(a)2iL

4 (b)2iL

2

(c)iL4 (d) 2iL

79. A uniform change Q is spread over an insulatedring of radius R. If the ring is rotated with anangular velocity co with respect to the normalaxis, find the magnetic moment of the ring

(a)2Q R

2

(b) 2Q R

(c) 2Q R

4

(d)2Q R

3

80. The electron circulates round the nucleus inthe a path of radius ‘r’ at a frequency ‘f’. Calculatethe magnetic dipole moment.

(a)2f r eM

(b) 2M r ef

(c) 2

efMr

(d) 2

efrM

81. An insulting rod of length L carries a charge qdistributed uniformly on it. The rod is pivoted atMID-POINT and is rotated at a frequency f andabout a fixed perpendicular axis. The magneticdipole moment of the system is-

(a) 3q f L (b) 21 qfL3

(c) fq/L (d)2fqL

2

5. INSTUMENTS82. The operating magnetic field for accelerating

protons in a cyclotron oscillator having fre-quency of 12 MHz is (q = 1.6 × 10–19 C, mp = 1.67× 10–27 kg and 1 MeV = 1.6 × 10–13 J)(a) 0.69 T (b) 0.79 T(c) 0.59 T (d) 0.49 T

83. The cyclotron frequency vc is given by

(a)qB

2 m (b)mB2 q

(c)2 mqB

(d)2 Bqm

84. Which of the following is not correct about cy-clotron?(a) It is machine to accelerate charge particles

or irons of high energies.(b) Cyclotron uses both electric and magnetic

fields in combination to increase the en-ergy of charged particles.

(c) The operation of the cyclotron is based onthe fact that the time for one revolution ofan ion is independent of its speed or radiusof its orbit.

(d) The charged particles and ions in cyclotroncan move on any arbitrary path.

85. A solenoid of length 50 cm, having 100 turnscarries a current of 2.5 A. The magnetic field atone end of the solenoid is(a) 3.14 × 10–4T (b) 6.28 × 10–4T(c) 1.57 × 10–4T (d) 9.42 × 10–4T

86. Which of the following statement is correct?(a) The magnetic field in the open space in-

side toroid is constant.(b) The magnetic field in the open space exte-

rior to the toroid is constant.(c) The magnetic field inside the core of tor-

oid is constant.(d) The magnetic field inside the core of tor-

oid is zero.

87. A galvanometer of resistance 10 gives full-scale deflection when I mA current passesthrough it. The resistance required to convertit into a voltmeter reading upto 2.5 V is(a) 24.9 (b) 249

(c) 2490 (d) 24900

88. A galvanometer of resistance 70 , is converted

to on ammeter by a shunt reistance sr 0.03 .The value of its resistance will become.(a) 0.025 (b) 0.022(c) 0.035 (d) 0.030

89. Two moving coil metres M1 and M2 have thefollowing particular

3 21 1 41 1R 10 ;N 30 : A 3.6 10 m ;B 0.25T;

3 22 2 2 2R 14 ;N 42 : A 1.8 10 m ;B 0.50 T The spring constants are identical for the twometres. What is the ratio of current sensitivityand voltage sensitivity of M2 to M1 ?(a) 1.4, 1 (b) 1.4, 0(c) 2.8, 2 (d) 2.8, 0

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90. A galvanometer of resistance 40 gives a de-flection of 5 divisions per mA. There are 50 di-visions on the scale. The maximum current thatcan pass through it when a shunt resistace of2 is connected is(a) 210 mA (b) 155 mA(c) 420 mA (d) 75 mA

6. BAR MAGNET91. Two short bar magnets of equal dipole moment

M are fastened perpendicularly at their centres.The magnitude of the magnetic field at a dis-tance d from the centre of each on the bisectorof the right angle is:

(a) 03

µ M.4 d

(b) 03

µ 2M.4 d

(c) 03

µ 2 2M.4 d

(d) 03

µ 2M.4 d

92. Two bar magnets of the same mass, same lengthand breadth but having magnetic mometns Mand 2M are joined together pole to pole andsuspended by a string. The time period ofassembly in a magnetic field of period ofassembly in a magnetic field of strength H is 3seconds. If now the polarity of one of the magnetsis reversed and the combination is again madeto oscillate in the same field, the time ofoscillation is :(a) 3 secs (b) 3 3 secs(c) 3 secs (d) 6 secs

93. A magnetic needle is kept in a non-uniformmagnetic field. It experiences(a) a force and torque(b) a force but not a torque(c) a torque but not a force(d) neither a force nor a torque

94. A straight steel wire of length L has a magneticmoment. M when it is bent in the form of a semicircle, its magnetic moment will be

(a) M (b) M/(c) M/2 (d) M

95. Two mutually perpendicular lines are drawn ona table. Two small magnets of magneticmoments M1 and M2 are placed on these lines.If the distance of the point intersection of theselines be respectively d1 and d2 fra these magnets,there find the resultant magnetic field at thepoint of intersection.

(a)2 2

0 1 16 61 2

2µ M M4 d d

(b)

2220 1

6 61 2

M2µ M4 d d

(c)2220 1

6 61 2

Mµ M4 d d

(d) None

96. The times period of a freely suspended magnetnot depend upon ;(a) length of the magnet(b) the pole strength of the magnet(c) the horizontal component of magnetic field

of the(d) the length of the suspension

97. A thin bar magnet of length 2L is bent at themid point so that the angle between them is60°. The new length of the magnet is ;(a) 2 L (b) 3 L(c) 2L (d) L

98. A bar magnet of length 3 cm has points A and Balong its axies at distances of 24 cm and 48 cmon the opposite sides. Ratio of magnetic fieldsat these points will be :

(a) 8 (b)1

2 2(c) 3 (d) 4

99. A magnet of dipole moment m is aligned inequilibrium position in a magnetic field of

Topper’s Pacakge Physics- XII Permutation and CombinationsMagnetic Effect of Current, Magnetism

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intensity B. The work done to rotate it throughan angle with the magnetic field is:(a) mBsin (b) mB cos(c) mB(1 – cos) (d) mB(1 – sin)

100. A bar magnet has a magnetic moment 2J/Tand is placed in a magnetic field of 0.1 T.Calculate the work done in turning the magnetfrom parallel to antiparallel position relative tofield direction.(a) 0.2 J (b) 1 J(c) 4 J (d) 0.4J

7. EARTH MAGNETISM101.Lines of constant dip are called :

(a) isobaric lines (b) isogonic lines(c) isoclinic lines (d) isodynamic lines

102.The earth’s magnetic field may be consideredto be due to a short magnet placed at the centerof the earth and oriented along the magneticsouth-north direction. The ratio of themagnitude of the magnetic field on the earth’ssurface of magnetic equator to that at themagnetic poles is :(a) 1 : 2 (b) 2 : 1(c) 1 : 4 (d) 4 : 1

103.A magnetic needle lying parallel to a magneticfield requires W units of work to turn it through60°. The torque needed to maintain the needlein this position will be :(a) (3)W (b) W(c) (3)W/2 (d) 2W

104.The correct value of dip angle at a place is 45°.If the dip circle is rotated 45° out of the merid-ian, then the tangent of the angle of apparentdip angle, is :

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

105.A magnetic is suspended in such a way that itoscillates in the horizontal plane. It makes 20opm at a place where dip angle is 30° and 15opm at a place where dip angle is 60°. The ratioof earth’s total magnetic field at the two placesis

(a)4

3 3 (b) 43

(c)169 3 (d)

169

106.The angles of dip at the poles and the equator

respectively are(a) 30°, 60° (b) 0°, 90°(c) 45°, 90° (d) 90°, 0°

107.A compass needle whose magnetic moment is60 A m2 pointing geographical north at a cer-tain place where the horizontal component ofearth's magnetic field is 40 × 10–6 Wb m2 expe-riences a torque of 1.2 x 10–3 N m.The declination of the place is(a) 20° (b) 45°(c) 60° (d) 30°

108.Assume the dipole model for earths magneticfield B which is given by the vertical component

of magnetic 0V 3

µ 2mcosB4 r

and the horizontal

component of magnetic field 0H 3

µ mcosB4 r

,

where 90º – latitude as measured frommagnetic equator, then the loci of point forwhich dip angle is ± 45°.(a) tan–1 (3) (b) tan–1 (2)(c) tan–1(0.5) (d) tan–1(l)

8. MAGNETIC PROPERTIES OF MATERICAL109. When a diamagnetic substance is brought near

N or S pole of a bar magnet it is : (a) Attracted

(b) Repelled(c) Attracted by N and repelled by S pole(d) Repelled by N pole and attracted by S pole

110.When a material is used in a magnetic field B,a magnetic moment proportional to B but oppo-site in direction is induced. The metal is :(a) diamagnetic (b) paramagnetic (c) ferromagnetic (d) antimagnetic

111.A thin bar magnet of length 2l and breadth 2b,pole strength p and magnetic moment M is di-vided into four equal parts with length andbreadth of each part being half of the originalmagnet. Then the pole strength of each part is:(a) p (b) p/2(c) p/4 (d) 2p

112.Susceptibility is positive and small for a :(a) paramagnetic substance(b) ferromagnetic substance(c) non-magnetic substance(d) diamagnetic substance

113.Soft iron is used to manufactureelectromagnets because their :

Topper’s Pacakge Physics- XII Permutation and CombinationsMagnetic Effect of Current, Magnetism

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(a) magnetic saturation limit is high whileretentivity and coercive force are small

(b) retentivity is high but coercive force issmall

(c) retentivity is small but coercive force ishigh

(d) area of hysteresis loop is large

114.The relationship between rµ and is

(a) rµ 1 (b) rµ 1 (c) 0 rµ µ (d) r 0µ /µ

115.Hysteresis loops for two magnetic materials Aand B are given below:

These materials are used to make magnets forelectric generators. transformer core andelectromagnet core. Then it is proper to use:(a) A for electromagnets and B for electric

generators.(b) A for transformers and B for electric

generators.(c) B for electromagnets and transformers.(d) A for electric generators and transformers.

116.A 25 cm long solenoid has radius 2 cm and 500total number of turns. It carries a current of 15A. If it is equivalent to a magnet of the samesize and magnetisation M

(magnetic moment/volume), then M

is

(a) 13 Am (b) 130000 Am

(c) 1300 Am (d) 130000 Am117.The correct M-H curve for a paramagnetic

material at a constant temperature (T) isrepresented by

(a) (b)

(c) (d)

118.Point out the wrong statement about the magnproperties of soft iron and steel.(a) Retentivity of soft iron is more than

retentivity steel.(b) Coercivity of soft iron is less than coercivity

steel.(c) Area of B-H loop in soft iron is smaller than

area of B-H loop for steel.(d) Area of B-H loop in soft iron is greater than

area of B-H loop for steel.119.Point out the best representation of relation

between magnetic susceptibility andtemperature (T) for a paramagnetic material

(a) (b)

(c) (d)

120.The hysteresis cycle for the material of a transfocore is(a) short and wide (b) Tall and narrow(c) tall and wide (d) short and narrow

121.A paramagnetic liquid is taken in a U-tube andarranged so that one of its limbs is kept betweenpole pieces of the magnet. The liquid level inthe limb(a) goes down(b) rises up(c) remains same(d) first goes down and then rise

9. EARTH MAGNETISM122.A conducting loop carrying a current I is placed

in a uniform magnetic field pointing into theplane of the paper as shown. The loop will havea tendency to

Topper’s Pacakge Physics- XII Permutation and CombinationsMagnetic Effect of Current, Magnetism

59

(a) contract(b) expand(c) move towards + ve x-axis(d) move towards –ve x-axis

123.A thin flexible wire of length L is connected totwo adjacent fixed points and carries a currentI in the clockwise direction, as shown in thefigure. When the system is put in a uniformmagnetic field of strength B going into the planeof the paper, the wire takes the shape of a circle.The tension in the wire is:

(a) IBL (b)IBL

(c)IBL2 (d)

IBL4

124.A particle of mass m and charge q, moving withvelocity v enters Region II normal to the bound-ary as shown in the figure. Region II has a uni-form magnetic field B perpendicular to the planeof the paper. The length of the Region II is tChoose the increacte choice(s):

(a) The particle enters Region III only if its

veolcityqlBvm

(b) The particle enters Region III only if its

velcoity qlBvm

(c) Path length of the4 particle in Region II is

maximum when velocity qlBvm

(d) Tiem spent in Region II is same for anyvelocity v as long as the particle returns toRegion I

125.A particle of mass M and positive charge Q,

moving with a constant velocity –11

ˆu 4i ms ,

enters a region of uniform static magnetic fieldnormal to the x-y plane. The region of themagnetic field extends from x = 0 to x = L for allvalues of y. After passing throught this region,the particle emerges on the other side after 10milliseconds with a velocity –1

2ˆ ˆu 2( 3 i j )ms

.The correct statement(s) is (are)(a) The direction of the magnetic field is –z

direction(b) The direction of the magnetic frield is +z

direction(c) The magnitude of the magnetic field

50 M3Q

units

(d) The magnitude of the magnetic field is100 M

3Q

units

126.A steady current I flows along an infinitely alonghollow cylindrical conductor of radius R. Thiscylinder is placed coaxially inside an infinitesolenoid of radius 2R. The solenoid has I turnsper unit length and carries a steady curernt I.Consider a point P at a distance r from thecommon axis. The correct statement(s) is (are)(a) In the region 0 < r < R, the magnetic field

is non-zero(b) In the region R < r < 2R, the magnetic field

is along the common axis(c) In the region R < r < 2R, the magnetic field

is tangential to the circle of radius r,centred on the axis

(d) In the region r < 2R, the magnetic field isnon-zero

127. A coil in the shape of an equilateral triangle ofside l is suspended between the pole pieces of apermanent magnet such that B

is in plane ofthe coil. If due to a current i inthe triangle atorque acts on it the side l of the triangtle is

(a) 1/22

Bi3

(b) 2

Bi3

(c) 1/2

23Bi

(d) 1

Bi3

128.A closed loop PQRS carrying a current is placedin a unifrom magnetic field. If the magneticforce on segmetns PS, SR and RQ are F1, F2 andF3 respectively and are in the plane of the pa-

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60

per and a long the directions shown, the forceon the segment QP is

P

Q

F3

RF2

S

F1

(a) F3 – F1 – F2 (b) 2 23 1 2F F F

(c) 2 23 1 2F F F (d) F3 – F1 + F2

129.A galvanometer having a coil resistance of 60shows full scale deflection when a current of1.0A passes through it. It can be converted intoan ammeter to read upto 5.0 A by(a) putting in parallel a resistance of 240(b) putting in series a resistance of 15(c) putting in series a resistance of 240(d) putting in parallel a resistance of 15

9. INTEGER TYPE QUESTION1. An arc of a circular loop of radius R is kept in

the horizontal plane and a uniform magneticfield B is applied in the vertically downward di-rection as shown in the figure. If the arc car-ries current i then the force on the arc is x i R B,what is the value of 3x2?

IB

90o

2. A square loop of wire is oriented with the leftcorner at the origin, one edge along X-axis andthe other edge along Y-axis as shown in thefigure. A magnetic field is into the page and hasa magnitude that is given by = y where iscontant. Then the total magnetic force on theloop if it carries current i is 2 ˆp a ij , what is thevalue of 8p?

B

Y

X

a

a

3. Find the magnetic field at point P shown infigure.

ii/2

i/2

P(2,0,0)

x

y

4. A current carrying circular loop having singleturn has magnetic field B1 at its centre. Nowthis loop is turned in circular coil of two turnsand having same current. Now the magnetic fieldat the centre will become n times. Find n.

5. A wire, carrying current 1 A is kept in x-y planealong curve y = A sin(x). A uniform magneticfield B = 3T exist in z-direction. Find the magni-tude of the magnetic force on the segment ofthe wire between x = 0 and x = 2m.

6. An infinite long wire carrying current i = 10 Ais placed along y-axis such that one end is at (0,3). The magnitude of magnetic field at P(4, 0) isn × 10–7. Find n.

y

xP(4, 0)

i(0, 3)

(0, 0)

7. A charge particle is moving on a circular path ofradius r. A point P lies in the plane of the circleat distance d from centre such that d >> r. Themagnetic field at P becomes zero after a regulartime interval /2 sec. Find the angular speedof the particle in rad/sec.

8. A charge particle having charge 1 mC and mass15 g enters in a uniform magnetic field B = Tas shown in figure. Find the time spent in sec-ond by the charge particle in magnetic field.

× ××××××

××××

××××30oq

m9. A uniformly changed non-conducting rod of

length 2 m and having total charge 1 C is rotat-ing with constant angular speed 3 rad/s aboutthe axis passing through one end and perpen-dicular to its length. Find the magnetic momentof the rod in A-m2.

Topper’s Pacakge Physics- XII Permutation and CombinationsMagnetic Effect of Current, Magnetism

61

1. CHARGES IN MAGNETIC FIELD1. b 2. d 3. a 4. d 5. a6. d 7. b 8. b 9. b 10. b11. d 12. b 13. c 14. c 15. d16. c 17. d 18. c 19. c 20. d21. a 22. a 23. b 24. a

2. FORCE ON CURRENT CARRYING CONDUCTOR25. c 26. b 27. c 28. c 29. a30. a 31. b 32. d 33. a 34. a35. a 36. a 37. d 38. c 39. a40. c

3. BIO-SAVART’S LAW, AMPERE CIRCUITAL LAW41. c 42. b 43. a 44. b 45. c46. d 47. c 48. b 49. a 50. d51. a 52. d 53. c 54. a 55. c56. c 57. d 58. d 59. d 60. d61. a 62. b 63. a 64. b 65. a66. a 67. b 68. a

4. MAGNETIC MOMENT & TORQUE ON THE COIL69. c 70. a 71. c 72. c 73. c74. b 75. a 76. d 77. b 78. a79. a 80. a 81. b

5. INSTRUMENTS82. b 83. c 84. a 85. a 86. a87. c 88. c 89. a 90. a

6. BAR MAGNET91. c 92. b 93. a 94. c 95. a96. d 97. d 98. a 99. c 100. d

7. EARTH MAGNETISM101. c 102. a 103. a 104. c 105. c106. d 107. d 108. b

8. MAGNETIC PROPERTIES OF MATERIAL109. b 110. a 111. b 112. a 113. a114. a 115. c 116. d 117. a 118. d119. a 120. b 121. b

9. MISCELLANEOUS122. b 123. c 124. a, c, d 125. a, c 126. a, d137. c 128. b 129. d

10. INTEGER TYPE QUESTION1. 6 2. 8 3. 0 4. 4 5. 66. 1 7. 2 8. 5 9. 2