iit (mains + advance) physics module 2013

7/29/2019 IIT (Mains + Advance) Physics Module 2013

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AIEEE PHYSICS Module

Conceptual Questions

1. A long metallic pipe carries a current. What is the magnetic field (i) inside and (ii) outside the

pipe?

2. Will two parallel beams of electrons moving with normal velocities in vacuum repeal or

attract?

3. When a current is passed through a spring, it contracts. Why?

Multiple choice Questions

4. A current of 25 A flows through an overhead power cable form the north to south direction.

The magnitude and direction of current 5m below the cable is

a) 10-6

T towards east b) 10-6

T towards west c) 10-5

T towards north d) 10-5

T

towards south

5. The magnetic field at the point of intersection of diagonals of a square loop of side L carrying

a current I is given by

a)L

I

02 b)L

I

022 c)L

I

0

2

1d)

L

I

0

22

1

6. Two straight and long conductors placed along the x and y axis carry currents I1 and I2. The

magnitude of the magnetic field at a distance d from the origin on the z-axis is

a) ( )210

2II

d+

b) ( )21

0

2II

d

c)

2

2

2

10

2II

d+

d)

21

210

2 II

II

d +

7. O is the common centroid of two inverted equilateral triangle of side d. The two triangles are

insulated from each other and carry same currents I as shown in the figure. The net magnetic

field at the centre O is


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a)d

I

4

3 0 b)d

I

2

3 0 c)d

I

09 d) zero

8. O is a point on the perpendicular bisector of a straight wire AB of length L at a distance2

L.

The magnetic field at O due to the current I flowing in the wire is

a)L

I

422

1 0 b)L

I

42 0 c)

L

I

422 0 d)

L

I

42 0

9. A uniform conducting wire is bent to form an equilateral triangle CBA

^

of side L. A current Ienters at A leaves at C. What is the magnetic induction at the centroid O?

a) L

I

4320

b) L

I

4

0

c) L

I

430

d) Zero

10. The figure shows two long straight wires passing each other perpendicularly without

touching. The magnetic field is zero


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a) in quadrant 1 b) in quadrant 2 c) in quadrant 3 d) at the point of

intersection

11. A current I flows along the length of an infinitely long, straight, thin walled pipe. Then, themagnetic field,

a) At all points inside the pipe is the same but not zero

b) At any point inside the pipe is zero

c) Is zero only on the axis of the pipe

d) Is different at different point inside the pipe

12. Two mutually perpendicular conductors carry current I1 and I2 x and y axis respectively. The

locus of points at which the magnetic induction is zero is

a) xI

Iy

=

2

1 b) xI

Iy

=

1

2 c) xII

IIy

+

=

22

21 d)

xII

IIy

+=

22

21

13. A uniform metallic wire forms the edges of a cube of length l. A current I enters at one edge

of the cube and leaves form the diagonally opposite edge. The magnitude of the magneticfield at the centre of the cube is

a) Zero b)l

i

n

3

240

c)

l

i

n

0

3

12d)

l

i

n

0

3

6

14. In the loops shown, all curved sections are either semicircles or quarter circles. All the loops

carry the same current. The magnetic fields at the centers have magnitudes B1, B2, B3 and B4.

Then

a) B4 is maximum b) B3 is minimum c) B4 > B1 >

B2 > B3

d) B2 cannot be found unless the dimensions of the section B are known.


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15. Two infinitely long conductors carrying equal currents are shaped as shown. The short

sections are all of equal length. The point P is located symmetrically with respect to the

conductors. The magnetic field at P due to any conductor is B. The total field at P is

a) Zero b) B c) B2 d) 2B

16. Three infinitely long thin conductors are joined at the origin of coordinates and lie along x, y

and z-axis. A current I flowing along the conductor lying along the x-axis divide equally into

the other two at the origin. The magnetic field at the point (0, -a, 0) has magnitude

a)a

i

4

0 b)a

i

24

3 0 c)a

i

8

5 0 d)a

i

2

3 0

17. A long straight wire along the z-axis carries a current in the negative z-direction. The

magnetic vector field

B at a point having coordinate (x, y) on the z = 0 plane is

a)( )22

^^

0

2 yx

jxiyi

+

b)( )22

^^

0

2 yx

jyixi

+

+

c)( )22

^^

0

2 yx

jyixi

+

d)

( )

22

^^

0

2 yx

jyixi

+

18. The ratio of magnetic field at the cetnre of a current carrying circular coil to its magnetic

moment is K. If both the current and radius are doubled, the new ratio will be

a)8

Kb)

4

Kc)

2

Kd) 2 K

19. In the set up shown below, the magnitude of the magnetic field at C is


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a)R

i

8

0 b)R

i

4

0 c)R

i

2

0 d)R

i0

20. A straight conductor carrying a current I splits into identical semicircular arcs, as shown. The

magnetic field at the centre C of the loop is

a) 2T b)R

i

2

0 c)i2

0 d) Zero

21. The wire shown in the figure carries a current I. The magnetic field

B produced at centre C

of the semicircle by each straight segment of wire is

a) Zero b)R

i

4

0 c)R

i

2

0 d)R

i0

22. In the above problem,

B produced at C by the semicircular segment is

a) Zero b)R

i

4

0 c)R

i

2

0 d)R

i0

23. A solenoid has a length L =1m and inner diameter d = 4cm and it carries a current I = 5A. It

consists of five close packed layers, each with 800 turns, along L. The value of the magnetic

field at the centre is

a) Zero b) 25 mT c) 5 mT d) 1 mT

24. The magnetic field at the point O due to current I flowing in the conductor shown in the

figure is


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a) Zero b)R

I

4

0 c)R

I

4

0 d) ( )14

0+

R

I

25. The magnetic field at the point O due to the current flowing in the conductor shown in the

figure is

a)

+

21

210

4 rr

rrIb)

21

210

4 rr

rrIc)

( )21

0

4 RR

I

d)

( )21

0

4 RR

I

+

26. The magnetic field at O due to the current flowing in the conductor shown in the figure is

a)

+

21

210

4 rr

rrIb)

21

210

4 rr

rrIc)

( )21

0

4 rr

I

+

d)

( )21

0

4 rr

I

27. Two coils P and Q carrying same current in same sense subtend the same solid angle at the

point O as shown in the figure. Then, the ratio of magnetic field BP : BQ produced at O is

a) 1 : 4 b) 1 : 3 c) 1 : 2 d) 1 : 1


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28. Two coils P and Q carrying currents I1 and I2 in opposite sense subtend the same solid angle

at point O as shown in the figure. What must be the ratio of currents (I1/I2) in order that the

net magnetic field produced at O be zero?

a) 2 b) 4 c)4

1d)

2

1

29. P and Q are two concentric circular conductor of radii r1 and r2 carrying currents I1 and I2

respectively. If the magnetic field at the cetnre O is zero then

a)1

2

2

1

r

r

I

I= b)

2

1

1

1

r

I

r

I= c) 2211 rIrI = d)

2

1

1

2

r

r

I

I=

30. The variation of magnetic field due to a staright current carrying conductor of radius r along a

direction perpendicular to its length is

a) b) c) d)

31. A current I flows through a circular arc of wire which subtends an angle of3

at the centre. If

the radius of the circular arc is R, the magnetic induction B at the centre is

a)R

I

4

0 b)R

I

12

0 c)r

I

2

3 0 d)r

I

6

0


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32. A long solenoid carrying a current produces a magnetic field B at its centre. If both the

number of turns per centimeter and the current are doubled, the new value of the magnetic

field will bea) B b) 2 B c) 3 B d) 4B

33. For a long solenoid carrying a current the ratio of magnetic field at centre to the magnetic

field at one end along the axis of the solenoid is

a) 1 b) 2 c)2

1d) 3

Problems

34. A ling horizontal wire AB which is free to move in a vertical plane and carries a steady

current of 20 A is in equilibrium at a height of 0.01m over another parallel long wire CD

which is fixed in a horizontal plane and carries a steady current of 30 A as shown. Show that

when AB is depressed slightly it executes SHM. Find its period.

35. An -particle of mass 6.65 x 10-27kg is moving at normal to a magnetic field with a speed of

6 x 105

ms-1

. The strength of the magnetic field is 0.2 T. Find the force on the -particle and

its acceleration.

36. A long straight conductor has a current of 100 A passing through it. Find the distance from

the conductor at which the magnetic field caused by the current is equal to 0.5 x 10-4

T.

37. Show that the magnetic field induction at the centre of a coil bent in the form of a square of

side 2a, carrying current I isa

I

02 .

38. A circular coil has horizontal plane. It has 10 turns each of 8cm radius. A current of 2A flows

through it, which appears clockwise form a point vertically above it. What is the magnitude

and direction of the magnetic field at the centre of the coil due to current?


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39. An electron (mass 0.90 x 10-30

kg), under the action of magnetic field travels in a circle of

radius 2.0cm at a speed of 3.0 x 106

ms-1

. If proton (mass 1.8 x 10-27

kg) were to move in a

circle of the same radius in the same magnetic field, what is its speed?


40. A loop of irregular shape carrying current is located in an external magnetic field. If the wire

is flexible, why does it change to a circular shape?

41. What is the advantage of using radial magnetic field in a moving coil galvanometer?

42. Which has greater resistance

a) Ammeter or milliammeter and b) Voltmetere of milliammeter?

43. Why the resistance of an ammeter should be very low?

44. Why the resistance of a voltmeter should be very high?

Multiple Choice Questions with Correct alternative

45. A charged particle enters a region of magnetic field at right angles to the magnetic field. The

length of the region of the magnetic field is 1.1 times the radius of the circular path of the

particle. The deviation of the particle from its original path is

a) 450

b) 900

c) 1350

d) 1800

46. A particle of charge q and mass m is released form origin with a velocity^

0 ivv =

in a

uniform magnetic field

0B along the

k direction. If the particle passes through P(o, y, o),

then the value of y is

a)Bq

vm 02 b)02 vm

Bqc)Bq

vm 0 d)m

vBq 0

47. Two particle A and B of masses mA and mB and having the same charge are moving in a plane

with speeds vA and vB. A uniform magnetic field exists perpendicular to this plane. The

trajectories of the particle are shown in figure. Then


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b) May or may not complete one full rotation

c) Will always complete half a rotation before leaving the field

d) May follow a helical path

53. A proton, a deuteron and an -particle with the same kinetic energy are moving in circular

trajectories in a constant magnetic field. If Rp, Rd and R , respectively, denote the radii of

the trajectories, then

a) dp RRR = c) pd RRR >= d)

RRR dp ==

54. A neutral atom which is at rest at the origin emits an electron in the Z direction. The productatom is P. A uniform magnetic field exists in the +x direction.

a) The electron and P will move along circular paths of equal radii

b) The electron has same time period as P

c) The electron has same kinetic energy as P

d) The two meet again

55. A region has uniform electric and magnetic fields along the positive x direction. An electron

is projected from the origin at an angle 800

with the x-axis. The electron willa) Move along a helical path of increasing pitch

b) Move along a helical path of decreasing pitch

c) move in a circle

d) Momentarily come to rest

56. A proton projected with a velocity v describes a circle of radius R in uniform magnetic field

B. With what velocity should an -particle be projected so that it describes a circle of the

same radius R in the same magnetic field?

a)4

vb)

2

vc) v d) 2 v

57. The cyclotron frequency of an electron moving in a uniform magnetic field 0.02 T is

a) 5.6 x 108

Hz b) 6.6 x 108

Hz c) 6.6 x 108

Hz d) 7.6 x 108

Hz


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58. A stream of electrons passes through a velocity filter when the crossed electric and magnetic

fields are 50kV/m and 0.2mT respectively. The kinetic energy of the electron passing through

the filter is (in eV)

a) 15.8 b) 16.2 c) 16.9 d) 17.7

59. A proton enters a region of uniform magnetic field 0.5 T with a velocity u at an angle 450

with

B. If P is the pitch of the path followed, the radius of the helix is

a)2

Pb)

P

2c)P

d)

P

60. A proton is projected in a plane perpendicular to a uniform magnetic field B. The area

velocity (area swept per unit time) of the proton is proportional to

a) kinetic energy b) B c) 2B d) q

61. Two protons enter a uniform magnetic field with the same speed but at angles 300

and 600

with the field. If x is the ratio of their time periods, y of their radii and z of their pitches, then

a) xyz = 1 b) xyz > 1 c) xyz < 1 d) x = y + z

62. Two protons enter a uniform magnetic field with velocity v^

i and (2v)^

i . The angular

frequency rotation is . Then

a) 21 = b) 21 > c) 21 < d)

021 ==

63. In the above problem, the time periods T1 and T2 are related as

a) T1 = 0 = T2 b) T1 > T2 c) T1 < T2 d) T1 = T2

64. Figure shows the circular paths (radii R1 and R2) of a proton and an electron traveling at the

same velocity in a uniform magnetic field

B

a) R1 corresponds to the proton b) R1 corresponds to the electron

c) R2 corresponds to the electron d) direction of motion of the electron is anticlockwise


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65. A magnetic field with a slit system shown in the figure is used as momentum fitter for high

energy particles. For a field B, the fitter transmits -particle each of energy 5 MeV. If

magnetic field is increased of 2B, the energy of the deuteron passed by the filter is

a) 5 MeV b) 10 MeV c) 2.5 MeV d) 1 MeV

66. Two particles with same charge but of different mass m1 and m2 are accelerated through the

same potential difference and enter a uniform magnetic field describing circular paths of radii

r1 and r2. Then2

1

m

mis equal to

a)2

1

r

rb)

2

1

r

rc)

2

2

2

1

r

rd)

1

2

r

r

67. An electron traveling with a velocity of 1.6 x 108

ms-1

enters into a uniform magnetic field

and moves along a circular arc. If the strength of the magnetic field is 9.1 x 10 -3T and extends

upto a distance of 5cm form the point of entry of the electron, the angle of deflection of the

electron when it comes out of the magnetic field is

a) 300

b) 450

c) 600

d) 900

68. For a positively charged particle moving in the x-y plane initially along the x-axis, there is a

sudden change in its path due to the presence of electric and/or magnetic fields beyond P as

shown in the figure. The curved path in the x-y plane is found to be non-circular. Which one

of the following combinations are possible?

a)^^

;0 kcjbBE +==

b)^^^

; ibkcBiaE +==

c)^^

;0 kbjcBE +==

d)

^^^

; jbkcBiaE +==


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69. A particle of mass m and charge q moves with a constant velocity v along the positive

direction. It enters a region containing a uniform magnetic field B directed along the negative

z-direction, extending from x = a to x = b. The minimum value of v required so that it can just

enter the region x > b is

a)m

bqBb)

m

aqBc)

( )

m

qBba +d)

( )

m

qBba

Problems

70. A circular coil of 20 turns and radius 10cm has a current of 5 A. It is located in uniform

magnetic field of 0.10T. What is the torque acting on the coil when the magnetic field is

applied (i) perpendicular to the plane of the coil (ii) in the plane of coil? Also calculate the

total force acting on the coil.

71. Two infinitely long parallel wires, carry same current will there be a magnetic field at a point

exactly halfway between the wires when the currents in them are (a) along the same direction,

(b) along opposite direction ?

72. A current of 2.00 A flows in a square loop of edge 0.1m. What is the magnetic field B at the

centre of the square loop?

73. Two long wires, having currents i1 and i2, are placed normal to each other in such a way that

they just are not in contact. What is the magnetic force on a small length d/of the second wire

situated at a distance l form the first wire?

74. ABCD is a rectangular loop made of uniform wire. The length AD = BC = 1cm. AB and DC

are long compared to the other two sides. What is the magnetic force per unit length acting on

the wire DC due to the wire AB if the ammeter in series reads 10A?


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75. A current loop having two circular arcs joined by two radial lines as shown in figure. What is

the magnetic field B at the centre O?

76. A current carrying circular loop of radius 12cm produces a magnetic field

B at its centre

equal to 0.05 x 10-4

T. What is the magnetic field due to this loop at a point on the axis at a

distance of 5.0cm form the centre.

Multiple Choice Questions with one correct alternative

77. Two particle having the same mass m and carrying charges +q and q enter a region of

uniform magnetic field B directed normally inwards into the paper, with speeds v1 and v2 as

shown in figure. If d is the initial separation between the particles, then the particles will not

collide if (ignore electrostatic force)

a) ( )212

vvqB

md +> b) ( )21 vv

qB

md +> c) 21 vv = d)

( )21 vvqB

md +<

78. A charged particle of specific charge is released form origin at time t = 0 with velocity

+=

^^

01 jivv in a uniform magnate field^

0 iBB =

. The co-ordinates of the particle at time

0Bt= are

a)

0

0

0

0

0

0 ,2

,2 B

v

B

v

B

vb)

0

0

0

0

2,

2,0

B

v

B

v


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c)

0.0,

2 0

0

B

vd)

0

0

0

0 2,0,B

v

B

v

79. A particle having charge q enters a region of uniform magnetic field

B (directed inwards)

and is deflected by a distance y after traveling a distance x as shown in the figure. The

magnitude of the momentum of the particle is

a)2

qBxb)

2

qByc)

+ y

y

xqB2

2d)

x

qBy

2

2

80. In a region where both nonzero uniform electric field and magnetic field coexist, the path of a

charged particle

a) Must be a circle b) May be a circle c) May be a straight line d) Must be a

helix

81. Mark correct option or options

a) Electric field and magnetic field are basically independent

b) Electric field and magnetic field are aspects of the electromagnetic field

c) Electric field and magnetic field may be produced by charge in rest

d) Both (1) and (3) are correct

82. A charged particle moving a uniform magnetic field penetrates a layer of lead and loses one

half of its kinetic energy. The radius of curvature changes to

a) Twice the original radius b) 2 times the original radius

c) half of the original radius d)2

1times the original radius

83. Two charged particles M and N are projected with same velocity in a uniform magnetic field

as shown in the figure. Then M and N are


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a) An electron and a proton respectively b) a He+

ion and proton respectively

c) a He+

ion and an electron respectively d) a proton and -particle respectively

84. A charged particle moving in a uniform magnetic field loses 4% of its kinetic energy. The

radius of curvature of its path changes by

a) 2 % b) 4 % c) 10 % d) None of these

85. A charged particle of mass m and charge q is in a uniform magnetic field B. The magnetic

field acts into the plane of the paper. The plane is frictional having coefficient of friction .

The speed of charged particle just before entering into the region is v0. The radius of curvature

of the path after the timeg

v

2

0 is

a)qB

vm 0 b)qB

vm

2

0 c)qB

vm

4

0 d) None of these

86. A charged particle +q of mass m is placed at a distance d from another charged particle -2q of

mass 2m in a uniform magnetic field of induction B (as shown in figure). The particles are

projected towards each other with equal speed v0. The maximum value of the projection speed

v0, so that the two particle do not collide, is (assume only magnetic force of interaction

between particles)

a)m

qBdb)

m

qBd

2c)

m

qBd2d) None of these

87. A positive charge q is projected in magnetic field of widthBq

vm

2with velocity v as shown

in figure. Then time taken by charged particle to emerge form the magnetic field is


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a)Bq

m

2b)

Bq

m

4

c)

Bq

m

2

d)

Bq

m

2

88. A charged particle enters a uniform magnetic field B with velocity

v at an angle as shown

in the figure. Then the ratio of radius to pitch of helix is

a)

tan2 b) tan c) cot d)

2tan

89. An electron is moving along x^

i . A uniform electric field E(-^

j ) is present. What should be

the direction of the magnetic field so that the net force on the electron is zero?

a)^

i b)^

j c)^

k d) -^

k

90. Which of the following statement is correct?

a) A magnetic field can acceleration a charged particle

b) A magnetic field cannot acceleration a charged particle

c) A magnetic field can increase the speed of a charged particle

d) A magnetic field cannot change the velocity of a charged particle

91. In which of the following situations will a charge experience zero force?

a) It is at rest in an electric field b) It moves parallel to an electric field

c) It at rest in a magnetic field d) It moves perpendicular to a magnetic field

92. A proton is released form rest in a region of steady and uniform electric and magnetic fields

which are parallel to each other. The particle will move in a

a) Straight line b) Circle c) Helix d) Cycloid


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93. A proton moving in a magnetic field has a velocity^^

43 jiv +=

and acceleration

^^

3 jxia +=

. Then x =

a) 1 b) 1 c) 1.5 d) -2.025

94. A charged particle with a kinetic energy K enters a region of a uniform magnetic field

perpendicular to the direction of the particle. Its kinetic energy now is

a) K b) 2 K c)2

Kd) 14 K

95. An electron having a velocity v^

i enters a region of a uniform magnetic field B^

j . The

direction of the magnetic force on it along

a)^

k b) -^

k c)^

i d)^

j

96. In the following diagram, the force on the particle is

a) along v b) along v c) to the left d) to the right

97. The figure shows four directions for the velocity

v of a proton moving through uniform

BandE . In which direction is the net force on the proton zero?

a) N b) S c) E d) W

98. An observer A and a charge q are fixed in a certain frame of reference FA. Another observer B

is fixed in a frame FB which is moving with respect to FA

a) B will not observe an electric field b) A will observe a magnetic field


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c) A will not observe an electric field d) B will observe a magnetic field

99. An electron accelerated by a potential difference of V volts enters a uniform transverse

magnetic field where it experiences a force F. If the accelerating potential is tripled, the forcewill be

a) F b) 3 F c) 3 F d)3

F

100. A uniform electric field and a uniform magnetic field are produced, pointed in the same

direction. A proton is projected with its velocity pointed in the same direction.

a) The proton velocity with increase in magnitude

b) The proton velocity will decrease in magnitude

c) The proton will turn towards its left

d) The proton will turn towards its right

101. The power associated with magnetic force acting on a moving charged particle

a) Is a always zero b) is never zero

c) Is zero only when

v is perpendicular to

B d) Is zero only when

v is parallel to

B

102. A rectangular current loop carrying a current I is placed near a long straight parallel conductor

as shown in the figure. Then the loop will

a) Remain stationary b) Move away from the wire

c) Move towards the wire d) Rotate around the wire with the wire as

the axis

103. The force of repulsion between two parallel wires separated by a distance d and carrying

current I in opposite direction is F. If the current in each wire is doubled but the separation

between them is halved, the force will be

a) F b) 2 F c) 4 F d) 8 F

104. Three long straight parallel and equally spaced wires carry identical currents as shown in thefigure. If F1, F2 and F3 represent the net force on the wires 1, 2, 3 respectively then


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a) 132 FFF >> b) 312 FFF >> c) 321 FFF >> d) 321 FFF ==

105. Three ling, straight and parallel wires 1, 2 and 3 carry currents I, 2I and 3I respectively as

shown in the figure. If F12 represents the force acting on the wire 1 due to the wire 2 and F 13

represents that on the wire 1 due to the wire 3 then

a) F12 =F13 b) F12 =2F13 c) F13 =2F12 d) F13 =-F12

106. A current carrying conductor of length 5m carrying a current of 1 A in a magnetic field 2T

experiences force 5N. The angle of inclination of the conductor with the magnetic field is

a) 900

b) 600

c) 450

d) 300

107. Two long straight parallel conductors separated by a distance of 2m, carry unequal currents I1

and I2. When the currents are in the same direction the magnetic field at a point midway

between them is 1 x 10-5

T. If the currents are in the opposite direction the magnetic field at

the same point is 3 x 10-5

T. Then the ratio of the currents2

1

I

Iis

a) 2 b) 3 c)3

2d)

5

h


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108. Three long straight wire are connected parallel to each other across a battery of negligible

internal resistance. The resistance of the three wire are in the ratio 1 : 2 : 3. What is the ratio

of the distances of middle wire form the others if the net force experienced by it is zero?

a) 3 : 1 b) 1 : 2 c) 2 : 3 d) 3 : 4

109. A conductor PQ of length L, carrying a current I, is placed perpendicular to a long straight

conductor x-y carrying a current i, as shown. The force on PQ will be

a) upward b) downwards c) to the right d) to the left

110. The loop shown carries a current I in a uniform magnetic field. The force on loop is

a) BIL b)2

3BIL c) Zero d)

2

BIL

111. A current carrying wire AB is placed near a very long straight conductor

a) Only translate b) Only rotate c) Translate as well as rotate d) oscillate

112. In the figure, a messy loop of wire is placed with points a and b fixed. If a current is then sent

as shown, the area within the loop


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a) Increases b) Decreases c) Remains the same d) Becomes

zero

113. A magnetic needle is kept in a non-uniform magnetic field. It experiences

a) A force and a torque b) A force but not a torque

c) A torque but not a force d) Neither a force nor a torque

114. Two long straight parallel wires separated by a distance r carry same currents I flowing in the

same direction. The work that has to be done to increase their separation to 2r is

a)

2

0I b)

2

2

0I c) rI

ln2

2

0

d) 2ln

2

2

0

I

115. A wire loop carrying current I consists of straight portion AB of length L1 and an arbitrarily

curved portion ACB of length L2. A uniform magnetic field B exists perpendicular to the

plane of the loop. Then the force on the curve portion ACB is

a) BIL1 b) BIL2 c) BI(L2 L1) d) Zero

116. The same current I is flowing in a wire frame as shown. The frame is a combination of two

equilateral triangle PQR and QRS of side 2m. It is placed in a uniform magnetic field 4T

acting perpendicular to the plane of the frame. If the magnitude of the magnetic force on the

frame is 48N, the value of I is

a) 2 A b) 3 A c) 4 A d) 8 A


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117. A square loop having a mass m and carrying a current is kept above the ground (x-z plane) at

a height H. In which direction should a magnetic field be applied so that the loop is

stationary?

a) along x b) along y c) along +z d) it cannot be done

118. A metallic rod of length 50cm and mass 100g carrying a current of 2A is suspended

horizontally by means of two vertical wires at its ends. What magnetic field must be set up

normal to the conductor in order that the tension in the wires is zero? (take g =10ms-2

)

a) 10 T b) 1 T c) 0.1 T d) 100 T

119. A conducting circular loop of radius r carries constant current i. It is placed in uniform

magnetic field B such that B is perpendicular to the plane of the loop. The magnetic force

acting on the loop is

a) irB b) ( )Bri 2 c) ( )Bri d) Zero

120. An insulating rod of length l carries a charge q distributed uniformly on it. The rod is pivoted

at an end and is rotated at a frequency f about a fixed perpendicular axis. The magnetic of the

system is

a) Zero b)21fq c)

212

1fq d)

213

1fq

121. The magnitude of magnetic moment of current loop in the figure is

a) Ia

2

b) 2 Ia

2

c) Zero d) 2

3

Ia

2

122. A current carrying loop is placed in a uniform magnetic field in four different orientations, I,

II, III and IV. Arrange them in the decreasing order of potential energy


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I) II) III) IV)

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

123. A wire l met long is bent in the form of a circular coil of some (N) turns. The coil is placed in

uniform magnetic field

B and a current I is sent through it and for maximum torque to be

experienced by the coil, the value of N is

a) 4 b) 3 c) 2 d) 1

124. A semicircular wire of radius R, carrying a current I, is placed in a magnetic field B. The

force acting on it

a) can never be zero b) can have a maximum magnitude 2BIR

c) can have a value BIR2 d) can have a magnitude BIR

125. Magnetic induction at the centre of circular loop of area A is B. Then magnetic moment of

the loop will be

a)0

2

BRAb)

0

BRAc)AR

B0 d)0

ABR

126. A wire of a conductor is folded to form a square loop of side L. It carries a current i and is

placed perpendicular to a uniform magnetic field B. If the shape of the loop is slowly changed

to a circular one without changing its length, the amount of work done is

a)

41

2iBL b)

+

41

2iBL c) zero d) infinity

Problems

127. Two infinitely long, thin, insulated straight wires are along the x and y axes respectively as

shown. Each wire has a current I, respectively in the positive x-direction and the positive y

direction. What is the locus of a point in this plane where the magnetic field is zero?


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128. A square loop of wire with edge a has a current i flowing through it. Find the magnetic field

at the centre of the loop.

129. An electron subjected to a potential difference V = 1kV is accelerated and moves in a uniform

magnetic field at an angle0

30= to the field B = 29mT. What is the pitch of the helical

trajectory?

130. Find the ratio of radii of paths when an electron and a proton enter to a uniform field with

same velocity and kinetic energy? [Given that 1840=

e

p

m

m]

131. A solenoid with length 40cm carries a current of 3 ampere. It has 500 turns. A thin coil

having with turns of wire and of radius 0.01m carries a current of 0.4 ampere. Find the torque

to hold the coil in the middle of the solenoid with its axis normal to the axis of the solenoid

132. A solenoid of length 40cm and diameter 60cm consists of a single layer of 1000 turns carries

a current of 5.0 x 10-3

ampere. Find the magnetic field on the axis at the middle and at the

ends of the solenoid. (Given: )/1047

0 mASV =


133. The magnetic moment of the current carrying loop shown in the figure is equal to

a)( )

2

22

abbI +b) Iab c)

( )2

2baaI +

d) None of the above

134. An equilateral triangular loop ADC of side l carries a current i in the directions shown in

figure. The loop is kept in a uniform horizontal magnetic field

B as shown in figure. Net

force on the loop is

a) Zero b) Bi/3

2

c) Bi/3

2perpendicular to paper inwards d) Bi/3 perpendicular to paper outwards


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135. A conducting loop carrying a current I is placed in a uniform magnetic field pointing into the

plane of the paper as shown. The loop will have a tendency to

a) contract b) expand c) move towards positive x-axis d) move towards negative x-

axis

136. If two point charges q of sufficiently large masses move parallel to one another with the same

non-relativistic velocity

v (non relativistic means that their velocities are very small

compared with the velocity of light in vacuum) as shown in the figure, the ratio of the

magnitude of the magnetic and electric interaction forces between charges is

a)c

vb)v

cc)

2

2

v

cd)

2

2

c

v

137. A proton traveling at 150

with respect to the direction of the magnetic field of strength 2.6 mT

experiences a magnetic force of 6.5 x 10-17

N. The kinetic energy of the proton is

a) 0.65 x 10-16

J b) 5.86 x 10-19

J d) 0.58 x 10-17

J d) 5.86 x 10-16

J

138. Consider the following

A) The magnetic force is always perpendicular to the velocity of the particle.

B) A current loop in a magnetic field behaves like small magnet.a)both (A) and (B) are true b) both (A) and (B) are false

c) only (A) is true d) only (B) is true

139. The magnetism of a magnet is reduced by hitting it with a hammer because

a) of the loss of electrons in the magnet

b) of the breaking of the molecular bonds if any

c) of the ionization of the material of which the magnet is made

d) of the misalignment of the domains and heating (due to the stroke)


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140. Two charged particles are projected into a region where the magnetic field is perpendicular to

their velocities. If the charges are deflected in the opposite directions, it follows that,

a) the charges are of opposite signs b) the charges are of same signs

c) one charged particle has more mass than the other.d) one charged particle has larger charge magnitude than the other.

141. A charged particle of charge q and mass m moves in a circle of radius r with an angular

velocity . The magnetic moment associated with the charge is

a)3

2rq

b)2

2rq

c)2

2rq

d)3

2rq

142. In question number 9, the angular momentum of the particle in terms of the magnetic moment

of the charged particle is

a) mq

L

=

2b) m

qL

=

2

c) m

qL

=

2

3d) m

qL

=

143. A coil having N turns is wound tightly in the form of spiral with inner radium r1 and outer

radius r2. When a current I is passed through the coil the magnetic induction at the center

is

a)( ) 1

2

12

0 ln2 r

r

rr

NI

b)

( )21

0

2 rr

NI

c)

( )21

0

rr

NI

+

d)

( )21

0

2 rr

NI

+

144. A current I flows through a circular arc of wire which subtends an angle of3

at the centre. If

the radius of the circular arc is R, the magnetic induction B at the centre is

a)

R

I

4

0 b)

R

I

12

0 c)

r

I

2

3 0 d)

r

I

6

0

145. When a long current carrying wire is bent into a circle of one turn the magnetic field produced

at the centre is B. If the same wire is bent into a loop of n turns, the magnetic field at the

centre is

a)n

Bb) nB c) n

2B d)

2n

B


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146. The magnetic field due to a current carrying circular coil of radius 6cm at point on its axis

distant 8cm form its centre is 18 T . What is the magnetic field at its centre

a) 83 T b) 8.3 T c) 83 mT d) 8.3 mT

147. The magnetic field at the centre of a current carrying circular coil of radius 3cm is 10 T .

What is the magnetic field, at a point on its axis at a distance of 4cm form its centre?

a) 2.16 mT b) 2 c) 2.16 T d) 2 T

148. A short bar magnet placed such that its axis makes 300

with the horizontal experiences a

torque of 0.016N m is an external field of 800G. The magnetic moment of the magnet is

a) 0.40 A m2

b) 0.30 A m2

c) 0.20 A m2

d) 0.25 A m2

149. The magnitude of the equatorial field due to a bar magnet of length 5cm at a distance of 50cm

from its mid-point is (The magnetic moment of the bar magnet is 0.40 A m2).

a) 3.2 x 10-3

G b) 4.2 x 10-3

G c) 2.2 x 10-3

G d) 1.2 x 10-3

G

150. Given the earths magnetic field at the equator approximately as 0.4G. The earths dipole

moment is. (Radius of earth = 6.4 x 106m).

a) 2.04 x 1023

Am2

b) 3.04 x 1023

Am2

c) 4.04 x 1023

Am2

d) 1.04 x 1023

Am2

151. The horizontal component of the earths magnetic field is 0.26 G (in the magnetic meridian of

a certain place) the dip angle there is 600. The magnetic field of the earth in this location is

a) 0.42 G b) 0.52 G c) 0.32 G d) 0.45 G

152. The magnetic moment of the system shown in figure will be

a) ma3 b) ma c) 2 ma d) None of these

153. Two short magnets of magnetic moments 2 Am2

and 5 Am2

are placed along two lines drawn

at right angle to each other on the sheet of paper as shown in the figure. The net magnetic

field at the point of intersection of their axes is


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a) 2.15 x 10-5

T b) 215 x 10-5

T c) 2.15 x 10-3

T d) 21.5 x 10-5

T

154. A dip needle oscillating in a vertical plane makes 40 oscillations per minute in a magnetic

meridian and 30 oscillations per minute in a vertical plane at right angle to the magnetic

meridian. The angle of dip is

a) ( )5625.0sin 1= b) ( )325.0sin 1= c) ( )425.0sin 1= d)

( )235.0sin 1=

155. The force between two short bar magnets with magnetic moments M1 and M2 whose centre

are r meters apart is 8.0N when their axes are in the same line. If the separation is increased to

2r, then force between them is reduced to

a) 4.0 N b) 2.0 N c) 1.0 N d) 0.5 N

156. A bar magnet suspended by a horses hair lies in the magnetic meridian where there is notwist in the hair. On turning the upper end of the hair through 150

0, the magnet is deflected

through 300

from the meridian. Then the angle through which upper end of the hair has to be

twisted to deflect the magnet through 900

form the meridian is

a) 4500

b) 3600

c) 3300

d) 1500

157. A solenoid of 500 turns per meter is carrying a current of 3 A. It has a core made of iron with

relative permeability of 5000. The magnitude of intensity of magnetization is

a) 5 x 106 A m2 b) 6 x 106 A m2 c) 7.5 x 106 A m2 d) 5.5 x 106 A m2

158. The magnetic induction at P, for the arrangement shown in the figure, when two similar short

magnets of magnetic moment are joined at the middle so that they are mutually

perpendicular, will be


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a)3

0

4

3

d

b)

3

0

4

2

d

c)

3

0

4

5

d

d)

3

0

4

2

d

159. The B H curves S1 and S2 in the adjoining figure are associated with

a) diamagnetic and paramagnetic substances respectively

b) paramagnetic and ferromagnetic substances respectively

c) soft iron and steel respectively

d) steel and soft iron respectively

160. A magnet is suspended in such a way that it oscillates in a horizontal plane. It makes 20

oscillations per minute at a place where dip angle is 300

and 15 oscillations per minute at a

place where dip angle is 600. Ratio of the earths total magnetic fields at the two places is

a) 8:33 b) 39:16 c) 4 : 9 d) 3:32

161. A thin rectangular magnet suspended freely has a period of oscillation T. Now it is broken

into two halves. One piece is made to oscillate freely in the same field. If new period of

oscillation is T, thenT

T'is

a)2

1b) 2 c)

4

1d)

22

1

162. The magnetic lines of force inside a bar magnet

a) do not exist b) depend upon area of cross section of

the magnet

c) are form S pole to N pole of the magnet d) are from N pole to S pole of the magnet

163. Curie temperature is the temperature above which

a) a paramagnetic material becomes diamagnetic

b) a ferromagnetic material becomes diamagnetic

c) a paramagnetic material becomes ferromagnetic


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d) a ferromagnetic material becomes paramagnetic

164. Points A and B are situated along the extended axis of a 2cm long bar magnet at distances x

and 2x respectively form the pole nearer to the points. The ratio of magnetic fields at A and Bwill be

a) 4 : 1 exactly b) 4 : 1 approximately c) 8 : 1 exactly d) 8 : 1 approximately

165. A bar magnet is undergoing oscillation in earths magnetic field with a period T. If its mass is

quadrupled, then

a) motion remain simple harmonic with time period2

T=

b) motion remain simple harmonic with time period = 2 T

c) motion remain simple harmonic with time period = 4 T

d) motion remain simple harmonic and period remains nearly constant

166. Cosmic rays are supposed to be highly energetic protons hitting the earth due to earths

magnetic field. They should get deflected to

a) north b) south c) east d) west

167. A toroidal solenoid has 3000 tuns and a mean radius of 10cm. It has a soft iron core of

relative permeability 2000. The magnitude of the magnetic field in the core when a current of

1 A is passed through the solenoid is

a) 0.012 T b) 0.12 T c) 1.2 T d) 12 T

168. A magnetic needle vibrates in a vertical plane parallel to the magnetic meridian about the

horizontal axis with a frequency n. If the plane of oscillation is turned about a vertical axis by

900, the frequency of oscillation will be

a) n b) zero c) less than n d) greater than n

169. Consider the following statement.


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A) Diamagnetism occurs in all materials

B) Diamagnetism is the result of induced magnetic dipole moments

Then,

a) only (A) is rue b) only (B) is truec) both (A) and (B) are true d) both (A) and (B) are false

170. Consider the following

A) Para magnetism is the result of partial alignment of permanent dipole moments.

B) Hysteresis is associated with a loss in electromagnetic energy

Then,

a) only (A) is true b) only (B) is true

c) both (A) and (B) are true d) both (A) and (B) are false

171. Two identical bar magnets each of dipole moment and length l are placed perpendicular to

each other as shown. The magnetic dipole moment of the combination is

a) 2 b) 2 c)2

d)

2

172. A magnetic dipole is under the effect of two magnetic fields inclined at 750

to each other. One

of the fields has a magnitude of 1.5 x 10-2

T. The magnet comes to stable position at angle of

300

with the direction of above field. The magnitude of the other field is

a) T21022

15 b) T210225.1 c) T

210215 d) T2

105.1


173. An artificial satellite with a metal surface has an orbit above the equator. Will the earths

magnetism induce a current in it?

174. A copper ring and a wooden ring of same dimension are placed so that there is same magnetic

flux through each. Is induced current same in each?


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175. A copper ring is suspended in a vertical plane by a thread. A steel bar is passed through the

ring in horizontal direction and then a magnet is similarly passed through will the motion of

the bar and the magnet affect the position of the ring?

Multiple Choice Questions with correct alternative

176. A uniform magnetic field B exists at right angles to the plane of a square frame made of silver

wire. The wire has a diameter D and a total length L. The magnetic field is increasing with

time. Find the current induced in the frame. ( is the specific resistance)

a)

64

2LD

b)dt

dBLD

64

2

c)dt

dBLD

2

d)

BLD

2

177. A circular loop of copper wire of radius a is rotated about its diameter at a constant angular

velocity in a uniform magnetic field B perpendicular to the axis of rotation. The induced

current is zero when has the value given by ( being the angle between

B and normal to

the area vector of the loop)

a) 2 b)2

c) 45

0d) 60

0

178. Figure shows a conducting loop placed in a time varying uniform magnetic field B =

5t2+3t+3. An ideal battery with emf 2V is connected to the loop. The resistance of the loop is

5 . Find the approximate magnitude of the induced emf along the loop by the magnetic field

at t = 10s (Radius of the circular part is 0.3m)


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a) 4.6 V b) 14.6 V c) 10.6 V d) 12.6 V

179. A uniformly wound long solenoid ahs an inductance L and resistance R. It is broken into two

equal parts and the two parts are joined in parallel to a cell of emf E. The time constant of the

circuit is

a) R

L2

b) R

L

c) R

L

2 d) LR

180. The two rails of railway track, insulated form each other and ground are connected to a milli

voltmeter. What is the reading of the voltmeter when a train travels at a speed of 180km h-1

along the track? Given vertical component of earths magnetic field 0.2 x 10-4

T and the

separation between the rails 1m?

a) 1 mV b) 3 mV c) 6 mV d) 9 mV

181. A current I is flowing through a coil. The emf induced in it is 0.2 V when the current is

changed from 5A to -5A in 0.2s. The self inductance of the coil is

a) 4 mH b) 8 mH c) 10 mH d) 12 mH

182. A rectangular coil of 100 turns and dimensions 0.1m x 0.05m is placed perpendicular to a

magnetic field of 0.1T. The induced emf when the field drops by 0.05T in 0.05s is

a) 0.5 V b) 1.0 V c) 1.5 V d) 2.0 V

183. An ideal solenoid of cross-sectional area 10-4

m2

has 500 turns per meter. At the centre of this

solenoid, another coil of 100 turns is wrapped closely around it. If the current in the solenoid

changes from 0 to 2A in 3.14ms-1

, the emf developed in the second coil is

a) 1 mV b) 2 mV c) 3 mV d) 4 mV

184. A rectangular loop of sides 8cm and 2cm is moving out of a region of uniform magnetic field

of 0.3T, directed normal to the loop. What is the emf developed across the points A and B if

the velocity of the loop is 1cm s

-1

in a direction normal to the longer side of the loop?


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a) 0.06 mV b) 0.12 mV c) 0.18 mV d) 0.24 mV

185. A rectangular loop of sides 8cm and 2cm having resistances of 1.6 is placed in a magnetic

field of 0.3 T directed normal to the loop. The magnetic field is gradually reduced at the rate

0.02 T s-1

. How much power is dissipated in the loop as heat?

a) 1.6 x 10-10 W b) 3.2 x 10-10 W c) 6.4 x 10-10 W d) 12.8 x 10-10 W

186. A motor having an armature of resistance 2 is designed to operate at 220 V mains. At full

speed, it develops a back emf of 210 V. What is the current in the armature when the motor is

running at full speed?

a) 2.5 A b) 5.0 A c) 7.5 A d) 10 A

187. An electron moves along the line PQ which lies in the same plane as a circular loop of

conducting wire, as shown in the figure. What will be the direction of the induced current, if

any, in the loop?

a) Anti-clockwise b) Clockwise c) Alternating d) No current will be induced in the

loop

188. Flux (in weber) in a closed circuit of resistances 10 varies with time t(in seconds)

according to the equation 1532

+= tt . The magnitude of the induced current in the

circuit at t = 0.25s is

a) 0.2 A b) 0.6 A c) 0.8 A d) 1.2 A

189. A coil of N turns is connected in an external magnetic field B as shown in the figure. If Q is

the total charge passing through it when it is rotated through 900

, and if R is its radius, A is

the area of the coil of the coil, then


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a)2

2

NA

QRB = b)

NA

RQB = c)

NA

RQB

5= d)

NARQeB

TI

Q

=

190. A conducting rod of length l rotates about one end with a constant angular velocity ofin an

external magnetic field B as shown. The potential difference between the ends of the rod is

a)2

2lB

b) Bl2 c)2

2lB

d)Bl2

2

191. A square frame with side a and a long straight wire carrying a current I is located in the same

plane as shown in the figure. If the frame translates to the right with a constant velocity v, the

induced emf in the frame as a function of x is


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a)( )xaxvaI

+

2

0

2

b)

( )2

3

2

0

4 xax

aI

+

c)

( )xax

aI

+2

2

0

2

d)

( )axa

aI

+

2

0

192. A bar of mass m and length l moves on two frictionless rail in the presence of the magnetic

field as shown in the figure. If the bar is given an initial velocity u, the acceleration a of the

bar is

a)m

IlBa

2

= b)m

lIBa = c)

m

lIBa

5= d)

m

lIBa

3=

193. The following graph gives the magnitude B(t) of a uniform magnetic field that exists

throughout a conducting loop and perpendicular to its plane. Rank the five regions of the

graph according to the magnitude of the emf induced in the loop. Greatest first.

a) a > b > c > d > e b) a < c < b < d < e

c) a and c will tie, b and d will tie and then e d) b first, d and e will tie and then a and c will

tie

194. A circular coil of radius 10cm and 500 turns placed on a horizontal table is turned upside

down in 0.5s. The mean emf generated in the coil is (Earths vertical field is 0.43 x 10-4

T).

a) 0.2 V b) 0.02 V c) 2.7 mV d) 2.8 V

195. An all metal aero plane flies horizontally at 600 km/hr at a place where the vertical

component of earths magnetic field is 4 x 10-5

T. If the wing span is 10m, the resulting

potential difference between the tips of the wings is


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a) V80

1b) V

20

1c) V

15

1d) V

3

20

196. Half of the core of a solenoid of area of cross section 2 x 10

-3

m

2

is made of air and the otherhalf is made iron. The length of the solenoid is 2m and the total number of urns in the coil

1000. The self inductance of the coil is (Assume r for iron is 500)

a) 0.29 H b) 0.315 H c) 0.528 H d) 0.625 H

197. The figure shows a circular loop of wire of area 3m2

immersed in a magnetic field given by

the graph. The resistance of the wire is 9 . The magnitude and direction of the current in the

loop at t = 0.5s is

a) 1 mA clockwise b) 1 mA anticlockwise c) 0.5 mA clockwise d) 0.5 mA

anticlockwise

198. An air core solenoid with 90 turns is 10cm long and has a diameter ofx

4. How much

energy is stored in its magnetic field when it carries a current of 0.8 A?

a) 24 mJ b) 0.13 J c) 0.05 J d) 0.002 J

199. A magnetic flux through a metal ring varies with time t according to the relation

( )233 btat = weber with a = 2 s-3 and b = 6 s-2. The resistance of the ring is 3 . The

maximum current induced in the ring during the interval from t = 0s to t = 2s is

a) 2 A b) 3 A c) 5 A d) 6 A

200. The blades of a helicopter 3m log, rotate at 2 rev/s. If the Earths vertical component of the

magnetic field has a magnitude of 50 T , the emf induced in the blades tip form the center

hub as shown in the figure is


40/55

a) 8 mV b) 4 mV c) 2.83 mV d) 1 mV

Problems

201. A conducting rod of length l is rotated at an angular velocity about one end in a uniform

magnetic field acting normal to the plane of rotation. Obtain an expression for the inducede.m.f. developed in the rod.

202. A copper wire of length 20cm and area of cross section 1 mm2

is bent into a square loop and

kept in a magnetic field of 0.4T acting normal to its plane. Find the total amount of charge

that passes through the loop when the magnetic field disappears (Given specific resistance of

copper = 1.7 x 10-8

m )

203. An infinitely long straight wire carries a current I = 10A. Another metallic rod PQ kept

perpendicular to XY moves with a uniform velocity of 10ms-1

of the near end of the rod is at a

distance of 1 mm and the far end at a distance of 1m form XY, then what is the e.m.f. induced

in PQ.


204. In a L-R circuit, the current increases with a time constant . The emf across the coil at t is

a)

tb) ( )/1 teE c) /tEe d) /2tEe

205. An L-R circuit is in its growth mode. After what time will the potential difference across the

coil be equal to that across the resistance?

a) 2ln b) c) ( )2ln1

d) 2ln/


41/55

206. A steady current is flowing in a coil. When the coil is short circuited, the current in it decrease

K times in a time t0. What is the time constant of the circuit?

a) Kt ln0 b)K

t

ln

0 c)n

t0 d)

1

0

n

t

207. Two circular loops are placed with their centres separated by a distance l. The angle between

their area vectors is . The value of for obtaining the maximum mutual inductance

between the coils is

a) Zero b) 450

c) 900

d) 1200

208. If L, C and R represent the inductance, capacitance and resistance then (R/L) has dimensions

of

a) Frequency b) Time c) emf d) Ampere

209. In the above problem, which of the following has dimension of time?

a) RC b)L

Rc)RC

1d)

C

LR

210. In an L-R cicuit, the switch is closed at t = 0. Which of the following graph correctly

represents Eind vs t behavior?

A) B) C) D)

a) D b) C c) B d) A

211. A solenoid has an inductance of 53 mH and a resistance of 0.37 . If it is connected to a

battery of constant emf, long will the current take to reach 50% of its equilibrium value?

a) 0.5 s b) 0.3 s c) 0.2 s d) 0.1 s

212. In the above problem, if the emf of the battery is 12V, how much energy is stored in the

magnetic field after the current has built up to its equilibrium value?

a) 27.9 J b) 31 J c) 39 J d) 41 J


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213. A 4H inductor is placed in series with a 12.8 resistor and an emf of 3.24V is suddenly

applied across the LR combination at t = 0. At 0.313s what is the rate P at which energy is

being delivered by the battery?

a) 516 mW b) 600 mW c) 800 mW d) 1 W

214. In the above problem, at t = 0.313s at what rate is thermal energy appearing in the resistor?

a) Zero b) 323 mW c) 623 mW d) 1 W

215. In the above problem at what rate is energy stored in the magnetic field at 0.313s?

a) 193 mW b) 391 mW c) 516 mW d) 1 W

216. Two coils of different radii are made of copper wires of same length. The ratio of number of

turns in the two coils is 1 : 4. Then the ratio of their self inductances is

a)4

1b)

16

1c)

2

1d)

32

1

217. Two inductors L1 and L2 are connected in parallel. A time varying current flows as shown in

the figure. Then at any instant t, the ratio of currents

2

1

i

iis

a)

21

2

LL

L

+b)

21

1

LL

L

+c)

1

2

L

Ld)

2

1

L

L

218. In the circuit shown the switch S is closed at a time t = 0. The charge which passes through

the battery in one time constant is


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a) 1 mH b) 10 H c) 10 H d) 10 mH

219. When the radius of a coil is doubled without changing the length of the wire, its self

inductance is

a) doubled b)halved c) tripled d) quadrupled

220. Two circular coils can be arranged in three following different ways. Their mutual inductance

will be

1) 2) 3)

a) maximum in situation (1) b) maximum in situation (2)

c) maximum in situation (3) d) same in all situations

221. A uniformly wound solenoid of self inductance 20 mH and resistance 8 is broken into two

identical solenoids, which are then connected in parallel across a 6V battery. The time

constant of the parallel combination is

a) 2.5 ms b) 5 ms c) 2.5 s d) 5 s

222. A circuit has a self inductance coil of self inductance 10 H and carries a current of 1 A. To

prevent sparking when the circuit is switched off, a capacitor which can withstand 1000 V is

connect parallel to the switch. The minimum value of the capacitance that is to be used is

a) 0.1 F b) 0.1 Fm c) 0.1 Fp d) 10 F

223. In the circuit shown in the figure, the current shown by the ammeter is I1 just after closing the

switch and I2 long after closing the switch. Then the ratio

2

1

I

Iis

a)4

3b) 1 c)

3

4d)

2

3


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224. Two concentric coplanar coils of radius R and r (R > r) contain the same number of turns.

Then the mutual inductance between the two coils is proportional to

a)R

rb)r

Rc)R

r2

d)r

R2

225. Two self inductance coil are arranged so close to one another that the flux produced by one

coil is completely connected with the other. What is the mutual inductance between the two

coils if the sum and difference of their self inductance is respectively 26 mH and 10 mH?

a) 2.6 mH b) 12 mH c) 26 mH d) 10 mH

226. An inductor with self inductance L resistance R and time constant is connected in series

with a battery of e.m.f. E and a switch. When the switch is closed the voltage across the

inductor at any instant t is given by

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

227. Two coils have self inductances L1 and L2 and are supplied with same power. At some instant

the current in the two coil is found to be increasing at the same rate. If i1 and i2 are the

instantaneous currents and e1 and e2 the instantaneous emfs at this instant, then

a)2

1

2

1

L

L

i

i= b)

2

1

2

1

L

L

e

e= c)

2

1

2

1

L

L

e

e= ;

2

1

2

1

L

L

i

i= d)

1

2

2

1

L

L

e

e= ;

1

2

2

1

L

L

i

i=

228. A transformer is used to step up an alternating emf of 220 V to 4.4 kV in order to transmit

6.6kW of power. If the primary coil has 100 turns, what is the number of turns in the

secondary?

a) 20 b) 200 c) 2000 d) 20000

229. A circuit has a self inductance of 1 henry and carries a current of 2A. To prevent sparking

when the circuit is broken, a capacitor which can withstand 400 volts is used. The least

capacitance of the capacitor connected across the switch must be equal to


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a) 12.5 F b) 25 F c) 50 F d) 100 F

230. A circuit containing a resistor, an inductor and a battery source are connected as shown in the

figure to the right. Which one of the graphs shown in following figure represents the variation

of current I with time t?

a) b) c) d)

231. An inductive coil has a resistance of 100 . When an signal of frequency 1000 Hz is fed to

the coil, the applied voltage leads the current by 450. What is the inductance of the coil?

a) 10 mH b) 12 mH c) 16 mH d) 20 mH

232. Two circuits 1 and 2 are connected to identical dc source each of emf 12V. Circuit 1 has a srlf

inductance L1= 10H and circuit 2 has a self inductance L2 = 10 mH. The total resistance of

each circuit is 48 . The ratio of steady current in circuits 1 and 2 is

a) 1000 b) 100 c) 10 d) 1

233. In Q.5, what is the ratio of the times required for the currents in circuits in circuits 1 and 2 to

reach

e

11 of their steady state value?

a) 1000 b) 100 c) 10 d) 1

234. In Q.231, what is the ratio of energy consumed in circuit 1 and 2 build up the current steady

state value?

a) 1000 b) 100 c) 10 d) 1

235. A radio tuner has a frequency range from 500 kHz to 5 MHz. If its LC circuit has a effective

inductance of 400 H , what is the range of its variable capacitor? Take 102 = .


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a) 2.5 pF to 250 pF b) 5.0 pF to 500 pF c) 7.5 pF to 750 pF d) 10 pF to

1000 pF

236. L, C and R, respectively represent inductance, capacitance and resistance. Which one of thefollowing combinations has the dimensions of frequency?

a)RC

1b)LC

1c)R

Ld)L

C

237. A capacitor of capacitance 2 F is charged to a potential difference of 12V. The charging

battery is then removed and the capacitor is connected across an inductor of self inductance

0.6 mH. The current in the circuit at a time when the potential difference across the capacitor

6V is

a) 0.3 A b) 0.6 A c) 0.9 A d) 1.2 A

238. An ac generator consists of 8 turns of wire each of area 0.09 m2

and total resistance 12 . If

the loop rotates in a external magnetic field of 0.5 T at a constant frequency of 50 Hz, the

induced emf and current are respectively

a) v = (125 V) sin 277t and i = (20A) sin 277t b) v = (136 V) sin 377t and i = (40A) sin

377t

c) v = (113 V) sin 314t and i = (9.42A) sin 314t d) v = (20 V) sin 377t and i = (136A) sin

377t

239. For an RL circuit, inductance L has a value of 3H, the resistance 8 and the battery emf

36V. The ratio of the voltage across the inductor to that across the resistor when the current is

2A is

a)5

4b)

4

5c)

25

16d)

16

25

240. A rectangular coil of N loops of a conducting wire of length L and w lies along the sides of a

current carrying wire which carries a current of ( )+= tII sinmax as shown in the figure.

The induced emf in the loop is


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a) ( )

+

= t

h

wLNIe sinln

4 2max0 b)

( )

+

+

= t

h

wLNIe cos1ln

2 2max0

c) ( ) +

= t

hwLINe 22max

2

0 sinln4

d) max2

22

0

4ILNe

=

241. If cmwhNsAI 5,100,200,501

max =====

and L = 20cm, the maximum power

generated in the coil in Question No. 47 is

a) 2.82 W b) 2.52 W c) 2.11 W d) 1.38 W

242. The circuit shown in the following circuit is mainly of

a) Inductive load b) Capacitive load

c) Resistive load d) inductive and capacitive loads

243. An RLC circuit has an impendence Z and resistance R. if is the constant then

a)R

RZ22

tan

= b)R

RZ22

tan+

=

c)R

RZ=tan d)

Z

R=tan

244. In an RLC circuit, Vm = 10V, R = 10 , L = 1 H and C = 1 F . Then the amplitude of the

voltage across the inductor is

a) Greater than 10 V always b) Less than 10 V always


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c) Equal to 10V always d) Greater than 10 V at some point

245. An ac generator has an emf

=

4

sinmax

tVv and current

=

4

3sinmax

tIi .

The time t at which the emf and current in the generator become maximum are respectively

a)

4

2

4

3== tandt b)

3

10

4

3== tandt

c)

5

8

3

2== tandt d)

4

5

4

2== tandt

246. The resonant frequency in the circuit shown below is

a) Hz2122 b) Hz

577c) Hz

2

623

d) Hz

3

100

247. A coil of inductance 88 mH and a capacitance of 2 F are in series with an alternating emf of

frequency 1 kHz. If the phase constant between the applied voltage and current is 750, the

resistance in the coil is

a) 86 b) 300 c) 126 d) 800

248. A transformer has 500 primary turns and 10 secondary turns. If VP = 220V, and the secondary

has a load of 15 across it, the secondary current is

a)A28

15b)

A79

35c)

A38

82d)

A75

22

249. A coil has a resistance of 48 . At a frequency of 80 Hz, its voltage leads the current in it by

600. The inductance of the coil is

a) 25 mH b) 80 mH c) 165 mH d) 188 mH

250. The current in a certain circuit varies as shown in the following graph. The average current in

the circuit is


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a) Zero b) I0 c)2

0I d)02I

251. In Q.249, the rms current in the circuit is

a)2

0I b)3

0I c)2

0I d)5

0I

252. A series RLC circuit has a band width of . If R, L and C represent the resistance,

inductance and capacitance in the circuit, the impedance is approximately

a)

+=

22 L

RZ b)( )

2

2

2

LRZ

+=

c) ( )222 4 += LRZ d) ( ) 222 LRZ +=

Problems

253. A coil of resistance 50 , an inductance of 10H and a capacitor of 5 F are connected in

series with an AC source of 200V, 50 Hz. Calculate

a) The impedance of the circuit

b) The phase difference between current voltagw

c) Potential difference across the inductor, capacitor and resistor

254. An LCR circuit has L = 10 mH, R = 5 and C = 1 F connected in series with an AC

source of emf E = 10sin t. Calculate the current amplitude at a frequency that is 20% lower

than the resonant frequency.

255. A 24V, 10w lamp is to be put on AC mains of 220V, Hz. Calculate the

(i) inductance and (ii) capacitance (iii) resistance required to be put in series with the

lamp.


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256. A circuit draws a power of 500W form an AC source of 220V, 50Hz. The power factor of the

circuit is 0.6 and the current lags in phase behind the potential difference. To make the power

factor unity, what capacitance has be connected in the circuit?


257. An electron enters a region of uniform perpendicular

E and

B fields. It is observed that the

velocity

v of the electron is unaffected. A possible explanation is

a)

v is parallel to

E and has magnitude E/B

b)

v is parallel to

B

c)

v is perpendicular to both

E and

B and has magnitude B/E

d)

v is perpendicular to both

E and

B and has magnitude E/B

258. The current is from left to right in the conductor shown. The magnetic field is into the page

and point S is at a higher potential than point T. The charge carries are

a) Positive b) Negative c) Neutral d) Absent

259. A square loop of current-carrying wire with edge length a is in the xy plane, the origin being

at its centre, along which of the following lines can a charge move without experiencing a

magnetic force?

a)2

,0a

yx == b)2

,2

ay

ax == c) 0,

2== y

ax d) 0,0 == yx

260. The magnetic field B inside a long ideal solenoid is independent of

a) The current b) The core material

c) The spacing of the windings d) The cross-sectional


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261. A rod of length l rotates about its perpendicular bisector with a uniform angular velocity w in

uniform magnetic field B parallel to the axis of rotation. The potential difference between its

end and its centre is

a) Zero b) 2

8

1wBl c)

2Bwl d)

2

222lwB

262. A long straight wire is in the plane of a rectangular conducting loop. The straight wire carries

a constant current I, as shown. While the wire is being moved towards the rectangle thecurrent in the rectangle is

a) Zero b) Clockwise c) Counter clockwise

d) Clockwise in the left side and counter clockwise in the right side

263. The figure shows a bar moving to the right on two conducting rails. To have an induced

current i in the direction indicated, a constant magnetic field in region A should be in what

direction?

a) Right b) Left c) Into the page d) Out of the page

264. A rod of length l is moving at a velocity v making an angle with its length in a uniform

magnetic field B as shown. The figure representing the induced emf (with polarity) by an

equivalent battery is


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a) b) c)

265. The flux of the magnetic field through the loop shown increases as ( ) 32 1076 += tt . The

magnitude of the emf induced in the loop at t = 2 see is

a) 31 mV b) 21 mV c) 16 mV d) 9 mV

266. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero.

If the period of the resulting oscillations, the next time, after t = 0 the current is zero. If T is

the period of the resulting oscillations, the next time, after t = 0 that the current is maximum is

a) T b)4

Tc)

2

Td) T

267. A proton is fired form origin with velocity^

0

^

0 kvjvv +=

in a uniform magnetic field

^

0 jBB =

. In the subsequent motion of the proton

a) Its z co-ordinate can never be negative

b) Its x co-ordinate can never be positive

c) Its x and z co-ordinates cannot be zero at the same time

d) Its y co-ordinate will be proportional to its time of flight

268. Velocity and acceleration vector of a charged particle moving in a magnetic field at some

instant are

^^

43 jiv +=

and jxia +=

^

2 . Select the correct alternative(s).

a) x = - 15 b) x = 3


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c) magnetic field is along z-direction d) kinetic energy of the particle is constant

269. A conducting rod AB moves with a uniform velocity v in uniform magnetic field as shown.

a) The rod becomes electrically charged b) The rod continues to be neutral

c) The end a becomes negatively charged d) The end B becomes negatively

charged

270. An observer A and a charge Q are fixed in a stationary frame F1. An observer B is fixed in a

frame F2, which is moving with respect to F1.

a) Both A and B will observe electric fields

b) Both A and B will observe magnetic fields

c) Neither A nor B will observe magnetic field

d) B will observe a magnetic field, but A will not

271. A square coil AECD of side 0.1m is placed in a magnetic field B = 2t2. Here t is in seconds

and B is in Tesla. The magnetic field is into the paper. At time t = 2s, induced electric field in

DC is

a) 0.05 V/m b) along DC c) along CD d) 0.2 V/m


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Passage Questions

A square loop of are 4m2

is perpendicular to a uniform magnetic field with half the are of the

loop outside the field as shown. The loop contains a 20V ideal battery. If the magnetic field

varies with time according to B = 0.04 0.87 t

272. The magnetic flux through the circuit is

a) 2 B b) B c)2B d)

4B

273. The induced emf in the circuit is

a) 0.8 V b) 1.74 V c) 2.3 V d) 3.1 V

274. The total emf in the circuit is

a) 16.3 V b) 19.4 V c) 21.7 V d) 24.0 V

Match the following Type Questions

275. Column-I Column-II

i) Torque + magnetic field p) Magnetic field

ii) Induced emf q) Lenzs Law

iii) Result opposing the cause r) Eddy currents

iv) Moving conducting plane s) current

276. Column-I Column-II

i) Induced electric field p) Cross product

ii)

+

dsE q) Weber / m2

iii) Magnetic force r) Capacitor

iv) Tesla s) Charging magnetic flux

Numerical Problems


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277. A 1 mH inductor and 1 F capacitor are connected in series. The current in the circuit is

I = 20t. The capacitor is initially uncharged. Determine (a) The voltage across the inductor

and (b) The voltage across the capacitor.

278. Two wires A1B1 and A2B2 are made to slide on the rails with the same 5 cm/s. Find the

current in the 19 resistor if both the wires more toward right. The resistance of each is 2 .

iit (mains + advance) physics module 2013

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