APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems. We started to develop ways to enhance students IQ. We started to leave an indelible mark on the students who have undergone APEX training. That is why APEX INSTITUTE is very well known of its quality of education and the dedication towards its target.

1. IIT Mains 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) 10-6T towards east
5.
b) 10-6T towards west
c) 10-5T towards north
d) 10-5T towards south
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)
6.
2
0 I
L
b) 2 2
0 I
L
c)
1 0 I
2 L
d)
1 0 I
2 2 L
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)
7.
0
I 1  I 2 
2d
b)
0
I 1  I 2 
2d
c)
0
2
I12  I 2
2d
d)
 0 I1 I 2
2d I1  I 2
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
a)
3 0 I
4d
b)
3 0 I
2d
c)
9 0 I
d
d) zero
1

2. 8.
O is a point on the perpendicular bisector of a straight wire AB of length L at a distance
L
. The magnetic field
2
at O due to the current I flowing in the wire is
a)
0 I
2 2 4 L
1
b)
2
0 I
4 L
c) 2 2
0  I 
 
4  L 
d) 2
0 I
4 L
^
9.
A uniform conducting wire is bent to form an equilateral triangle A B C of side L. A current I enters at A
leaves at C. What is the magnetic induction at the centroid O?
a) 2 3
10.
0 I
4 L
b)
0 I
4 L
c)
3
0 I
4 L
d) Zero
The figure shows two long straight wires passing each other perpendicularly without touching. The magnetic
field is zero
a) in quadrant 1
11.
b) in quadrant 2
c) in quadrant 3 d) at the point of intersection
A current I flows along the length of an infinitely long, straight, thin walled pipe. Then, the magnetic field,
a) At all points inside the pipe is the same but not zero
b) At any point inside the pipe is zero
2

3. 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
 I1 
x

 I2 
a) y  

13.
 I2 
x

 I1 
b) y  

 I1  I 2 
x

 I2  I2 
c) y  

 I1  I 2 
x

 I2  I2 
d) y  

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 magnetic field at the centre of the cube is
a) Zero b)
14.
 0  24  i


n  3  l


c)
12  0 i
3 n l
d)
6 0 i
3 n l
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.
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)
2B
d) 2B
3

4. 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)
 0i
4 a
b)
3 0 i
c)
4 2 a
5 0 i
8 a
d)
3 0 i
2 a

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
 0 i y i  x j 


^
a)
18.


2 x  y
2

2

^
^
 0 i x i  y j 


^
^
 0 i x i  y j 


^
b)


2 x  y
2

2

c)


2 x  y
2

2

^
^
 0 i x i  y j 


d)


2 x  y
2

2

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)
19.
b)
K
4
c)
K
2
d) 2 K
In the set up shown below, the magnitude of the magnetic field at C is
a)
20.
K
8
 0i
8R
b)
 0i
4R
c)
 0i
2R
d)
 0i
R
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)
 0i
2R
c)
 0
2i
d) Zero
4

5. 
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)
 0i
4R
c)
 0i
2R
d)
 0i
R

22.
In the above problem, B produced at C by the semicircular segment is
a) Zero b)
23.
 0i
4R
c)
 0i
2R
d)
 0i
R
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
24.
0 I
4R
c)
0 I
4R
d)
0 I
  1
4R
The magnetic field at the point O due to the current flowing in the conductor shown in the figure is
a)
26.
d) 1 mT
The magnetic field at the point O due to current I flowing in the conductor shown in the figure is
a) Zero b)
25.
c) 5 mT
 0 I  r1  r2 


4  r1r2 


b)
 0 I  r1  r2 


4  r1r2 


c)
0 I
4R1  R2 
d)
0 I
4R1  R2 
The magnetic field at O due to the current flowing in the conductor shown in the figure is
5

6. a)
27.
 0 I  r1  r2 


4  r1r2 


b)
 0 I  r1  r2 


4  r1r2 


c)
0 I
4r1  r2 
d)
0 I
4r1  r2 
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
28.
b) 1 : 3
c) 1 : 2
d) 1 : 1
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
29.
b) 4
c)
1
4
d)
1
2
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)
I1 r2

I 2 r1
b)
I1 I1

r1 r2
c) I1r1  I 2 r2
d)
I 2 r1

I1 r2
6

7. 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)
31.
b)
c)
d)
A current I flows through a circular arc of wire which subtends an angle of

at the centre. If the radius of the
3
circular arc is R, the magnetic induction B at the centre is
a)
32.
0 I
4 R
b)
0 I
12 R
c)
3 0 I
2 r
d)
 0 I
6r
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 be
a) B
33.
b) 2 B
c) 3 B
d) 4B
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)
1
2
d) 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-
. The strength of the magnetic field is 0.2 T. Find the force on the  -particle and its acceleration.
1
7

8. 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 10-4T.
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 is
38.
2 0 I
.
a
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?
39.
An electron (mass 0.90 x 10-30kg), 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 10-27kg) were to move in a circle of the same radius in the same
magnetic field, what is its speed?
Conceptual Questions
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
8

9. 
46.
^
A particle of charge q and mass m is released form origin with a velocity v  v0 i in a uniform magnetic field


B0 along the  k direction. If the particle passes through P(o, y, o), then the value of y is
a)
47.
2 m v0
Bq
b)
Bq
2 m v0
c)
m v0
Bq
d)
Bq v0
m
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
a) mAvA < mBvB
48.
b) mAvA > mBvB
c) mA < mB and vA < vB
d) mA = mB and mA = vA
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 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 the particle can just enter the region x > b is
a)
49.
qb B
m
b)
q b  a  B
m
c)
qaB
m
d)
q b  a  B
2m
A particle with a q/m =  is shot with a speed v towards a wall at distance d, perpendicular to the wall. What

is the minimum B that must exist in this region for the particle not to hit the wall?
a)
50.
v
d
b)
2v
d
c)
v
2 d
d)
v
4 d
Protons moving with different speeds enter a region of a uniform magnetic field in a direction at right angles to
the field. They will move along circular paths
a) Of the same radius
b) With larger radii for the faster protons
c) With smaller radii for the faster protons
d) either (2) or (3) depending on the magnitude of the magnetic field
51.
In the previous question, time periods of rotation (T) will be
9

10. a) The same for all the protons
c) Smaller for faster protons
52.
b) Greater for faster protons
d) Either (2) and (3) depending on the magnitude of B
A charged particle entering a magnetic field from outside in a direction perpendicular to the field,
a) Can never complete one rotation inside the field
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) R  R p  Rd
54.
b) R  Rd  R p
c) R  Rd  R p
d) R p  Rd  R
A neutral atom which is at rest at the origin emits an electron in the Z direction. The product atom 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 will
a) 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)
57.
v
4
b)
v
2
c) v
d) 2 v
The cyclotron frequency of an electron moving in a uniform magnetic field 0.02 T is
10

11. a) 5.6 x 108 Hz
58.
b) 6.6 x 108 Hz
c) 6.6 x 108 Hz
d) 7.6 x 108 Hz
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
59.
b) 16.2
c) 16.9
d) 17.7
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)
60.
P
2
b)
2
P
c)

P
d)
P

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
61.
b) B
c) 2B
d) q
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
^
62.
d) x = y + z
^
Two protons enter a uniform magnetic field with velocity v i and (2v) i . The angular frequency rotation is
 . Then
a) 1  2
63.
b) 1  2
d) 1  2  0
In the above problem, the time periods T1 and T2 are related as
a) T1 = 0 = T2
64.
c) 1  2
b) T1 > T2
c) T1 < T2
d) T1 = T2
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
11

12. c) R2 corresponds to the electron
65.
d) direction of motion of the electron is anticlockwise
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
66.
b) 10 MeV
c) 2.5 MeV
d) 1 MeV
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. Then
r1
r
b) 1
r2
r2
a)
67.
c)
r12
r22
d)
m1
is equal to
m2
r2
r1
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
68.
b) 450
c) 600
d) 900
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) E  0; B  b j  c k

^ 
^
^
b) E  a i; B  c k  b i


^
^
c) E  0; B  c j  b k

^ 
^
^
d) E  a i; B  c k  b j
12

13. 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)
bqB
m
b)
aqB
m
c)
a  bqB
m
d)
a  bqB
m
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?
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?
13

14. 
76.
A current carrying circular loop of radius 12cm produces a magnetic field B at its centre equal to 0.05 x 10-4T.
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) d 
78.
2m
v1  v2 
qB
b) d 
m
v1  v2 
qB
c) v1  v2
d) d 
m
v1  v2 
qB
^

^


A charged particle of specific charge  is released form origin at time t = 0 with velocity v1  v0  i  j  in a

^
uniform magnate field B  B0 i . The co-ordinates of the particle at time t 
 v0
2v 0  v 0 

,
 2 B  B , B  
0
0
 0

b)  0,

  v0

, 0.0 

 2 B0


are
B0
d) 

a) 
c) 



2v0 v0 

,
B0 2 B0 

 v 0
 2v0 

,0,
B0 
 B0

14

15. 
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)
80.
qBx
2
qBy
2
c)

qB  x 2
  y
 y

2 

d)
qBy 2
2x
In a region where both nonzero uniform electric field and magnetic field coexist, the path of a charged particle
a) Must be a circle
81.
b)
b) May be a circle
c) May be a straight line
d) Must be a helix
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
2 times the original radius
c) half of the original radius
83.
b)
d)
1
times the original radius
2
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
a) An electron and a proton respectively
b) a He+ ion and proton respectively
15

16. c) a He+ ion and an electron respectively
84.
d) a proton and  -particle respectively
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 %
85.
b) 4 %
c) 10 %
d) None of these
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 time
a)
86.
m v0
qB
b)
m v0
2qB
c)
m v0
4qB
v0
2 g
is
d) None of these
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)
87.
qBd
m
b)
qBd
2m
c)
2qBd
m
A positive charge q is projected in magnetic field of width
d) None of these
mv
with velocity v as shown in figure. Then
2 qB
time taken by charged particle to emerge form the magnetic field is
a)
m
2 qB
b)
m
4 qB
c)
m
d)
2 qB
m
2 qB

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
16

17. a)
2
tan 
b) tan
c) cot 
^
89.
d)
tan 
2
^
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?
^
90.
^
^
^
a) i
b) j
c) k
d) - k
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
c) It at rest in a magnetic field
92.
b) It moves parallel to an electric field
d) It moves perpendicular to a magnetic field
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

93.
a) 1
94.
^
^

^
^
A proton moving in a magnetic field has a velocity v  3 i  4 j and acceleration a  3 i  x j . Then x =
b) – 1
c) – 1.5
d) -2.025
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)
K
2
d) 14 K
17

18. ^
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
^
96.
^
^
^
a) k
b) - k
c) i
d) j
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 E and B . In which
direction is the net force on the proton zero?
a) N
98.
b) S
c) E
d) W
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
c) A will not observe an electric field
99.
b) A will observe a magnetic field
d) B will observe a magnetic field
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 force will be
18

19. a) F
100.
b) 3 F
c)
3F
d)
F
3
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

102.


c) Is zero only when v is perpendicular to B

d) Is zero only when v is parallel to B
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
c) Move towards the wire
103.
b) Move away from the wire
d) Rotate around the wire with the wire as the axis
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
104.
b) 2 F
c) 4 F
d) 8 F
Three long straight parallel and equally spaced wires carry identical currents as shown in the figure. If F1, F2
and F3 represent the net force on the wires 1, 2, 3 respectively then
19

20. a) F2  F3  F1
105.
b) F2  F1  F3
c) F1  F2  F3
d) F1  F2  F3
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 F13 represents that on the wire 1 due to the
wire 3 then
a) F12 =F13
106.
b) F12 =2F13
c) F13 =2F12
d) F13 =-F12
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
107.
b) 600
c) 450
d) 300
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 10-5T. If the
currents are in the opposite direction the magnetic field at the same point is 3 x 10-5T. Then the ratio of the
currents
a) 2
108.
I1
is
I2
b) 3
c)
2
3
d)
h
5
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
20

21. 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
110.
b)
3
BIL
2
c) Zero
d)
BIL
2
A current carrying wire AB is placed near a very long straight conductor
a) Only translate
112.
d) to the left
The loop shown carries a current I in a uniform magnetic field. The force on loop is
a) BIL
111.
b) downwards c) to the right
b) Only rotate c) Translate as well as rotate
d) oscillate
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
a) Increases
b) Decreases
c) Remains the same
d) Becomes zero
21

22. 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
114.
d) Neither a force nor a torque
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
0 I 2
a)

115.
0 I 2
c)
ln r
2
0 I 2
b)
2
0 I 2
d)
ln 2
2
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
116.
c) BI(L2 – L1)
b) BIL2
d) Zero
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
117.
b) 3 A
c) 4 A
d) 8 A
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
118.
b) along y
c) along +z
d) it cannot be done
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
22

23. 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
b) i2 r B
a) irB
120.
c) i r B
d) Zero
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
121.
b)  q f 12
1
 q f 12
2
d)
1
 q f 12
3
The magnitude of magnetic moment of current loop in the figure is
a) Ia2
122.
c)
b)
2 Ia2
c) Zero
d)
3 2
Ia
2
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
I)
II)
III)
a) I > III > II > IV
b) I > II > III > IV c) I > IV > II > III
IV)
d) III > IV > I > II
23

24. 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
124.
b) 3
c) 2
d) 1
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
c) can have a value 2BIR
125.
b) can have a maximum magnitude 2BIR
d) can have a magnitude BIR
Magnetic induction at the centre of circular loop of area A is B. Then magnetic moment of the loop will be
a)
126.
2 BRA
b)
0
BRA
c)
0
0 B
AR
d)
BR A
0
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) iBL2 1 
4




b) iBL2 1 
4


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?
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 angle   30 0 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
 mp
 me
kinetic energy? [Given that 


  1840 ]


24

25. 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:
0  4 10 7 V  S / A  m)
Multiple Choice Questions with one correct alternative
133.
The magnetic moment of the current carrying loop shown in the figure is equal to
a)
134.


I b 2  2ab 
2
b) Iab
c)


I a 2  ba 
d) None of the above
2
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
c)
135.
b)
2
i / B perpendicular to paper inwards
3
d)
2
i/B
3
3 i / B perpendicular to paper outwards
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
25

26. 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
v
a)
c
137.
c
b)
v
c2
c) 2
v
v2
d) 2
c
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 10-17N. 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
c) only (A) is true
139.
b) both (A) and (B) are false
d) only (B) is true
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)
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
26

27. a)
142.
q r 2
3
b)
q r 2
2
c)
q r 2
2
d)
q r 2
3
In question number 9, the angular momentum of the particle in terms of the magnetic moment of the charged
particle is
 2 
m

 q 
 
m

 2q 
b) L  

a) L  

143.
 3 

 2q  m


c) L  
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
a)
144.

m

q
d) L  

 0 NI
2r2  r1 
ln
r2
r1
b)
 0 NI
2r1  r2 
c)
at the center is
 0 NI
r1  r2 
d)
A current I flows through a circular arc of wire which subtends an angle of
 0 NI
2r1  r2 

at the centre. If the radius of the
3
circular arc is R, the magnetic induction B at the centre is
a)
145.
0 I
4 R
b)
0 I
12 R
c)
3 0 I
2 r
d)
 0 I
6r
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)
146.
B
n
b) nB
c) n2B
d)
B
n2
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
147.
b) 8.3 T
c) 83 mT
d) 8.3 mT
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
27

28. 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
149.
b) 0.30 A m2
c) 0.20 A m2
d) 0.25 A m2
The magnitude of the equatorial field due to a bar magnet of length 5cm at a distance of 50cm from its midpoint is (The magnetic moment of the bar magnet is 0.40 A m2).
a) 3.2 x 10-3G
150.
b) 4.2 x 10-3G
c) 2.2 x 10-3G
d) 1.2 x 10-3G
Given the earth’s magnetic field at the equator approximately as 0.4G. The earth’s dipole moment is. (Radius
of earth = 6.4 x 106m).
a) 2.04 x 1023Am2
151.
b) 3.04 x 1023 Am2
c) 4.04 x 1023Am2
d) 1.04 x 1023Am2
The horizontal component of the earth’s 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
152.
c) 0.32 G
d) 0.45 G
The magnetic moment of the system shown in figure will be
a)
153.
b) 0.52 G
3 ma
b) ma
c) 2 ma
d) None of these
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
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
28

29. 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)   sin 1 0.5625
155.
b)   sin 1 0.325
c)   sin 1 0.425
d)   sin 1 0.235
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
156.
b) 2.0 N
c) 1.0 N
d) 0.5 N
A bar magnet suspended by a horse’s hair lies in the magnetic meridian where there is no twist in the hair. On
turning the upper end of the hair through 1500, 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
157.
b) 3600
c) 3300
d) 1500
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
158.
d) 5.5 x 106 A m2
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
a)
0  3
4 d 3
b)
 0 2
4 d 3
c)
0  5
4 d 3
d)
 0 2
4 d 3
29

30. 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
earth’s total magnetic fields at the two places is
a) 3 3 : 8
161.
b) 16 : 9 3
c) 4 : 9
d) 2 3 : 3
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, then
a)
162.
1
2
b) 2
c)
d)
1
2 2
The magnetic lines of force inside a bar magnet
a) do not exist
c) are form S pole to N pole of the magnet
163.
1
4
T'
is
T
b) depend upon area of cross section of the magnet
d) are from N pole to S pole of the magnet
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
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 B will be
30

31. a) 4 : 1 exactly b) 4 : 1 approximately c) 8 : 1 exactly d) 8 : 1 approximately
165.
A bar magnet is undergoing oscillation in earth’s magnetic field with a period T. If its mass is quadrupled, then
a) motion remain simple harmonic with time period 
T
2
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 earth’s magnetic field. They
should get deflected to
a) north
167.
b) south
c) east
d) west
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
168.
b) 0.12 T
c) 1.2 T
d) 12 T
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
169.
b) zero
c) less than n
d) greater than n
Consider the following statement.
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 true
c) both (A) and (B) are true
d) both (A) and (B) are false
31

32. 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
c) both (A) and (B) are true
171.
b) only (B) is true
d) both (A) and (B) are false
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 
172.
b)
2
c)

2
d)

2
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 10-2T. The magnet comes to stable position at angle of 300 with the direction of above
field. The magnitude of the other field is
a)
15
 10 2 T
2 2
b)
1.5
 10 2 T
2 2
c) 15  2 10 2 T
d) 1.5 10 2 T
Conceptual Questions
173.
An artificial satellite with a metal surface has an orbit above the equator. Will the earth’s 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?
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?
32

33. 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)
177.
 D2L
64 
b)
 D 2 L dB
64  dt
c)
 D 2 L dB
 dt
d)
 D2L
B

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 
178.
b)

2
c) 450
d) 600
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)
a) 4.6 V
179.
b) 14.6 V
c) 10.6 V
d) 12.6 V
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)
2L
R
b)
L
R
c)
L
2R
d) LR
33

34. 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 earth’s magnetic field 0.2 x 10-4T and the separation between the rails 1m?
a) 1 mV
181.
b) 3 mV
c) 6 mV
d) 9 mV
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
182.
b) 8 mH
c) 10 mH
d) 12 mH
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
183.
b) 1.0 V
c) 1.5 V
d) 2.0 V
An ideal solenoid of cross-sectional area 10-4m2 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
184.
b) 2 mV
c) 3 mV
d) 4 mV
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?
a) 0.06 mV
185.
b) 0.12 mV
c) 0.18 mV
d) 0.24 mV
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
34

35. 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
187.
b) 5.0 A
c) 7.5 A
d) 10 A
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
188.
b) Clockwise
c) Alternating d) No current will be induced in the loop
Flux  (in weber) in a closed circuit of resistances 10  varies with time t (in seconds) according to the
equation   3t 2  5t  1 . The magnitude of the induced current in the circuit at t = 0.25s is
a) 0.2 A
189.
b) 0.6 A
c) 0.8 A
d) 1.2 A
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
a) B 
190.
2
R Q
NA 2

b) B 
RQ
NA
c) B 
RQ
5 NA
d) B 
RQe
NA
Q
IT
A conducting rod of length l rotates about one end with a constant angular velocity of  in an external
magnetic field B as shown. The potential difference between the ends of the rod is
35

36. a)
191.
B 2 l
2
b)
2 Bl
c)
 Bl2
2
d)
2
2 Bl
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
a)
192.
0 I a 2v
2 xa  x 
b)
0 I
a3
4 2 xa  x 2
c)
0 I
a2
2 x 2 a  x 
d)
0 I
2
a
ax  a 
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) a 
193.
Bl2I
m
b) a 
BIl
m
c) a 
5B I l
m
d) a 
BIl
3m
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.
36

37. 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
194.
d) b first, d and e will tie and then a and c will tie
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 (Earth’s vertical field is 0.43 x 10-4T).
a) 0.2 V
195.
b) 0.02 V
d) 2.8  V
c) 2.7 mV
An all metal aero plane flies horizontally at 600 km/hr at a place where the vertical component of earth’s
magnetic field is 4 x 10-5T. If the wing span is 10m, the resulting potential difference between the tips of the
wings is
a)
196.
1
V
80
b)
1
V
20
c)
1
V
15
d)
20
V
3
Half of the core of a solenoid of area of cross section 2 x 10-3 m2 is made of air and the other half 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
197.
b) 0.315 H
c) 0.528 H
d) 0.625 H
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
37

38. 198.
An air core solenoid with 90 turns is 10cm long and has a diameter of
4
. How much energy is stored in its
x
magnetic field when it carries a current of 0.8 A?
a) 24 mJ
199.
b) 0.13 J
c) 0.05 J
d) 0.002 J


A magnetic flux through a metal ring varies with time t according to the relation   3 at 3  bt 2 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
200.
b) 3 A
c) 5 A
d) 6 A
The blades of a helicopter 3m log, rotate at 2 rev/s. If the Earth’s 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
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 induced e.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.
38

39. Multiple Choice Questions with one correct alternative
204.
In a L-R circuit, the current increases with a time constant  . The emf across the coil at t is
a)
205.
t

b) E 1  e t / 


c) Ee t / 
d) Ee 2t / 
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?
206.
c)  1 ln 2
b) 
a)  ln 2
d)  / ln 2
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) t 0 ln K
207.
b)
t0
ln K
c)
t0
n
d)
t0
n 1
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
208.
d) 1200
b) Time
c) emf
d) Ampere
In the above problem, which of the following has dimension of time?
a) RC
210.
c) 900
If L, C and R represent the inductance, capacitance and resistance then (R/L) has dimensions of
a) Frequency
209.
b) 450
b)
R
L
c)
1
RC
d)
LR
C
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)
39

40. a) D
211.
b) C
c) B
d) A
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
212.
b) 0.3 s
c) 0.2 s
d) 0.1 s
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
213.
b) 31 J
c) 39 J
d) 41 J
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
214.
d) 1 W
b) 323 mW
c) 623 mW
d) 1 W
In the above problem at what rate is energy stored in the magnetic field at 0.313s?
a) 193 mW
216.
c) 800 mW
In the above problem, at t = 0.313s at what rate is thermal energy appearing in the resistor?
a) Zero
215.
b) 600 mW
b) 391 mW
c) 516 mW
d) 1 W
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)
217.
1
4
b)
1
16
c)
1
2
d)
1
32
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
i1
is
i2
40

41. a)
218.
L2
L1  L2
b)
L1
L1  L2
c)
L2
L1
d)
L1
L2
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
a) 1 mH
219.
c) 10 H
d) 10 mH
When the radius of a coil is doubled without changing the length of the wire, its self inductance is
a) doubled
220.
b) 10 H
b)halved
c) tripled
d) quadrupled
Two circular coils can be arranged in three following different ways. Their mutual inductance will be
1)
2)
3)
a) maximum in situation (1)
c) maximum in situation (3)
221.
b) maximum in situation (2)
d) same in all situations
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
222.
b) 5 ms
c) 2.5  s
d) 5  s
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 m F
c) 0.1 p F
d) 10  F
41

42. 223.
In the circuit shown in the figure, the current shown by the ammeter is I1 just after closing the switch and I2
I
long after closing the switch. Then the ratio  1
I
 2
a)
224.
3
4
b) 1

 is


c)
4
3
d)
3
2
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)
225.
r
R
b)
R
r
c)
r2
R
d)
R2
r
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
226.
b) 12 mH
c) 26 mH
d) 10 mH
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) E e t / 
227.

c) E 1  e t / 
b) E e t / 


d) E 1  e t / 

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 emf’s at this instant, then
a)
i1
L
 1
i2 L2
b)
e1
L
 1
e2 L2
c)
L
e1
L i
 1; 1  1
e2 L2 i2 L2
d)
e1 L2 i1 L2
;


e2 L1 i2 L1
42

43. 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
229.
b) 200
c) 2000
d) 20000
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
a) 12.5  F
230.
b) 25  F
c) 50  F
d) 100  F
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)
231.
b)
c)
d)
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
232.
b) 12 mH
c) 16 mH
d) 20 mH
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
233.
b) 100
c) 10
d) 1
  1 
In Q.5, what is the ratio of the times required for the currents in circuits in circuits 1 and 2 to reach 1   
  e 
of their steady state value?
a) 1000
234.
b) 100
c) 10
d) 1
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
43

44. 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  2  10 .
a) 2.5 pF to 250 pF
236.
b) 5.0 pF to 500 pF
c) 7.5 pF to 750 pF
d) 10 pF to 1000 pF
L, C and R, respectively represent inductance, capacitance and resistance. Which one of the following
combinations has the dimensions of frequency?
a)
237.
1
RC
b)
1
LC
c)
L
R
d)
C
L
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
238.
b) 0.6 A
c) 0.9 A
d) 1.2 A
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)
240.
4
5
b)
5
4
c)
16
25
d) 25
16
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 I  I max sin  t    as shown in the figure. The induced emf in the loop is
44

45. a) e 
b) e 
 0 NI max L 
w
ln 1   cos t   
2
2
h

c) e 
241.
  0 NI max L  w 
ln   sin  t   
4 2
h
  0 N 2 I max L  w  2
ln   sin  t   
4 2
h
d) e 
 0 N 2 L2
I max
4 2
If I max  50 A,   200 s 1 , N  100, h  w  5cm and L = 20cm, the maximum power generated in the
coil in Question No. 47 is
a) 2.82 W
242.
b) 2.52 W
c) 2.11 W
d) 1.38 W
The circuit shown in the following circuit is mainly of
a) Inductive load
c) Resistive load
243.
b) Capacitive load
d) inductive and capacitive loads
An RLC circuit has an impendence Z and resistance R. if  is the constant then
a) tan  
b) tan  
c) tan  
244.
Z 2  R2
R
ZR
R
d) tan  
Z 2  R2
R
R
Z
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
c) Equal to 10V always
245.
always
b) Less than 10 V always
d) Greater than 10 V at some point

3


An ac generator has an emf v  Vmax sin   t   and current i  I max sin   t 
4
4


 . The time t at which


the emf and current in the generator become maximum are respectively
a) t 
3
2
and t 
4
4
b) t 
3
10
and t 
4
3
45

46. c) t 
246.
2
8
and t 
3
5
2
5
and t 
4
4
The resonant frequency in the circuit shown below is
a) 122  2 Hz
247.
d) t 
b)
577

c)
Hz
623

2
d)
Hz
100
Hz
3
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 
248.
b) 300 
c) 126 
d) 800 
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)
249.
15
A
28
b)
35
A
79
c)
82
A
38
d)
22
A
75
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
250.
b) 80 mH
c) 165 mH
d) 188 mH
The current in a certain circuit varies as shown in the following graph. The average current in the circuit is
a) Zero
b) I0
c)
I0
2
d)
2I 0
46

47. 251.
In Q.249, the rms current in the circuit is
a)
252.
I0
2
b)
I0
3
c)
I0
2
d)
I0
5
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) Z 
L2
R 

c) Z 
R 2  4 L2   
 2

b) Z 
2
R
d) Z 
2
R 2     L2
2
L2
2
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
256.
(ii) capacitance
(iii) resistance required to be put in series with the lamp.
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?
Multiple Choice Questions with one correct alternative

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
47

48. 

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
259.
b) Negative
c) Neutral
d) Absent
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) x  0, y 
260.
a
2
b) x 
a
a
, y
2
2
c) x 
a
, y0
2
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
261.
d) x  0, y  0
d) The cross-sectional
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
262.
b) 
1
wBl 2
8
c) Bwl 2
d)
B 2 w2l 2
2
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 the current in the rectangle is
48

49. 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
264.
b) Left
c) Into the page
d) Out of the page
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
a)
265.
b)
c)


The flux of the magnetic field through the loop shown increases as   6t 2  7t 10 3 . The magnitude of the
emf induced in the loop at t = 2 see is
49

50. a) 31 mV
266.
b) 21 mV
c) 16 mV
d) 9 mV
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)
T
4
c)

267.
T
2
^
d) T
^

^
A proton is fired form origin with velocity v  v0 j  v0 k in a uniform magnetic field B  B0 j . 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

^
^

^
v  3 i  4 j and a  2 i  x j . Select the correct alternative(s).
a) x = - 15
c) magnetic field is along z-direction
269.
b) x = 3
d) kinetic energy of the particle is constant
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
50

51. c) The end a becomes negatively charged
270.
d) The end B becomes negatively charged
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
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
51

52. 272.
The magnetic flux through the circuit is
a) 2 B
273.
b) B
B
2
d)
B
4
The induced emf in the circuit is
a) 0.8 V
274.
c)
b) 1.74 V
c) 2.3 V
d) 3.1 V
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
i) Torque + magnetic field
Column-II
p) Magnetic field
ii) Induced emf
q) Lenz’s Law
iii) Result opposing the cause
r) Eddy currents
iv) Moving conducting plane
s) current
276.
Column-I
i) Induced electric field
Column-II
p) Cross product

ii)
 E ds
q) Weber / m2

iii) Magnetic force
r) Capacitor
iv) Tesla
s) Charging magnetic flux
Numerical Problems
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  .
52