1. OBJECTIVE UNSOLVED LEVEL - I
1. The flux linked with a coil changes with time according to the equation 2
at bt c
    . Then S I
unit of a is :
(a) Volt (b) Volt / sec
(c) Volt. sec (d) Weber.
2. Lenz’s law is consistent with law of conservation of
(a) current (b) emf
(c) energy (d) all of the above.
3. A charged particle entering into a uniform 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 rotation in the field depending on its angle of entry into the field
(c) will always complete exactly half of a rotation before leaving the field
(d) may follow a helical path depending on its angle of entry into the field.
4. The magnetic flux linked with a coil is  and the emf induced in it is  .
(a) If  = 0,  must be 0
(b) If 0
  ,  cannot be 0
(c) If  is not 0,  may or may not be 0
(d) None of the above is correct.
5. A metal ring is placed in a uniform magnetic field, with its plane  to the field. If the magnitude of
the field begins to change with time, the ring will experience
(a) a net force (b) a torque about its axis
(c) a torque about a diameter (d) a tension along its length.
6. There will be no induced emf in a straight conductor moving in a uniform magnetic field, if :
(a) it is moving parallel to magnetic field
(b) it is moving along its length
(c) it is moving in the magnetic field with its length parallel to field
then correct statement (s) is / are :
(a) a only (b) a, b only
(c) a, c only (d) a, b, c.
x
y
A B
7. Consider the situation shown in figure. If the current I in the long
straight wire xy is increased at a steady rate the induced current in
loop A and B will be :
(a) clockwise in A and anticlockwise in B
(b) anticlockwise in A and clockwise in B
(c) clockwise in both A and B
(d) anticlockwise in both A and B.

2. 8. A metallic ring is held horizontal and a magnet is allowed to fall vertically through it with N-pole
pointing upwards. The acceleration of magnet near the ring is a. Then
(a) a = g
(b) a < g while approaching but a > g while receding
(c) a < g while approaching as well as receding
(d) a > g while approaching but a < g while receding.
9. The current in a L – R circuit in a time t = 2L/R reduces to
(a) 36.5% of maximum (b) 13.5% of maximum
(c) 0.50% of maximum (d) 63.2% of maximum.
10. A field of 4
5 10 /
  ampere-turns / meter acts at right angle to a coil of 50 turns of area 2 2
10 m
 .
The coil is removed from the field in 0.1 second. Then the induced emf in the coil is :
(a) 0.1 V (b) 80 KV
(c) 7.96 V (d) none of the above.
11. The flux linked with a coil is 0.8 Wb when 2A current flows through it. If this current begins to
increase at the rate of 0.4 A/s, the emf induced in the coil will be
(a) 0.02 V (b) 0.04 V
(c) 0.08 V (d) 0.16 V.
12. A non-conducting ring of radius r has charge Q. A magnetic field perpendicular to the plane of the
ring changes at the rate
dB
dt
. The torque experienced by the ring is :
(a) zero (b)
2 dB
Qr
dt
(c)
2
1 dB
Qr
2 dt
(d)
2 dB
r Q
dt
 .
13. The magnetic flux through a circuit of resistance R changes by an amount  in time t
 . Then the
total quantity of electric charge Q that during this time passes any point of the circuit is given by :
(a) Q / t
   (b) Q R
t

 

(c) Q R
t

 

(d) Q
R

 .
14. Auniformlywoundlong solenoid ofinductanceLand resistance Ris cut into twoequalparts. The
two partsare then joined inparallel. Further this combinationis joined to a cellofemfE. The time
constant ofthe circuit is
(a)
L
4R
(b)
L
2R

3. (c)
2L
R
(d)
L
R
B
C
r
x

x
x
x
x
x
x
x
15. A conducting disc of radius r spins about its axis with an angular
velocity . There is a uniform magnetic field of magnitude B per-
pendicular to the plane of the disc. C is the center of the ring.
(a) no emf is induced in the disc
(b) the potential difference between C and the rim is 2
Br 
(c) C is at a higher potential than the rim
(d) Current flows between C and the rim.
OBJECTIVE UNSOLVED LEVEL - II
A
D
B v
1. The conductor AD moves to the right in a uniform magnetic field
directed into the paper. Mark the CORRECT option.
(a) the free electrons in AD will move towards A
(b) D will acquire a positive potential with respect to A
(c) If D and Aare joined by a conductor externally, a current will
flow from A to D in AD
(d) all the above.
2. A square loop ABCD of edge a moves to the right with a velocity , parallel to AB. There is a
uniform magnetic field of magnitude B, directed into the paper, in the region between PQ and RS
only. I, II and III are three positions of the loop. [Indicate the FALSE statement]
a
A B
C D
P
Q
I
v
A B
C D
II
B
(a) the emf induced in the loop has magnitude Bav in all three positions
(b) the induced emf is zero in position II
(c) the induced emf is anticlockwise in position I
(d) the induced emf is clockwise in position III.
3. In figure shown, wire P1
Q1
and P2
Q2
, both are moving towards right with speed 5 cm/sec. Resis-
tance of each wire is 2  . Then current through 19  resistor is :

4. 4 cm
P1 P2
19
Q1
Q2 B = 1 Tesla
(a) 0 (b) 0.1 mA
(c) 0.2 mA (d) 0.3 mA.
A B
C
D
E
x
4. A vertical conducting ring of radius R falls vertically in a horizontal
magnetic field of magnitude B. The direction of B is perpendicular
to the plane of the ring. When the speed of the ring is :
(a) no current flows in the ring
(b) A and D are at the same potential
(c) C and E are at the same potential
(d) the potential difference between A and D is BR  , with D at
a higher potential.
5. There is a uniform magnetic field B normal to the xy plane. A conductor ABC has length AB = l1
,
parallel to the x-axis, and length BC = l2
parallel to the y-axis. ABC moves in the xy plane with
velocity x y
ˆ ˆ
i j
   . The potential difference between A and C is proportional to :
(a) x 1 y 2
l l
   (b) x 2 y 1
l l
  
(c) x 2 y 1
l l
   (d) x 1 y 2
l l
   .
6. The magnetic field perpendicular to the plane of a conducting ring of radius r changes at the rate
dB
dt
.
(a) the emf induced in the ring is
2
r dB
dt

(b) the emf induced in the ring is
2 dB
2 r
dt

(c) the potential difference between diametrically opposite points on the ring is half of the induced
emf.
(d) the emf induced in the ring is
2 dB
r .
dt
 .

5. 2v
B
x
S
v
2r
r
7. Two conducting rings of radii r and 2r move in opposite
directions with velocities 2  and  respectively on a con-
ducting surface S. There is a uniform magnetic field of
magnitude B perpendicular to the plane of the rings. The
potential difference between the highest points of the two
rings is :
(a) zero (b) 2r B
(c) 4r B (d) 8r B.
L
v
x B
P
Q
L L/2
8. The loop shown moves with a velocity  in a uniform magnetic
field of magnitude B, directed into the paper. The potential differ-
ence between P and Q is e.
(a)
1
e Bl
2
 
(b) e = Bl
(c) P is negative with respect to Q
(d) q is positive with respect to P.
A
B0
C
D
E
F
L

B
9. AB and CD are smooth parallel rails, separated by a dis-
tance L, and inclined to the horizontal at an angle  . A uni-
form magnetic field of magnitude 0
B , directed vertically up-
wards, exists in the region. EF is a conductor of mass m,
carrying a current i. For EF to be in equilibrium,
(a) i must flow from F to E (b) 0
B il = m gtan 
(c) 0
B il = m gsin (d) 0
B il = mg.
+Q
m
Y
Z
B

x
x
10. A particle with charge +Q and mass m enters a magnetic field of
magnitude B, existing only to the right of the boundary YZ. The
direction of the motion of the particle is perpendicular to the direc-
tion of B. Let
m
T 2
QB
  . The time spend by the particle in the
field will be :
(a) T (b) 2T
(c)
2
T
2
  
 
 

 
(d)
2
T
2
  
 
 

 
.
N S
Coil
Magnet
v
11. In the figure the magnet is moved along the axis of coil from one
position to another position in 3
10 sec. Now magnet is at rest for
2 sec, in its new position. The duration of induced emf in the coil is
:
(a) 3
10 sec (b) 2 sec
(c) 2 × 3
10 sec (d) 0.5 × 3
10 sec.

6. 12. A closed circuit consists of a source of emf E and an inductor coil of inductance L connected in
series. The active resistance of whole circuit is R. At the moment t = 0 the inductance of coil abruptly
decreased to
L
n
. Then the current in the circuit immediately after that moment is :
(a) 0 (b)
E
R
(c)
nE
R
(d)
E
nR
.
13. A solenoid of inductance L and resistance r is connected in parallel to a resistance R and a battery of
emf E. Initially the switch is closed for long time and and at t = 0, switch S is opened. Then,
R
L, r
E
S
(a) current through solenoid at any time t, after opening the switch is
(R r)
t
L
E
e
r

(b) induced emf across solenoid at time t = 0 is
E(R r)
r

(c) amount of heat generated in solenoid is
2
E L
2r(r R)

(d) potential difference across solenoid at t = 0 is E.
14. A small, flat coil of resistance r is placed at the center of a large, closed coil of resistance R. The coils
are coplanar. Their mutual inductance is M. Initially, a constant current i was flowing in the inner coil.
If this current is suddenly switched off, what charge will circulate in the other coil ?
(a) Mir / R2
(b) MiR / r2
(c) Mi / R (d) Mi / r.

7. 5
B' (x)

15. A pair of parallel conducting rails lie at right angle
to a uniform magnetic field of 2.0 T as shown in
the figure. Two resistors 10  and 5  are to
slide without friction along the rail. The distance
between the conducting rails is 0.1 m. Then
(a) induced current
1
150
 A directed clockwise
if 10  resistor is pulled to the right with
speed 0.5 1
ms
and 5 resistor is held fixed
(b) induced current
1
300
 A directed
anticlockwise if 10 resistor is pulled to the
right with speed 0.5
1
ms
and 5 resistor is
held fixed
(c) induced current
1
300
 A directed clockwise
if 5  resistor is pulled to theleft at 0.5
1
ms
and 10  resistor is held at rest
(d) induced current
1
150
 A directed
anticlockwise if 5 resistor is pulled to the
left at 0.5 1
ms
and 10  resistor is held at
rest.