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Electromagnetic Induction
Ranker
PHYSICS TEST
ELECTROMAGNETIC INDUCTION
1.
A closed coil with a resistance ‘R’ is placed in a magnetic field. The flux linked with
the coil is  . If the magnetic field is suddenly reversed in direction, the charge that
flows through the coil will be
A)
2.
3.
4.
6.
7.
8.
9.
10.
B)

R
C)
2
R
D) Zero
A coil of 1200 turns having mean area of 500 cm2 is held perpendicular to a uniform
magnetic field of induction 4×10–4T. The resistance of the coil is 20 Ohms. When the
coil is rotated through 180º in the field in 0.1s, the average electric current induced is
A) 12 mA
B) 24 mA
C) 36 mA
D) 6 mA
A train is moving towards north with a speed of 180 kmph. If the vertical component of
earth’s magnetic field is 2×10–5T, the emf induced in the axle of length 1.5m is
A) 1.5 mV
B) 15 mV
C) 54 mV
D) 5.4 mV
A coil having ‘n’ turns and resistance ‘R’ ohm is connected with a galvanometer of
resistance ‘4R’ ohm. This combination is moved in time‘t’s from a magnetic field W1
Wb to W2 Wb. The induced current in the circuit is
A)
5.

2R
W2  W1
5 Rnt
B)
n W2  W1 
5Rt
C)
 W2  W1 
Rnt
D)
n W2  W1 
Rnt
The flux linked with a coil at any instant‘t’ is given by  = 10t2–50t + 250. The induced
emf at t = 3s is
A) –190V
B) –10V
C) 10V
D) 190V
A metal conductor of length 1m rotates vertically about one of its ends at an angular
velocity 5 rad s–1. If the horizontal component of earth’s magnetic field is 2×10–5T, then
the emf developed between the two ends of the conductor is
A) 5 µV
B) 50 µV
C) 5 mV
D) 50 mV
A coil of inductance 300 mH and resistance 2Ω is connected to a source of voltage 2V.
The current reaches half of its steady state value in
A) 0.05 s
B) 0.1s
C) 0.15s
D) 0.03s
2
A coil has 1000 turns and 500 cm as its area. The plane of the coil is placed at right
angles to a magnetic induction field of 2×10–5 Wbm–2. The coil is rotated through 180º
in 0.2s. The average emf induced in the coil is
A) 5 mV
B) 10 mV
C) 15 mV
D) 20 mV
–1
A current of 2A is increasing at the rate of 4As through a coil of inductance 2H. The
energy stored in the inductor per unit time is
A) 2W
B) 1W
C) 16W
D) 4W
A physicist works in a laboratory where the magnetic field is 2T. She wears a necklace
enclosing an area 100 cm2 of field and having a resistance of 0.1Ω. Because of power
failure, the field decays to 1T in millisecond. The electric charge circulated in the
necklace assuming that the magnetic field is perpendicular to area covered by the
necklace is
A) 0.01C
B) 0.001C
C) 0.1C
D) 1C
Page 1
Electromagnetic Induction
11.
A small square loop of wire of side ‘l’ is placed inside a large square loop of side ‘L’ (L
> >l) carrying current i. If the loops are coplanar and their centers coincide, the mutual
induction of the system is directly proportional to
A)
12.
Ranker
L
l
B)
l
L
C)
L2
l
D)
l2
L
Two coils have self-inductance L1 =4mH and L2 = 1mH respectively. The currents in
the coils are increased at the same rate. At a certain instant of time, both the coils are
given the same power. If ‘I1’ and ‘I2’ are the currents in the two coils, at the instant of
I1

I2
1
B)
4
time respectively, then
A)
13.
14.
15.
1
8
C)
1
2
D) 1
Two parallel rails of a railway track insulated from each other and with the ground are
connected to a millivoltmeter. The distance between the rails is one meter. A train is
travelling with a velocity of 72 kmph along the track. If vertical component of earth’s
magnetic induction is 2×10–5T, the reading of millivoltmeter is
A) 144 mV
B) 0.72 mV
C) 0.4 mV
D) 0.2 mV
2
A coil of 30 turns of wire each of 10 cm area is placed with its plane perpendicular to a
magnetic field of 0.1T. When the coil is suddenly withdrawn from the field, a
galvanometer connected in series with the coil indicated that a 10 µC charge passes
around the circuit. The combined resistance of the coil and galvanometer is
A) 3Ω
B) 30 Ω
C) 300 Ω
D) 3000 Ω


4
ˆ
A magnetic field in a certain region is given by B  40iˆ  15k 10 T . The magnetic flux


2
16.
passes through a loop of area 5 cm which is placed flat on x – y plane is
A) 750 nWb
B) –750 nWb
C) 360 nWb
D) –360 nWb
Three resistances of magnitude ‘R’ each are connected in the form of an equilateral
triangle of side ‘a’. The combination is placed in a magnetic field B  B0e  t
perpendicular to the plane. The induced current in the circuit is given by
A
R
R
B
 a 2  B0   t
A) 
e
 2 3R 
17.
 a 2  B0   t
B) 
e
 4 3R 
C
R
 a 2 B0   t
C) 
e
 4 3R 
 a 2 B0 R   t
D) 
e
 4 3 
A non-conducting ring having charge ‘q’ uniformly distributed over its circumference
is placed on a rough horizontal surface. A vertical, time varying magnetic field B = 4t2
is switched on at time t = 0. Mass of the ring is ‘M’ and radius is R. The ring starts
rotating after 2s. The coefficient of friction between the ring and the table is
A)
4qmR
g
B)
2qmR
g
C)
8qR
mg
D)
qR
2mg
Page 2
Electromagnetic Induction
18.
Ranker

x
 
The magnetic field in a region is given by B  B0   kˆ . A square loop of side‘d’ is
a
placed with its edges along ‘X’ and ‘Y’ axes. The loop is moved with constant velocity

V  v0iˆ . The induced emf in the loop is
Y
Z
d
d
X
A) B0v0d
B)
B0 v0 d 2
2a
C)
B0 v0 d 2
a2
D)
B0 v0 d 2
a
19.
A solenoid has 2000 turns wound over a length of 0.3m. The area of its cross-section is
1.2×10–3m2. Around its central portion, a coil of 300 turns is wound. If an initial current
of 2A in the solenoid is reversed in 0.25s, the emf induced in the coil is
A) 48 mV
B) 48kV
C) 6×10–4
D) 6×10–2
20.
A coil of some internal resistance ‘r’ behaves like an inductance. When it is connected
in series with R1, the time constant is found to be τ1, and when it is connected in series
with another resistance ‘R2’. The time constant is found to be τ2. The inductance of coil
is
  R  R 
 2   1 
R R
 
A) 1 2 1 2
B)
C) 1 2
D) 2 1
 1 2  R1  R2 
 2 1
R1  R2
 2   1 
A condenser in series with a resistor is connected through a switch to a battery of
negligible internal resistance and having an emf of 12V. One second after closing the
switch, the condenser is found to have a potential difference of 6V. The time constant
of the system is
21.
A) 2s
22.
B)
1
log e 2
1
C) log e 2
D) log e  
2
An inductor of L = 100 mH, a resistor of R = 100 Ω and a battery of emf E = 100 V are
initially connected in series as shown. After a long time, the battery is disconnected
after short circuiting the points A and B. The current in the circuit 1 milli second after
the short circuit is
L
R
A
B
E
A)
1
A
e
B) eA
C) 0.1A
D) 1A
Page 3
Electromagnetic Induction
23.
Ranker
A 0.4m long straight conductor moves in a magnetic field of magnetic induction 0.9
Wbm–2 with a velocity of 7 ms–2. The emf induced in the conductor under the condition
when it is maximum is
V
q
l
A) 2V
24.
B) 2.52V
C) 5.22V
D) 3.5V
A square loop of side ‘a’ placed in a magnetic field as shown. The magnetic field varies
as B= (α – βt). The resultant emf of battery when its open circuit potential difference
across the terminals was found to be ‘E’ is
B= (a  b t)
a
a
E
A) E  a 2 
25.
E 2
a 
2
C)  E 
a2
2
D) E 
a2
2
In a car spark coil, an emf of 40,000V is induced in the secondary coil. When the
primary current changes from 4A to zero in 10μs, the mutual inductance between the
primary and the secondary windings of this spark coil is
A) 0.3 H
26.
B)
B) 0.4 H
C) 0.1 H
D) 0.2 H
A conducting square loop of side ‘L’ and resistance ‘R’ moves in its plane with a
uniform velocity ‘V’ perpendicular to one of its sides. Magnetic induction ‘B’ constant
in time and space pointing perpendicular into the plane of the loop exists everywhere.
Then the current induced in the loop is
A)
BL
clock wise
R
B)
BL
2BL
an to clock wise C)
an to clock wise
R
R
D) Zero
Page 4
Electromagnetic Induction
Ranker
27.
A vertical copper disc of diameter 20 cm makes 10 rps about a horizontal axis passing
through its centre. A uniform magnetic field 10-2 Wb m-2 acts perpendicular to the
plane of the disc. The potential difference between its centre and rim is
A) 2. 14  103V
B) 3.14  103V
C) 5. 14  103V
D) 1. 14  103V
28.
A plane loop shown in the figure is shaped in the form of two squares with sides a =
0.5m and b = 0.3m and is placed in a uniform magnetic field at right angles to the plane
of the loop. The magnetic induction varies with time as B = B0 sin t where Bo= 20
mT
and
1
w = 100 reds . The amplitude of induced current produced in the loop of its
resistance per unit length is 50m /m is
29.
30.
A) 1A
B) 2A
C) 3A
D) 2.5 A
Two parallel vertical metal rails AB and CD are separated by 1m. They are connected
at the two ends by resistances R1 and R2 as shown. A horizontal meta bar ‘L’ of mass
0.2kg slides without friction vertically down the rails under the action of gravity. There
is a uniform horizontal magnetic field of 0.6T perpendicular to the plane of the rails.
When the bar attains terminal velocity, the powers dissipated in R1 and R2 are 0.76 W
and 1.2 W respectively. The values of terminal velocity, R1 and R2 respectively are
A) 1ms – 1; 0.47 and 0.3
B) 2ms – 1; 0.6 and 0.3
–1
C) 1.5ms ; 0.2 and 0.4
D) 2.5ms – 1; 0.3 and 0.2
Figure shows two bulbs B1 and B2, resistor R and inductor L when the switch ‘S’ is
turned off then
A) Both B1 and B2 die out promptly
B) Both B1 and B2 die out with some delay
C) B2 dies out promptly but B1 with some delay
D) B2 dies out promptly but B2 with some delay
Page 5
Electromagnetic Induction
Ranker
KEY
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
C
B
A
B
B
B
B
B
C
C
D
B
C
C
B
B
C
D
A
A
B
A
B
D
C
D
B
B
A
D
Page 6
Electromagnetic Induction
Ranker
SOLUTIONS
1.
emf e 
d
d
d
dq d
 iR 
i


dt
dt
R  dt 
dt Rdt

d
 q  effective
R
R
2
When reversed, q 
R
4
4
2 NBA 2 1200   4  10  500  10 
i

 24  103 A
Rt
 20  0.1
 dq 
2.
= 24 mA
3.
emf induced e = Blv
  2  105  1.5  50 
4.
5.
 15  10 4 V  1.5mV
1  d  n  w2  w1 
i

Reff  dt 
5Rt
e
 d
   20t  50
dt
When t = 3s, e = – [60 – 50] = – 10V
6.
1 
 NB  l 2 
 d
 2    1 NBl 2
e

dt
t
2
1
 2 105 1 5  5 105  50V
2
t
t
t

 V
 

3


0.15
L  300  10 H
i  i0 1  e   1  e   1  e 

 R
 

L
i
R  2
Here    0.15s and i  0
R
2
t
1
1
pd = 2V
 t   e 0.15  2  t   0.15  log e 2
2
e 0.15
5
4
2 NBA 2 1000   2  10  500  10 
e

 10mV
t
0.2
1
Energy stored (V) = U   Li 2 and power
2
dv 1
di
 P    L  2i 
dt 2  dt 
1
  2   2  2  4   16W
2
B1  2T

7.
8.
9.
10.

A  100 10 4 m 2
e
N  B1  B2  A
d
i
dt
Rt
Page 7
Electromagnetic Induction
Ranker
q 
R  0.1
N  B1  B2  A
R
 0.1C
B2  IT
t  103 s
11.
12.
13.
14.
15.


 i

4 0
sin 45º  sin 45º   l 2

 4  L 

 


BA
2
N  Mi  M 

i
i
2
2 2l
l2
M 
 M
L
L
1 2
Energy U  Li
2
dU 1  di 
di
∴Power P 
 L  2i   Li
dt 2  dt 
dt
di
L i
Since powers are equal and is constant, L1i1  L2i2  1  2
dt
L2 i1
e  Blv   2  105  1 20   0.4mV
4
NBA
NBA  30  0.1 10  10 
q
R

= 300 Ω
R
q
10 106 
 
  B. A
  40iˆ  15kˆ 104  . 5 10 4 kˆ 


 
8
 75  10  750nWb
 3a 2 
  BA   B0e  t  

 4 
 t
 d
3B0 a 2
∴Emf induced e 

e
dt
4
2
e  B0  a   t
And current i 

e
3R  4 3R 

16.


17.

The ring starts rotating when the force due to electric field is equal to force of friction
along on it.
qE = µmg
(i)
  d
dB
d

Now  E. dl 
 s.
 s   4t 2  
dt
 El   R
dt
 dt
 8t 
 E  2 R     R   8t   E  4 Rt

2
2
(ii)
Substituting (ii) in (i)

qE 4qRt

mg
mg
When t = 2s,  
8qR
mg
Page 8
Electromagnetic Induction
18.
Ranker
Total flux linked with the coil at time t = 0 is
d
d
B0 d 3
 B0 x 
i   d   
  d  dx 
2a
0
0 a 
Flux linked with the coil at time t = 1s is
v0  dt
f 

v0  d
d 
v0
e
19.

v0
B0 d
 B0 x 
 a   d  dx  a


  v0  d  2 v 2 
 0

2
2 

 f  i B0v0 d 2

t
a
N
l
Magnetic induction produced around the central region of the solenoid due to the
current in its primary coil B = µ0nip
Number of turns per meter of the solenoid n 
s  N S BAS
 Mutual induction M =
 Induced emf e = M
20.
s
ip
di p
dt
 di 
Since current is reversed, e  2  M p   48mV
dt 

L
L
1 
and  2 
R1  r
R2  r
L
 r   R1
1
 1 2 
  R1  R2 



 2 1
Substituting in  2 , we get L  
21.
t 
t 


q  q0 1  e RC   CV  CV0 1  e RC 









1


6 
RC

 1  e   t  1s 
12 




 e
1
RC
1

2

1
RC
e
2
1
1
 log e2
 RC 
RC
log e 2
When battery is connected in series, current grows up from zero to maximum value
E 100
i0  
 1A
R 100

22.
Page 9
Electromagnetic Induction
Ranker
When the battery is removed and the terminals A and B are short circuited, the
current decays from i0 to zero exponentially as i  i0
23.
R
  t
e L
 100 

3 
 e 10010 
 e 1 
1
A
e
Flux linked with area generated by the motion of the conductor in time‘t’
  Bl V sin   t
 Induced emf e 
d
 Blv sin 
dt
When sinq =1, then ‘e’ will be maximum.
emax  Blv   0.9  0.4  7   2.52V
24.
 a2 
 d  d
d
e

 BA   A    t    A    
dt
dt
dt
 2 
Eres = E 
a2
2
Page 10

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