(PHYSICS-XII )

ELECTROMAGNETIC INDUCTION
CHAPTER-6
Very Short answer Questions(1-marks)
1. Two spherical bobs, one metallic and the other of glass, of the same size are allowed to fall freely from
the same height above the ground. Which of the two would reach earlier and why ?
2. When current in a coil changes with time, how is the back emf induced in the coil related to it ?
3. State the law that gives the polarity of the induced emf.
4. On what factors does the magnitude of the emf induced in the circuit due to magnetic flux depends?
5. The closed loop PQRS is moving into a uniform magnetic field acting at right angles to the plane of
the paper as shown. State the direction of the induced current in the loop.

P Q

S R

6. A rectangular loop of wire is pulled to the right, away from the long straight wire through which a
steady current I flows upwards. What is the direction of induced current in the loop?

7. A plane loop of rectangular shape is moved within the region of a uniform magnetic field acting
perpendicular to its plane. What if the direction and magnitude of the current induced in it ?
8. A rectangular loop of wire is pulled to the right, away from the long straight wire through which a
steady current I flows upwards. What is the direction of induced current in the loop ?
9. Predict the polarity of the capacitor C connected to coil, which is situated between two bar magnetic
moving as shown in figure.
A
B
S N S N

10. Predict the direction of induced current in metal rings 1 and 2 lying in the same plane where current
I in the wire is increasing steadily.

1 2
2
11. A triangular loop is placed in a dot ⊙ magnetic field as shown in figure. Find the direction of induced
current in the loop if magnetic field is increasing.

12. A rectangular loop is placer near a current carrying straight wire as shown in figure. If the loop is
rotated about an axis passing through one of its sides, find the direction of induced current in the loop.
ω

13. Predict the direction of induced current in resistance R in figure (a) and (b). Give reason for your
answer.
X R Y X1 R Y1 X2 R Y2

S N N S
(a) (b)
14. Give the direction in which the induced current flows in the coil mounted on an insulating stand when
a bar magnet is quickly moved along the axis of the coil from one side to the other as shown in figure.

S N S N

15. In the given figure, a bar magnet moving towards the right or left induces an emf in the coils (1) and
(2). Find, giving reason, the directions of the induced currents through the resistors AB and CD when
the magnet is moving (a) towards the right, and (b) towards the left.
(1) (2)
N S

A B C D
16. A current carrying straight wire passes inside a triangular coil as shown in figure. The current in the
wire is perpendicular to paper inwards. Find the direction of the induced current in the loop if current
in the wire is increased.

i
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Short Answer Questions(2-marks)
1. A long straight current carrying wire passes normally through the centre of circular loop. If the current
through the wire increases, will there be an induced emf in the loop ? Justify.
2. A rectangular frame of wire is placed in a uniform magnetic field directed outwards, normal to the
paper. AB is connected to a spring which is stretched to A ' B ' and then released at time t = 0 . Explain
qualitatively how induced e.m.f in the coil would vary with time.
A' A
C

D
B' B
3. The given figure shows an inductor L and resistor R connected in parallel to a battery B through a
switch S. The resistance of R is the same as that of the coil that makes L. Two identical bulbs. P and Q
are put in each arm of the circuit as shown in the figure. When S is closed, which of the two bulbs will
light up earlier ? justify your answer.
R P

L Q

s
B

Long Answer Questions( 3-marks)

1. (a) A rod of length l is moved horizontally with a uniform velocity v in a direction perpendicular to
its length through a region in which a uniform magnetic field is acting vertically downward. Derive the
expression for the emf induced across the ends of the rod.
(b) How does one understand this motional emf by invoking the Lorentz force acting on the free
charge carriers of the conductor ? Explain.
2. Figure shows planer loops of different shapes moving out of or into a region of magnetic field which
is directed normal to the plane of loops downwards. Determine the direction of induced current in each
loop using Lenz’s law.

(i ) B
(ii )

(iii ) (iv)
3. Answer the following questions :
(a) A closed loop is held stationary in the magnetic field between the north and south poles of two
permanent magnets held fixed. Can we hope to generate current in the loop by using very strong
magnets?
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(b) A closed conducting loop moves normal to the electric field between the plates of a large capacitor.
Is a current induced in the loop when it is (i) wholly inside the capacitor (ii) partially outside the
plates of capacitor? The electric field is normal to the plate of the loop.

(c) A rectangular loop and a circular loop are moving out of a uniform magnetic field region to a field
free region with a constant velocity. In which loop do you expect the induced emf to be constant
during the passage out of the field region? The field is normal to the loops.

v v

4. (a) How does the mutual induced of a pair of coils change when
(i) distance between the coils is increased and (ii) number of turns in the coils is increased?
(b) A plot of magnetic flux ( φ ) versus current ( I ) is shown in the figure for two inductors A and B.
Which of the two has large value of self-inductance?

φ B

O I
(c) How is the mutual inductance of a pair of coils affected when
(i) separation between the coils is increased?
(ii) the number of turns in each coil is increased?
(iii) a thin iron sheet is placed between the two coils, other factors remaining the same?
6. (i) Define self-inductance of a coil. Obtain the expression for the magnetic energy stored in an inductor
of self-inductance L to build up a current I through it.
(ii) The current flowing through an inductor of self inductance L is continuously increasing. Plot a
graph showing the variation of
(a) Magnetic flux versus the current
(b) Induced emf versus dI / dt
(c) Magnetic potential energy stored versus the current.
Long Answer Questions( 5-marks)
1. (a) State Faraday’s law of electromagnetic induction.
(b) Figure shows a rectangular conductor PQRS in which the S
conductor PQ is free to move in a uniform magnetic field B P
perpendicular to the plane of the paper. The field extends from
x = 0 to x = b and is zero for x > b . Assume that only the arm PQ
B
possesses resistances r . When the arm PQ is pulled outward from
x = 0 with constant speed v , obtain the expressions for the flux and Q
the induced emf. Sketch the variations of these quantities with R
distance 0 ≤ x ≤ 2b .
x=0 x=b dx x=2b
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2. (a) Derive an expression for the induced emf developed when a coil of N turns, and area of cross-
section A, is rotated at constant angular speed ω in a uniform magnetic field B.
3. (i) Define self inductance. Write its SI unit and dimension.
(ii) Derive an expression for the self-inductance of a circular coil. State the factors on which the self-
inductance of a coil depends.
4. (i) Define self inductance. Write its SI unit and dimension.
(ii) Derive an expression for the self-inductance of a long solenoid. State the factors on which the self-
inductance of a solenoid depends.
5. (i) Define the term mutual inductance. Give its unit and dimensions.
(ii) Derive an expression for the mutual inductance of a system of two coaxial coils of having turns
N1 , N 2 and radii r1 and r2 ( r2 > r1 ) . State the factors on which mutual inductance depends. What is the
coefficient of coupling ?
6. (i) Define the term mutual inductance. Give its unit and dimensions.
(ii) Derive an expression for the mutual inductance of two long coaxial solenoids of same length l ,
having turns N1 , N 2 and radii r1 and r2 ( r2 > r1 ) . State the factors on which mutual inductance
depends. What is the coefficient of coupling ?
7. What are the eddy current ? Give some experiments to demonstrate their existence. What is the effect
of eddy currents electrical appliances, where iron core is used ? How are eddy currents minimised ?
Describe some of the important applications of eddy currents.

NUMERICAL
1. A rectangular loop of area 20 cm × 30 cm is placed in a magnetic field of 0.3 T with its plane (i)
normal to the field (ii) inclined 30° to the field and (iii) parallel to the field. Find the flux linked with
the coil in each case.
Ans: (i) 1.8 ×10 −2 Wb (ii) 0.9 × 10−2 Wb (iii) 0
2. The magnetic flux through a coil perpendicular to the plane varying according to the relation :
φ = ( 5t 3 + 4t 2 + 2t − 5 ) Wb
Calculate the induced current through the coil at t = 2 s, if the resistance of the coil is 5 Ω.
Ans: 15.6A
3. The magnetic flux linked with a closed circular loop of radius 20cm and resistance 2Ω at any instant
of time is φ = 4t + 3 . Where φ is in milliweber and time t in sec.
Find (i) flux linked with a loop at t = 3s (ii) induced emf at t = 2 s and (iii) plot a graph between (a) φ
and t (b) ε and t .
4. A 10 Ω resistance coil has 1000 turns and at a time 5.5 × 10−4 Wb of flux passes through it. If the flux
falls to 0.5 ×10 −4 Wb in 0.1 second, find the emf generated in volts and the charge flown through the
coil in coulombs.
Ans: 0.05C
5. A coil with an average diameter of 0.02 m is placed perpendicular to a magnetic field of 6000 T
(Tesla). If the induced emf is 11 V when the magnetic field is changed to 1000 T in 4 s, what is the
number of turns in the coil?
Ans: 28
6. A coil of mean are 500 cm 2 and having 1000 turns is held perpendicular to a uniform field of 0.4
gauss. The coil is turn through 180° in 1/10 seconds. Calculate the average induced emf.
Ans: 0.04V
7. A coil of cross-sectional area A lies in a uniform magnetic field B with its plane perpendicular to the
field. In this position the normal to the coil makes an angle of 0° with the field. The coil rotates at a
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uniform rate to complete one rotation in time T . Find the average induced emf in the coil during the
interval when the coil rotates :
(i) from 0° to 90° position (ii) from 90° to 180° position
(iii) from 180° to 270° and (iv) from 270° to 360°
4BA 4BA 4BA 4BA
Ans: (i) (ii) (iii) − (iv) −
T T T T
8. The magnetic flux threading a coil changes from 12 ×10−3 Wb to 6 ×10−3 Wb is 0.01 s. Calculate the
induced emf.
Ans. 0.6 V
9. A coil of area 0.04 m 2 having 1000 turns is suspended perpendicular to a magnetic field of
5.0 ×10 −5 Wbm −2 . It is rotated through 90° in 0.2 s. Calculate the average emf induced in it.
Ans. 0.01 V
10. A magnetic field of flux density 10 T acts normal to a 50 turn coil of 100 cm 2 area. Find the emf
1
induced in it if the coil is removed from the field in s.
20
Ans. 100 V
11. A magnetic field of flux density 1.0 Wbm −2 acts normal to a 80 turn coil of 0.01 m 2 . Find the emf
induced in it, if this coil is removed from the field in 0.1 s.
Ans. 8 V
12. A 10 Ω resistance coil has 1000 turns and at a time 5.5 × 10−4 Wb of flux passes through it. If the flux
falls to 0.5 ×10 −4 Wb in 0.1 second, find the emf generated in volts and the charge flown through the
coil in coulombs.
Ans: 5V, 0.05C
13. A coil with an average diameter of 0.02 m is placed perpendicular to a magnetic field of 6000 T
(Tesla). If the induced emf is 11 V when the magnetic field is changed to 1000 T in 4 s, what is the
number of turns in the coil?
Ans: 28
14. A magnetic field of flux density 1.0 Wbm −2 acts normal to a 80 turn coil of 0.01 m 2 . Find the emf
induced in it, if this coil is removed from the field in 0.1 s.
Ans. 8 V
15. A 70 turn coil with average diameter of 0.02 m is placed perpendicular to magnetic field of 9000 T. If
the magnetic field is changed to 6000 T in 3 s, what is the magnetic of the induced emf?
Ans. 2.2 V
16. A magnetic field of flux density 10 T acts normal to a 50 turn coil of 100 cm 2 area. Find the emf
1
induced in it if the coil is removed from the field in s.
20
Ans. 100 V
17. A wire 40 cm long bent into a rectangular loop 15 cm ×15 cm is placed perpendicular to the magnetic
field whose flux density is 0.8 Wbm −2 . Within 1.0 second, the loop is changed into a 10 cm square and
flux density increases to 1.4 Wbm −2 . Calculate the value of induced emf.
Ans. –0.008 V
18. The magnetic flux through a coil perpendicular to its plane and directed into paper is varying
according to the relation φ = ( 5t 2 + 10t + 5 ) milliweber. Calculation the emf induced in the loop at
t = 5 s.
Ans. 0.06V
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19. A resistor of 1Ω and an inductor of 1 H are connected in series across a source of 10 V. Suppose the
current in the circuit is changing by the added device. Find the net emf of the circuit when
di di 1Ω 1V 1H
(a) = +5 A/s, (b) = −5 A/s
dt dt
Ans: (a) 5V (b) 15V
20. A 12 H inductor carries a steady current of 2.0 a. How can a 60 V self-induced emf be made to appear
in the inductor?
Ans: 5 A/s
21. The magnitude field through a circular loop of wire 12cm in radius and 8.5 Ω resistance, charges with
time as shown in the figure. The magnitude field is perpendicular to the plane of the loop. Calculate
the induced current in the loop and plot it as a function of time.

B(T)
2
1

O 2 4 6 t(s)
Ans: -0.0026A, 0, +0.0026A
22. A square metal wire loop of side 20cm and resistance 2Ω is moved with a constant velocity v0 in a
uniform magnetic field of induction B = 1Wb / m 2 as shown in the figure. The magnetic field lines are
perpendicular to the plane of the loop. The loop is connected to a network of resistance each of value
5Ω . The resistances of the lead wire BF and AE are negligible. What should be the speed of the loop,
so as to have a steady current of 2mA in the loop ? Give the direction of current in the loop.
E
A 5Ω 5Ω
l v0 C D
5Ω
B 5Ω 5Ω
F
Ans: 7cm/s
23. A square loop MNOP of side 20cm is placed horizontally in a magnetic field acting vertically
downwards as shown in the figure. The loop is pulled with a constant velocity of 20 cms -1 till it goes
out of the field.
M 20cm N

v
P O
1m
(i) Depict the direction of the induced current in the loop as it goes out of the field. For how long
would the current in the loop persist ?
(ii) Plot a graph showing the variation of magnetic flux and induced emf as a function of time.
Ans: (a) 1s (b) self
24. The current through two inductor of self inductance 15mH and 25mH is increasing with time at the
same rate. Draw graphs showing the variation of the:
(i) emf induced with the rate of change of current.
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(ii) magnetic flux with current.
(iii) energy stored in each inductor with the current flowing through it.
(iv) energy stored in each inductor with the current flowing through it.
Compare the energy stored in the coils, if the powers dissipated in the coils are same.
Ans: self
25. The current flowing in the two coils of self-inductance L1 = 16mH and L1 = 12mH are increasing at the
same rate. If the power supplied to the two coils are equal, find the ratio of (i) induced voltage, (ii) the
current and (iii) the energies stored in the two coils at a given instant.
Ans: (i) 4/3 (ii) 3/4 (iii) 3/4
26. The current through two inductance of self-inductance 15mH is increasing with time at the same rate.
Draw graphs showing the variation of the:
(i) emf induced with the rate of change of current.
(ii) energy the energy stored in the coils, if the powers dissipated in the coil are same.
Ans: Self
27. There are two coils, which have mutual inductance of 10 H. When the circuit is closed, current in the
primary coil is raised to 3A within a time range of 1 millisecond. Calculate the emf induced in
secondary coil.
Ans: 3 × 104 V