NCERT Solutions Class 12 Physics Chapter 6 Electromagnetic Induction Download In Pdf

Chapter 6 Electromagnetic Induction Download in pdf

**Question 6.1** Predict the direction of induced current in the situations described
by the following Figs. 6.18(a) to (f ).

**Question 6.2** Use Lenz’s law to determine the direction of induced current in the
situations described by Fig. 6.19:

(a) A wire of irregular shape turning into a circular shape;

(b) A circular loop being deformed into a narrow straight wire.

**Question 6.3** A long solenoid with 15 turns per cm has a small loop of area 2.0 cm2
placed inside the solenoid normal to its axis. If the current carried
by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is
the induced emf in the loop while the current is changing?

**Question 6.4 **A rectangular wire loop of sides 8 cm and 2 cm with a small cut is
moving out of a region of uniform magnetic field of magnitude 0.3 T
directed normal to the loop. What is the emf developed across the
cut if the velocity of the loop is 1 cm s–1 in a direction normal to the (a) longer side, (b) shorter side of the loop? For how long does the
induced voltage last in each case?

**Question 6.5** A 1.0 m long metallic rod is rotated with an angular frequency of
400 rad s–1
about an axis normal to the rod passing through its one
end. The other end of the rod is in contact with a circular metallic
ring. A constant and uniform magnetic field of 0.5 T parallel to the
axis exists everywhere. Calculate the emf developed between the
centre and the ring.

**Question 6.6** A circular coil of radius 8.0 cm and 20 turns is rotated about its
vertical diameter with an angular speed of 50 rad s–1 in a uniform
horizontal magnetic field of magnitude 3.0 × 10–2 T. Obtain the
maximum and average emf induced in the coil. If the coil forms a
closed loop of resistance 10 Ω, calculate the maximum value of current
in the coil. Calculate the average power loss due to Joule heating.
Where does this power come from?

**Question 6.7** A horizontal straight wire 10 m long extending from east to west is
falling with a speed of 5.0 m s–1, at right angles to the horizontal
component of the earth’s magnetic field, 0.30 × 10–4 Wb m–2.

(a) What is the instantaneous value of the emf induced in the wire?

(b) What is the direction of the emf?

(c) Which end of the wire is at the higher electrical potential?

**Question 6.8** Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf
of 200 V induced, give an estimate of the self-inductance of the circuit.

**Question 6.9 **A pair of adjacent coils has a mutual inductance of 1.5 H. If the
current in one coil changes from 0 to 20 A in 0.5 s, what is the
change of flux linkage with the other coil?

**Question 6.10** A jet plane is travelling towards west at a speed of 1800 km/h. What
is the voltage difference developed between the ends of the wing

ADDITIONAL EXERCISES QUESTIONS

**Question 6.11** Suppose the loop in Exercise Question 6.4 is stationary but the current
feeding the electromagnet that produces the magnetic field is
gradually reduced so that the field decreases from its initial value
of 0.3 T at the rate of 0.02 T s–1. If the cut is joined and the loop
has a resistance of 1.6 Ω, how much power is dissipated by the
loop as heat? What is the source of this power?

**Question 6.12** A square loop of side 12 cm with its sides parallel to X and Y axes is
moved with a velocity of 8 cm s–1 in the positive x-direction in an
environment containing a magnetic field in the positive z-direction.
The field is neither uniform in space nor constant in time. It has a
gradient of 10 –3 T cm–1
along the negative x-direction (that is it increases
by 10 – 3 T cm–1
as one moves in the negative x-direction), and it is
decreasing in time at the rate of 10 –3 T s–1. Determine the direction and
magnitude of the induced current in the loop if its resistance is 4.50 mΩ.

**Question 6.13 **It is desired to measure the magnitude of field between the poles of a
powerful loud speaker magnet**. A **small flat search coil of area 2 cm2
with 25 closely wound turns, is positioned normal to the field
direction, and then quickly snatched out of the field region.
Equivalently, one can give it a quick 90° turn to bring its plane
parallel to the field direction). The total charge flown in the coil
(measured by a ballistic galvanometer connected to coil) is
7.5 mC. The combined resistance of the coil and the galvanometer is
0.50 Ω. Estimate the field strength of magnet.

**Question 6.14** Figure 6.20 shows a metal rod PQ resting on the smooth rails AB
and positioned between the poles of a permanent magnet. The rails,
the rod, and the magnetic field are in three mutual perpendicular
directions. A galvanometer G connects the rails through a switch K.
Length of the rod = 15 cm, B = 0.50 T, resistance of the closed loop
containing the rod = 9.0 mΩ. Assume the field to be uniform.

(a) Suppose K is open and the rod is moved with a speed of 12 cm s–1
in the direction shown. Give the polarity and magnitude of the
induced emf. experience magnetic force due to the motion of the rod. Explain.

(d) What is the retarding force on the rod when K is closed?

(e) How much power is required (by an external agent) to keep
the rod moving at the same speed (=12 cm s–1) when K is closed?
How much power is required when K is open?

(f ) How much power is dissipated as heat in the closed circuit?
What is the source of this power?

(g) What is the induced emf in the moving rod if the magnetic field
is parallel to the rails instead of being perpendicular?

**Question 6.15** An air-cored solenoid with length 30 cm, area of cross-section 25 cm2
and number of turns 500, carries a current of 2.5 A. The current is
suddenly switched off in a brief time of 10–3 s. How much is the average
back emf induced across the ends of the open switch in the circuit?
Ignore the variation in magnetic field near the ends of the solenoid.

**Question 6.16** (a) Obtain an expression for the mutual inductance between a long
straight wire and a square loop of side a as shown in Fig. 6.21.

(b) Now assume that the straight wire carries a current of 50 A and
the loop is moved to the right with a constant velocity, v = 10 m/s.
Calculate the induced emf in the loop at the instant when x = 0.2 m.
Take a = 0.1 m and assume that the loop has a large resistance.

**Question 6.17** A line charge λ per unit length is lodged uniformly onto the rim of a
wheel of mass M and radius R. The wheel has light non-conducting
spokes and is free to rotate without friction about its axis (Fig. 6.22).
A uniform magnetic field extends over a circular region within the
rim. It is given by,
B = – B0 k (r ≤ a; a < R)
= 0 (otherwise)
What is the angular velocity of the wheel after the field is suddenly
switched off?

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- Chapter 1 Electric Charges and Fields
- Chapter 2 Electrostatic Potential and Capacitance
- Chapter 3 Current Electricity
- Chapter 4 Moving Charges and Magnetism
- Chapter 5 Magnetism and Matter
- Chapter 6 Electromagnetic Induction
- Chapter 7 Alternating Current
- Chapter 8 Electromagnetic Waves
- Chapter 9 Ray Optics and Optical Instruments
- Chapter 10 Wave Optics
- Chapter 11 Dual Nature of Radiation and Matter
- Chapter 12 Atoms
- Chapter 13 Nuclei
- Chapter 14 Semiconductor Electronics: Materials, Devices and Simple Circuits
- Chapter 15 Communication Systems

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