**Problem 1:** Two identical coils A and B of 500 turns each has parallel planes such that 70% of flux produced by one coil links with the other. A current of 6 Amp flowing in coil A produces a flux of 0.06 Wb in it. If the current in coil A changes from 10 A to -10 A in .03 s, calculate (a) the mutual inductance and (b) the emf induced in coil B.

**Problem 2:** A wheel with 12 metal spokes each 0.6 m long with a speed of 180 r.p.m in a plane normal to earth’s magnetic field at a place. If the magnitude of the field is 0.6 G, what is the magnitude of the induced emf between the axle and rim of the wheel.

**Problem 3:** A circuit has 1000 turns enclosing a magnetic circuit 20 cm^{2} in section. With 4 A current, the flux density is 1 Wbm^{-2} and with 9 A current, it is 1.4 Wbm^{-2}. Find the mean value of the inductance between these current limits and the induced emf if the current falls from 9 A to 4 A in 0.05 s.

**Problem 4:** A coil of resistance 100 ohms is placed in a magnetic field of 1 mWb. The coil has 100 turns and a galvanometer of 400 ohms is connected in series with it. Find the average emf and the current if the coil is moved is 1/10th from the given field to a field of 0.2 mWb.

**Problem
5:** A horizontal straight wire 10 m long extending from east to west is
falling with a speed of 5 m/sec at right angle to the horizontal component of
the earth’s magnetic field of 0.3 × 10^{-4} Wb/m^{2}.

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

(b) What is the direction of emf?

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

**Problem 6**: Current in a circuit falls from 5.0 A to 0 A in 0.1 s. If an average emf of 200 V induced, give an estimate of the self-inductance of the circuit?

**Problem 7:** A long solenoid with 15 turns / cm has a small loop of area 2.0 cm^{2} placed inside the solenoid normal to its axis. If the current created by the solenoid changes steady from 2.0 A to 4.0 Amp in 0.1 s. What is the induced emf in the loop when the current is changing.

**Problem 8:** 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 cms^{-1} in a direction normal to (a) longer side (b) shorter side of the loop? For how long does the induced voltage lasts in each case?

**Problem 9:** A 90 mm length of wire moves with an upward velocity of 35 m/s between the poles of a magnet. The magnetic field is 80 mT directed to the right. If the resistance in the wire is 5.00 m ohms, what are the magnitude and direction of the induced current?

**Problem 10:** 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?

**Problem 11:** The back emf in a motor is 120 V when the motor is turning at 1680 rev/min. What is the back emf when the motor turns at 3360 rev/min?

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