# NCERT Physics Class 12 Exemplar Ch 6 Electromagnetic Inductions Part 3

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## Long Answer

Q 22 A magnetic field covers a large region where a wire AB slides smoothly over two parallel conductors separated by a distance d. The wires are in the x-y plane. The wire AB (of length d) has resistance R and the parallel wires have negligible resistance. If AB is moving with velocity v, what is the current in the circuit? What is the force needed to keep the wire moving at constant velocity?

Ans:

Let us assume that the parallel wires at are and. At , AB has and moves with a velocity .

At time t, wire is at.

Motional e.m.f.).

E.m.f due to change in field (along OBAC)

Total e.m.f

Along OBAC, Current (clockwise)

Force needed along

t.

Q 23. A conducting wire XY of mass m and negligible resistance slides smoothly on two parallel conducting wires as shown in. The closed circuit has a resistance R due to AC. AB and CD are perfect conductors. There is a magnetic field .

(i) Write down equation for the acceleration of the wire XY.

(ii) If B is independent of time, obtain , assuming.

(iii) For (b), show that the decrease in kinetic energy of XY equals the heat lost in R.

Ans:

Let the wire be at at time t.

Flux

(Second term due to motional emf)

Force

(ii)

At

(iii)

Power lost

= decrease in kinetic energy.