Chapter 29, Problem 29.51P

In Fig. P29.51 the loop is being pulled lo the right at constant speed ʋ. A constant current I flows in the long wire, in the direction shown. (a) Calculate the magnitude of the net emf ε induced in the loop. Do this two ways: (i) by using Faraday’s law of induction (Hint: See Exercise 29.7) and (ii) by looking at the emf induced in each segment of the loop due to its motion. (b) Find the direction (clockwise or counterclockwise) of the current induced in the loop. Do this two ways: (i) using Lenz’s law and (ii) using the magnetic force on charges in the loop. (c) Check your answer for the emf in part (a) in the following special cases to see whether it is physically reasonable: (i) The loop is stationary; (ii) the loop is very thin, so a → 0; (iii) the loop gets very far from the wire.

Figure P29.51