Halliday, Resnick & Walker — Induction and Inductance: Problem 55

55 Figure 30-46 shows a rod of length $L = 12.0 \text{ cm}$ that is forced to move at constant speed $v = 5.00 \text{ m/s}$ along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has resistance $0.400 \text{ }\Omega$; the rest of the loop has negligible resistance. A current $i = 100 \text{ A}$ through the long straight wire at distance $a = 5.00 \text{ mm}$ from the loop sets up a (nonuniform) magnetic field through the loop. Find the (a) emf and (b) current induced in the loop. (c) At what rate is thermal energy generated in the rod? (d) What is the magnitude of the force that must be applied to the rod to make it move at constant speed? (e) At what rate does this force do work on the rod?