Halliday, Resnick & Walker — Induction and Inductance: Problem 3

3 The conducting rod shown in Fig. 30-21 has length L and is being pulled along horizontal, frictionless conducting rails at a constant velocity \(\vec{v}\). The rails are connected at one end with a metal strip. A uniform magnetic field \(\vec{B}\), directed out of the page, fills the region in which the rod moves. Assume that \(L = 10 \text{ cm}\), \(v = 5.0 \text{ m/s}\), and \(B = 2.4 \text{ T}\). What are the (a) magnitude and (b) direction (up or down the page) of the emf induced in the rod? What are the (c) size and (d) direction of the current in the conducting loop? Assume that the resistance of the rod is \(0.40 \, \Omega\) and that the resistance of the rails and metal strip is negligibly small. (e) At what rate is thermal energy being generated in the rod? (f) What external force on the rod is needed to maintain \(\vec{v}\)? (g) At what rate does this force do work on the rod? (h) What is the magnitude of the magnetic force on the rod?