Question

A conducting rod AB of mass m slides without friction over two long conducting rails separated by a distance l (Fig. 3.88). At the left end the rails are interconnected by a resistance R. The system is located in a uniform magnetic field perpendicular to the plane of the loop. At the moment t = 0 the rod AB starts moving to the right with an initial velocity v0. Neglecting the resistances of the rails and the rod AB, as well as the self-inductance, find:

(a) the distance covered by the rod until it comes to a standstill;

(b) the amount of heat generated in the resistance R during this process.

Answer 1

(a) The flux through the loop changes due to the movement of the rod AB. Recording to Lenz’* law current should be anticlockwise in sense as we have assumed vector B is directed into the plane o f the loop. The motion e.m .f

and, induced current

From Newton’* law in projection form fx = mwx

(b) From equation of energy conservation; Ef - Ei + Heat liberated = Acell + Aext