A light, perfectly conducting rod of length is free to slide without friction on two…
PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A light, perfectly conducting rod of length l=0.50m is free to slide without friction on two long, horizontal, parallel rails that are l metres apart. The rails are connected at one end through a load resistance R=2Ω. A uniform magnetic field of magnitude B=0.80T is directed vertically downwards, perpendicular to the plane of the rails. At the instant shown, the rod is pulled to the right with a steady speed v=3.0ms−1 by a mechanical force applied parallel to the rails.
(i) Derive an expression for the magnitude of the emf induced between the ends of the rod in terms of B, l and v.
(ii) Using the result of part (i), calculate the induced current in the circuit and state its direction in the rails.
(iii) Determine the magnitude and direction of the magnetic force acting on the rod due to the induced current.
(iv) Hence find the mechanical power that must be supplied to keep the rod moving at the given constant speed.
(v) Show that the mechanical power obtained in part (iv) is equal to the electrical power dissipated in the resistor.