A circular wire loop of radius can slide without friction on two long
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A circular wire loop of radius r can slide without friction on two long, parallel, horizontal conducting rails that are connected through a resistor R. The region contains a uniform vertical magnetic field of magnitude B. The rails are pulled apart slowly and symmetrically so that the radius of the loop increases at a constant rate k (the loop remains circular). Neglect the resistance of the rails and the sliding contact.
(a) Derive an expression for the induced current in the loop in terms of B, r, k, and R at any instant.
(b) Show that the mechanical power required to pull the rails apart equals the electrical power i2R dissipated in the resistor.
(c) If B=0.30T, r=0.12m, k=1.5×10−3m s−1 and R=3.0Ω, calculate the magnitude of the force that must be exerted on each rail (assume symmetric pulling) to maintain the constant rate k. Treat the force as acting tangentially to the motion of the rails.