A light, conducting rod of length and mass is free to slide without friction on two…
PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A light, conducting rod of length ℓ and mass m is free to slide without friction on two long, parallel, conducting rails that are separated by the same distance ℓ. The rails lie in a vertical plane making an angle θ with the horizontal. Their lower ends are joined by a resistor of resistance R. A uniform magnetic field of magnitude B is directed horizontally and is perpendicular to the plane of the rails.
(i) Starting from Newton’s second law and the laws of electromagnetic induction, obtain an expression for the instantaneous acceleration a of the rod when its speed is v down the rails.
(ii) Show that the rod eventually attains a constant terminal speed vt and find vt in terms of the given symbols.
(iii) Write expressions for (a) the rate at which gravitational potential energy is lost at terminal speed and (b) the rate of thermal energy generation in the resistor. Prove that these two rates are equal, thereby justifying the conservation of energy for the system.