Two long, frictionless conducting rails are fixed on an incline that makes an angle…
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
Two long, frictionless conducting rails are fixed on an incline that makes an angle θ with the horizontal. The rails are separated by a distance ℓ and are connected at the bottom by a resistor of resistance R. A conducting rod of mass m and negligible resistance rests on the rails and is released from rest. A uniform magnetic field of magnitude B fills the entire region and is directed perpendicular to the plane of the incline (into the surface).
Neglect air resistance. Gravitational acceleration is g.
(a) Derive an expression for the magnitude of the induced emf in the rod when it is moving with speed v down the incline.
(b) Show that the instantaneous acceleration a of the rod can be written in the form a=gsinθ−mR(Bℓ)2v.
(c) Solve for the terminal speed vt that the rod approaches after a long time.
(d) Determine the rate at which electrical energy is dissipated in the resistor when the rod moves at terminal speed, and verify that this equals the rate at which the component of gravitational potential energy is being lost.
(e) After the rod has reached terminal speed, calculate the total distance it travels in an additional time interval Δt and the corresponding additional electrical energy converted in the resistor during that time.