A metal bar of length L is attached to two vertical metal rails as sketched in Figure P21.24. The connections are frictionless, but allow current to flow between the rails and the bar. A constant horizontal magnetic field is directed perpendicular to the area enclosed by the bar and rails.
(a) What closed path should we use for applying Faraday’s law to find the current induced in the bar?
(b) Suppose the bar is at height z above the bottom. Find the magnitude and direction of the magnetic flux B.
(c) If the bar is moving downward at speed v, is the flux in part (b) increasing or decreasing with time?
(d) What is the induced emf across the bar?
(e) Use your answer to part (d) to get the current I in the circuit. Be sure to give the direction of I.
(f) Now find the magnetic force on the bar. Notice that the magnitude of this force increases as v increases.
(g) What is the direction of the force on the bar?
(h) If the bar has mass m, there will also be a gravitational force on the bar. Eventually, the bar will reach a speed v at which the gravitational and magnetic forces cancel so that the total force on the bar is zero. Find v.

Transcribed Image Text:

-L- Metal bar х В R Figure P21.24