Two long fixed parallel vertical conducting rails AB and CD are separated by a distance L. They are connected by resistance R and a capacitance C at two ends as shown in the figure. There is a uniform magnetic field B directed horizon- tally into the plane of the figure. A horizontal metallic bar of length L and mass m can slide without friction along the rails. The bar is released from rest at t = 0. Neglect resistance of bar and rails and also neglect the self inductance of the loop.
(a) Find the maximum speed acquired by the bar after it is released.
(b) Find the speed of the bar as a function of time t.

Answer

(a) `(mgR)/(B^(2)L^(2))`
(b) `v = (mgR)/(B^(2)L^(2)) [1-e^(-(B^(2)L^(2)t)/(R(m+B^(2)L^(2)C)))]`