A wire of mass m and length I can freely slide on a pair of parallel, smooth, horizontal rails placed in a vertical magnetic field B . The rails are connected by a capacitor of capacitance C. The electric resistance of the rails and the wire is zero. If a constant force F acts on the wire as shown in the figure, find the acceleration of the wire.

Explanation

Suppose the velocity of the wire is v at time t
The induced emf is epsilon = vBl
As there is no resistance anywhere, the charge on the capacitor will be ` q =Cepsilon = C v Bl` at time t
The current in the circuit will be a magnetic force `F ` = ilB = CB^2 l^2a towards left
The net force on the wire is `F - F' From Newton's law, `F -F' = ma or, F- Cb^2 l^2 a = ma or, `a= (F)/(m+CB^2l^2)