A wire having mass m and length l 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. Then, the acceleration of the wire can be given as?

Correct option is D. a=F/(m+CB²l²)
Due to the movement of the rail with instantaneous velocity v, the e.m.f produced across the capacitor, V=Bvl
Charge stored in the capacitor = q = CV = CBvl
Therefore the current through the capacitor, i = dq/dt = CBl(dv/dt) = CBla
This same current passes through the wire.
Hence the magnetic force on it, F' = Bil = CB²l²a
Hence, ma = F - F'
=> ma = F - CB²l²a
=> a = F/(m+CB²l²)