Find the current in the sliding rod AB (resistance = R). B is constant and is out of the paper. Parallel wires have no resistance. v is constant. Switch S is closed at time t = 0.
The current induced in the loop is It = ε/R
It = 1/R.d/dt BA
It = vBd/R
The angle between B and A is zero.
As the switch S is closed at t = o,
Charge through the capacitor, is Q(t) = Cv
Current through the capacitor, I(c) = Q(t)/RC
Using the above information, we can calculate the current through the circuit as I = BvdC/RC e –t/RC.