Find the current in the sliding rod AB (resistance = R).

Question:

 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.

Solution:

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.

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