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 angle between A and B = 0o

Therefore, the emf is Bvd.

-LdI(t)/dt + Bvd = IR

LdI(t)/dt + RI (t) = Bvd

Solving the equation, we get

I = Bvd/R [1-e-Rt/2]

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