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  • Find the current in the sliding cod AB (resistance = R) for the arrangement shown in figure. 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.

Find the current in the sliding cod AB (resistance = R) for the arrangement shown in the figure. B is constant and is out of the paper. Parallel wires have no resistance, and v is constant. Switch S is closed at time t = 0.

Answers (1)

Explanation:-

According to Faraday's Law of Induction, an electromotive force (EMF) is induced in the rod due to its motion in the magnetic field.

By applying KVL in the given circuit, we have

-L\frac{dI}{dt}+vBd=IR\; or\; L\frac{dI}{dt}+IR=vBd

This is the linear differential equation. On solving,

I=\frac{vBd}{R}+Ae^{-\frac{Rt}{ L}}

At \; t=0, I=0

\Rightarrow A=-\frac{vBd}{R}\Rightarrow I=\frac{vBd}{R}\left ( 1-e^{\frac{-Rt}{L}} \right )

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