GATE EC 1998 Electromagnetics Solution Q 7

GATE EC 1998 Electromagnetics Solution Q 7

A loop is rotating about the y-axis in a magnetic field \overrightarrow B=B_0\cos\left(\omega t+\phi\right){\widehat a}_xT. The voltage in the loop is

(a) zero

(b) due to rotation only

(c) due to transformer action only

(d) due to both rotation and transformer action

Ans : d)

Explanation

The voltage induced in a loop moving with velocity ‘v’ in a steady magnetic field is given by:-

V_m=\oint\left(\overrightarrow v\times\overrightarrow B\right)\cdot\overrightarrow{dl}

This is called generator action.

The voltage induced in a stationary loop due to time changing magnetic field is given by Transformer action (Faraday’s Law)

V_t=-\int_s\frac{\partial\overrightarrow B}{\partial t}.\overrightarrow{ds}

So, the voltage induced in the loop is due to both rotation and transformer action.

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