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Q. A very small circular loop of radius $a$ is initially $(at\, t\, =\,0)$ coplanar and concentric with a much larger fixed circular loop of radius $b. A$ constant current $I$ flows in the larger loop. The smaller loop is rotated with a constant angular speed $\omega$ about the common diameter. The emf induced in the smaller loop as a function of time $t$ is

WBJEEWBJEE 2014Electromagnetic Induction

Solution:

We know that $\tau=N B A \omega \sin \omega t$
where $N= $ number of loops $=1 $
$ B=\frac{\mu_{0} I}{2 b} $ newton/amp-m
$ A=\pi a^{2} \text { metre }^{2} $
$\therefore \tau=\frac{\mu_{0} I}{2 b}\left(\pi a^{2}\right) \omega \sin \omega t $
$ =\frac{\pi a^{2} \mu_{0} I}{2 b} \cdot \omega \sin \omega t$