Question

A very small circular loop of radius $a$ is initially $(att=0)$ 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

• A. $\frac{\pi a^2{\mu }_{o}I}{2b}\omega cos\left(\omega t\right)$
• B. $\frac{\pi a^2{\mu }_{o}I}{2b}\omega sin\left({\omega }^2{t}^2\right)$
• C. $\frac{\pi a^2{\mu }_{o}I}{2b}\omega sin\left(\omega t\right)$
• D. $\frac{\pi a^2{\mu }_{o}I}{2b}\omega si{n}^2\left(\omega t\right)$

Answer 1

Answer: (C)

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