At the centre of a fixed large circular coil of radius $R$, a much smaller circular coil of radius $r$ is placed. The two coils are concentric and are in the same plane. The larger coil carries a current $I$. The smaller coil is set to rotate with a constant angular velocity $\omega$ about an axis along their common diameter. Calculate the emf induced in the smaller coil after a time $t$ of its start of rotation.
Answer: (C) $\dfrac{\mu_0I}{2R}\omega\pi r^2\sin\omega t$
The small coil sits in the nearly uniform field at the centre of the large coil, $B = \dfrac{\mu_0I}{2R}$. Starting in the same plane, after time $t$ its normal makes angle $\omega t$ with $\vec B$:
$$\phi = \frac{\mu_0I}{2R}\,\pi r^2\cos\omega t$$
$$\varepsilon = -\frac{d\phi}{dt} = \frac{\mu_0I}{2R}\,\omega\pi r^2\sin\omega t$$
Solution by Sreeraj P, M.Sc Physics