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.

• A
  $\frac{\mu_0 I}{2R} \omega r^2 \sin \omega t$
• B
  $\frac{\mu_0 I}{4R} \omega \pi r^2 \sin \omega t$
• C
  $\frac{\mu_0 I}{2R} \omega \pi r^2 \sin \omega t$
• D
  $\frac{\mu_0 I}{4R} \omega r^2 \sin \omega t$