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

1. A \(\frac{{{\mu _0}I}}{{2R}}\,\omega {r^2}\,\sin \,\omega t\)
2. B \(\frac{{{\mu _0}I}}{{4R}}\,\omega \pi {r^2}\,\sin \,\omega t\)
3. C \(\frac{{{\mu _0}I}}{{2R}}\,\omega \pi {r^2}\,\sin \,\omega t\)
4. D \(\frac{{{\mu _0}I}}{{4R}}\,\omega {r^2}\,\sin \,\omega t\)