A small circular loop of wire of radius \(a\) is located at the centre of a much larger circular wire loop of radius \(b\). The two loops are in the same plane. The outer loop of radius \(b\) carries an alternating current \(I = I_0\, cos\, (\omega t)\) . The emf induced in the smaller inner loop is nearly

1. A \(\frac{{\pi {\mu _0}{I_0}}}{2}.\frac{{{a^2}}}{b}\omega \,\sin \,\left( {\omega t} \right)\)
2. B \(\frac{{\pi {\mu _0}{I_0}}}{2}.\frac{{{a^2}}}{b}\omega \,\cos \,\left( {\omega t} \right)\)
3. C \(\pi {\mu _0}{I_0}\,\frac{{{a^2}}}{b}\omega \,\sin \,\left( {\omega t} \right)\)
4. D \(\frac{{\pi {\mu _0}{I_0}{b^2}}}{a}\,\omega \,\cos \,\left( {\omega t} \right)\)