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 $I=I_o \cos\; (ωt)$. The emf induced in the smaller inner loop is nearly :

Question

$\begin{array}{1 1}(1)\; \frac{\pi \mu_0I_0}{2}. \frac{a^2}{b} \omega \sin (\omega t) \\ (2)\;\frac{\pi \mu_0I_0}{2}. \frac{a^2}{b} \omega \cos (\omega t) \\ (3)\; \pi \mu_0I_0 \frac{a^2}{b} \omega \sin (\omega t) \\ (4)\;\frac{\pi \mu_0I_0b^2}{a} \omega \sin (\omega t) \end{array}$