A very small circular loop of radius \(a\) is initially (at \(t=0\) ) coplanar and concentric with a much larger fixed circular loop of radius b. A constant current \(I\) flows in the larger loop. The smaller loop is rotated with a constant angular speed \(\omega\) about the common diameter. The emf induced in the smaller loop as a function of time \(t\) is

1. A \(\frac{\pi a^{2} \mu_{0} l}{2 b} \omega \cos (\omega t)\)
2. B \(\frac{\operatorname{\pi a}^{2} \mu_{0}l}{2 b} \omega \sin \left(\omega^{2} t^{2}\right)\)
3. C \(\frac{\pi a^{2} \mu_{0} l}{2 b}\) \(\omega sin\) \((\omega t)\)
4. D \(\frac{\pi a^{2} \mu_{0}l}{2 b} \omega \sin ^{2}(\omega t)\)