$A$ 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

• A
  $\frac{\pi a^{2} \mu_{0} I}{2 b} \omega \cos (\omega t)$
• B
  $\frac{\pi a^{2} \mu_{0} I}{2 b} \omega \sin (\omega^{2} t^{2})$
• C
  $\frac{\pi a^{2} \mu_{0} I}{2 b} \omega \sin (\omega t)$
• D
  $\frac{\pi a^{2} \mu_{0} I}{2 b} \omega \sin^{2} (\omega t)$