Induced Emf in smaller loop $\xi = \pi a^2 \frac{dB}{dt} = \pi a^2 \frac{\mu_0 }{2b} \frac{dI}{dt}$

$\Rightarrow \text{Induced current } i = \frac{\xi}{R} = \frac{dq}{dt}$

$\Delta q = \pi a^2 \frac{\mu_0 }{2bR} I= \frac{\mu_0 I \pi a^2}{2Rb}$