$\text{ At time t , the smaller loop will rotate by an angle of }\omega t.$

$\text{ Angle between B and A will be } \omega t$

$ \text{Flux passing through smaller coil is }\phi = BAsin\omega t = \frac{\mu_0 I}{2R} \pi r^2 cos\omega t $

$\text{ EMF Induced is } \xi = \frac{-d\phi}{dt} = \frac{\mu_0 I}{2R}\omega \pi r^2 cos\omega t $