A very small circular loop of radius $a$ is initially coplanar and concentric with a much larger circular loop of radius $b$. A constant current $i$ is passed in the large loop which is kept fixed in space and the small loop is rotated with constant angular velocity $\omega$ about its diameter. The resistance of the small loop is $R$ and negligible $L$.

The induced emf in the large loop due to current induced in a smaller loop as a function of time is equal to $${\dfrac{1}{x}}\cdot \bigg(\dfrac{\pi a^2\mu_{o}\omega}{b}\bigg)^2\dfrac{i\cos2\omega t}{R}$$Find out $x$

For factor $\bigg(\dfrac{\pi a^2\mu_o\omega}{b}\bigg)^2$, I've got $\dfrac{(\pi a^2\mu_o\omega)^2}{4ab}$, not $b^2$.

I got, $i_a=\dfrac{\omega\mu_o i}{2bR}\cdot\pi a^2\sin\omega t$.

Now this will produce flux change through bigger loop,

$$\phi_b=\dfrac{\mu_o i_a}{2a}\cdot\pi a^2\cos\omega t=\dfrac{\mu_o}{2a}\cdot\bigg(\dfrac{\omega\mu_o i}{2bR}\cdot\pi a^2\sin\omega t\bigg)\cdot\pi a^2\cos\omega t$$ $$e_b={\dfrac{1}{4}}\cdot \dfrac{(\pi a^2\mu_o \omega)^2}{ab}\cdot\dfrac{i\cos2\omega t}{R}$$