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A very small circular loop of radius \( a \) is initially coplanar and concentric with a much larger circular loop of radius \( b(a) \). 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 a diameter. The resistance of the small loop is \( R \) and its inductance is negligible.
The induced emf in the large loop due to current induced in smaller loop as a function of time is equal to
\( \frac{1}{x}\left(\frac{\pi a^{2} \mu_{0} \omega}{b}\right)^{2} \frac{I \cos 2 \omega t}{R} \). Find out value of \( x \)
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