Figure (38-E8) shows a circular coil of \( N \) turns and radius \( a \), connected to a battery...

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Figure (38-E8) shows a circular coil of \( N \) turns and radius \( a \), connected to a battery of emf \( \varepsilon \) through a rheostat. The rheostat has a total length \( L \) and resistance \( R \). The resistance of the coil is \( r \). A small circular loop of radius \( a^{\prime} \) and resistance \( r^{\prime} \) is placed coaxially with the coil. The centre of the loop is at a distance \( x \) from the centre of the coil. In the beginning, the sliding contact of the rheostat is at the left end and then onwards it is moved towards right at a constant speed \( v \). Find the emf induced in the small circular loop at the instant (a) the contact begins to slide and (b) it has slid through half the length of the rheostat.
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