b
(b) In a constant magnetic field conducting ring oscillates with a frequency of \(100 \,Hz\).
i.e. \(T = \frac{1}{{100}}s,\)in time \(\frac{T}{2}\) flux links with coil changes from \(BA\) to zero

. ==> Induced emf = \(\frac{{{\rm{change in flux}}}}{{{\rm{time}}}}\)
\( = \frac{{BA}}{{T/2}} = \frac{{2BA}}{T}\) \( = \frac{{2B \times \pi {r^2}}}{T}\)\( = \frac{{2 \times 0.01 \times \pi \times {1^2}}}{{1/100}} = 4\pi V\)

Induced electric field along the circle, using Maxwell equation \(\oint {E.dl = - \frac{{d\phi }}{{dt}}} \)\( = A\frac{{dB}}{{dt}} = e\)

==> \(E = \frac{1}{{2\pi r}} \times \left( {\pi {r^2} \times \frac{{dB}}{{dt}}} \right) = \frac{e}{{2\pi r}} = \frac{{4\pi }}{{2\pi r}} = 2\,V/m\)