A conducting ring of radius 1 m is placed in an uniform magnetic field B of 0.01 T oscillating with frequency 100 Hz with its plane at right angles to B. What will be the induced electric field?

In a constant magnetic field, conducting ring oscillates with a frequency of 100 Hz.

i.e., $T=\frac{1}{100}\mathrm{s},$ in time $\frac{T}{2}$ flux links with coil changes from BA to zero.

$\Rightarrow \text{ Induced emf, }e=\frac{\text{ Change in flux }}{\text{ Time }}$

$=\frac{BA}{T/2}=\frac{2BA}{T}=\frac{2B\times \pi r^2}{T}=\frac{2\times 0.01\times \pi \times 1^2}{1/100}=4\pi \mathrm{V}$

Induced electric field along the circle, using Maxwell equation $\text{∮ }\mathrm{E}.\mathrm{dl}=-\frac{\mathrm{d\varphi }}{\mathrm{dt}}=-\mathrm{A}\frac{\mathrm{dB}}{\mathrm{dt}}=\mathrm{e}$

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