A coil of area $100 c{m}^2$ is kept at an angle of 30° with a magnetic field of ${10}^{-1} T$. The magnetic field is reduced to zero in ${10}^{-4} s$. The induced emf in the coil is –

Given in time t=10^-4, magnetic field reduced to zero
$\mathrm{\epsilon }=-\frac{\mathrm{d\varphi }}{\mathrm{dt}}=-\frac{\mathrm{d}}{\mathrm{dt}}(\mathrm{B}\cdot \mathrm{Acos}\mathrm{\theta })=-A\sin \mathrm{\theta }\frac{\mathrm{dB}}{\mathrm{dt}}$
Here, coil is kept at 30° with field so area vector of coil will have 60° with magnetic field.

For magnitude, $\mathrm{\epsilon }=A\sin \mathrm{\theta }\left|\frac{\mathrm{dB}}{\mathrm{dt}}\right|=\left(100\times {10}^{-4}\right)\sin {60}^{\circ }\left|\frac{\left(0-{10}^{-1}\right)}{{10}^{-4}}\right|=5\sqrt{3}\mathrm{V}$