A coil having an area $A_{0}$ is placed in a magnetic field which changes from $B_{0}$ to $4 B_{0}$

Question

A coil having an area $A_{0}$ is placed in a magnetic field which changes from $B_{0}$ to $4 B_{0}$ in time interval $t$. The emf induced in the coil will be\

Professor PC Thomas Classes · Answer

$\mathrm{e}=\frac{\mathrm{d} \phi}{\mathrm{dt}}=\frac{\mathrm{dB}}{\mathrm{dt}}(\mathrm{A})=\mathrm{A}_{0} \frac{\mathrm{~dB}}{\mathrm{dt}}$ $$ =A_{0}\left[\frac{4 B_{0}-B_{0}}{t}\right]=\frac{3 A_{0} B_{0}}{t} $$