\(\phi=B . A\)

\(\phi=\mathrm{B}_{0} \pi \mathrm{r}^{2} \mathrm{e}^{-1 / \tau}\)

\(\left(\because B=B_{0} e^{-t / \tau}\right)\)

Induced \(E.m.f.\) \(\varepsilon=\frac{\mathrm{d} \phi}{\mathrm{dt}}=\frac{\mathrm{B}_{0} \pi \mathrm{r}^{2}}{\tau^{2}} \mathrm{e}^{-t / \tau}\)

Heat \(=\int_{0}^{\infty} \frac{\varepsilon^{2}}{\mathrm{R}}=\frac{\pi^{2} \mathrm{r}^{4} \mathrm{B}_{0}^{2}}{2 \tau \mathrm{R}}\)