Given: Current density $J=\left(2\times {10}^{10}\right)r^2 \mathrm{A} {\mathrm{m}}^{-2}$, potential $V=50 \mathrm{V}$, time $t=100 \mathrm{s}$

Energy is given as $E=VIt$

Current $I={\int }_0^{2\times {10}^{-3}}JdA={\int }_0^{2\times {10}^{-3}}\left(2\times {10}^{10}\right)r^2\times 2\pi r dr$

(Since $A=2\pi r$)

 $I=\left(2\times {10}^{10}\right)2\pi {\int }_0^{2\times {10}^{-3}} r^3 dr=\left(4\pi \times {10}^{10}\right){\left(\frac{r^4}{4}\right)}^{2\times {10}^{-3}}$

$E=VIt=50\times 16\pi \times 100=800\pi$ .