A conducting metal circular-wire-loop of radius $r$ is placed perpendicular to a magnetic field which varies with time as $B=B_0{e}^{-\frac{t}{\tau }},$ where $B_0 \mathrm{and} \tau$ are constants at time $t=0$. If the resistance of the loop is $R$, then the heat generated in the loop after a long time $\left(t\to \infty \right)$ is

• A

  $\frac{{\pi }^2{r}^4{B}_0^4}{2\tau R}$
• Correct answer
  B

  $\frac{{\pi }^2{r}^4{B}_0^2}{2\tau R}$
• C

  $\frac{{\pi }^2{r}^4{B}_0^{2}R}{\tau }$
• D

  $\frac{{\pi }^2{r}^4{B}_0^2}{\tau R}$

Hence, the correct answer is option: 'B'.