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^{-t/τ} $= , where $B_0$ and $τ$ 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 $( t →\propto)$ is :

Question

$\begin{array}{1 1}(1)\frac{\pi^2r^4B_0^4}{2 \tau R} \\ (2) \frac{\pi^2r^4B_0^2}{2 \tau R} \\ (3)\frac{\pi^2 r^4 B_0^2R}{\tau} \\ (4) \frac{\pi^2r^4B_0^2}{\tau R} \end{array} $