A conducting metal circular-wire-loop of radius r is placed perpendicular to a magnetic field which varies with time as B = B0e${^{{{ - t} \over r}}}$ , where B0 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 (t $ \to $ $\infty $) is :

Question

A conducting metal circular-wire-loop of radius r is placed perpendicular to a magnetic field which varies with time as
B = B₀e${^{{{ - t} \over r}}}$ , where B₀ 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 (t $ \to $ $\infty $) is :

${{{\pi ^2}{r^4}B_0^4} \over {2\tau R}}$

${{{\pi ^2}{r^4}B_0^2} \over {2\tau R}}$

${{{\pi ^2}{r^4}B_0^2R} \over \tau }$

${{{\pi ^2}{r^4}B_0^2} \over {\tau R}}$

Solution

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