Physics

Problem

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/\tau}

, where

B_0

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: a.

\frac{\pi^2 r^4 B_0^4}{2\tau R}

\frac{\pi^2 r^4 B_0^2}{2\tau R}

\frac{\pi^2 r^4 B_0^2 R}{\tau}

\frac{\pi^2 r^4 B_0^2}{\tau R}