Question

A magnetic flux through a stationary loop with a resistance R

varies during the time interval τ as Ф = at (τ — t). Find the

amount of heat generated in the loop during that time. The

inductance of the loop is to be neglected.

Answer 1

Answer

Induced current in loop at a time to

$I=\frac{1}{R}\frac{d(\phi) }{dt}$

$I=\frac{1}{R}\frac{d(at(\tau-t)) }{dt}\\ I=\frac{(a\tau-2t)}{R}$

Heat generated

$P=I^2R\\P=(\frac{(a\tau-2t)}{R}) ^2R\\P=\frac{(a\tau-2t)^2}{R}$