Question

In a coil of resistance $8Ω$, the magnetic flux due to an external magnetic field varies with time as $Φ=\frac{2}{3}(9−t^2)$.The value of total heat produced in the coil, till the flux becomes zero, will be _ $J$.

Answer 1

$R = 8Ω$

$Φ=\frac{2}{3}(9−t^2)$

At$t = 3, φ = 0$

$∈ =|−\frac{dΦ}{dt}|=\frac{4}{3t}$

$H=∫_0^3\frac{V^2}{R}dt=∫_0^3\frac{1}{8}×16/9t^2dt$

= $\frac{2}{9} \times \bigg(\frac{t^3}{3}\bigg)^3_0$

= $\frac{2}{9} \times 3 \times 27$

= $2$ $J$