Question

A stretched circular loop is released in magnetic field B= 2t Tesla as shown in Figure.

Radius of loop is shrinking at the rate of 0.1 m/s. At t=0, radius of loop was 3.5m and its resistance is 2$\Omega$that is constant. Find current in loop at t= 5sec

Answer 1

$ϵ=\frac{d\varphi }{dt}=\frac{d}{dt}\left(B\pi r^2\right)$

$ϵ=2\pi \frac{d}{dt}\left(t{r}^2\right)=2\pi [r^2-2tr\frac{dr}{dt}]$

$i=\frac{ϵ}{R}=\frac{2}{2}\pi [r^2-2\times 5\times 3\times 0.1]$

$i=18.84$