Question

A conducting circular loop is placed in a uniform magnetic field $B=0.020T$ with its plane perpendicular to the field. Somehow, the radius of the loop starts shrinking at a constant rate of $1mm/s.$ Find the induced current in the loop at an instant when the radius is $2cm.$

Answer 1

Area $A=\pi r^2$
$\frac{dA}{dt}=2\pi r\frac{dr}{dt}$
when, $r=2cm=0.02m$
$\frac{dr}{dt}=1mm/s={10}^{-3}m/s$
emf $=N.B\times 2\pi r.\frac{dr}{dt}$
$=1\times 0.02\times 2\pi \times 0.02\times {10}^{-3}V$
$=2.51\times {10}^{-6}V$
$=2.51\mu V$