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 emf in the loop at an instant when the radius is $2cm$.

Answer 1

$\varphi =\pi r^{2}B$

$\Rightarrow \frac{d\varphi }{dt}=2\pi r.\frac{dr}{dt}B$

$\Rightarrow$ when $r=2\times {10}^{-2}m$

and $\frac{dr}{dt}={10}^{-3}m{s}^{-1}$

$\Rightarrow e=\frac{d\varphi }{dt}=2\times \frac{22}{7}\times (2\times {10}^{-2})\left(0.02\right)\times {10}^{-3}$

$=2.5\mu volt.$

Hence, the answer is $2.5\mu volt.$