Question

A conducting circular loop is placed in a uniform magnetic field, $B=0.025T$ with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of $1mm{s}^{-1}$. The induced emf when the radius is $2cm$ is :

• A. $2\pi \mu V$
• B. $\pi \mu V$
• C. $\frac{\pi }{2}\mu V$
• D. $2\mu V$

Answer 1

The correct option is B $\pi \mu V$

Here, Magnetic field, $B=0.025T$

Radius of the loop, $r=2cm=2\times {10}^{-2}m$

Constant rate at which radius of the loop shrinks,

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

Magnetic flux linked with the loop is

$\varphi =BAcos\theta =B\left(\pi r^2\right)cos{0}^0=B\pi r^2$

The magnitude of the induced emf is

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

$=0.025\times \pi \times 2\times 2\times {10}^{-2}\times 1\times {10}^{-3}$

$\pi \times {10}^{-6}V=\pi \mu V$