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. $\frac{\pi }{2}\mu V$
• C. $\pi \mu V$
• D. $4\pi \mu V$

Answer 1

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

Given: The magnetic field in the region is, $B=0.025T$.

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

Constant rate at which radius of the loop shrimks,$\frac{dr}{dt}=1\times {10}^{-3}m{s}^{-1}$

To find: The induced emf in the loop when radius is $2cm$.

The magnetic flux linked with the loop is given by:

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

The magnitude of induced emf is given as:

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

Substitute the values.

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

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

$\Rightarrow \pi \mu V$

Option $\left(C\right)$ is correct.