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

Answer: (B)

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,
$\frac{dr}{dt}=1\times 10^{-3}m{s}^{-1}$
Magnetic flux linked with the loop is
$\varphi =BAcos\theta =B\left(\pi r^2\right)cos{0}^{\circ }=B\pi r^2$
The magnitude of the induced emf is
$\left|\epsilon \right|=\frac{d\varphi }{dt}=\frac{d}{dt}\left(B\pi r^2\right)=B\pi 2r\frac{dr}{dt}$
$=0.025\times \pi \times 2\times 2\times 10^{-2}\times 1\times 10^{-3}$
$=\pi \times 10^{-6}V<br>=\pi \mu V$