Question

A conducting circular loop is placed in a uniform magnetic field of $0.04T$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at $2mm/s$. The induced emf in the loop when the radius is $2cm$ is

• A. $4.8\pi \mu V$
• B. $0.8\pi \mu V$
• C. $1.6\pi \mu V$
• D. $3.2\pi \mu V$

Answer 1

Answer: (D)

$3.2\pi \mu V$

Induced emf in the loop is given by
$e=-B.\frac{dA}{dt}$ where $A$ is the area of the loop.
$e=-B.\frac{d}{dt}\left(\pi r^2\right)=-B\pi 2r\frac{dr}{dt}$
$r=2cm=2\times {10}^{-2}m$
$dr=2mm=2\times {10}^{-3}m$
$dt=1s$
$e=-0.04\times 3.14\times 2\times 2\times {10}^{-2}\times \frac{2\times {10}^{-3}}{1}V$
$=0.32\pi \times {10}^{-5}V$
$=3.2\pi \times {10}^{-6}V$
$=3.2\pi \mu V$.