Question

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

The Correct Option is D

$e =\frac{ d \phi}{ dt }=\frac{ d }{ dt }\left( B \pi r ^{2}\right)$
$=2 \pi rB \frac{ dr }{ dt }$
$=2 \times \pi \times 2 \times 10^{-2} \times 4 \times 10^{-2} \times 2 \times 10^{-3}$
$=3.2 \times 10^{-6} \pi Vol =3.2\, \pi \mu V$