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  4. 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

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Q. 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

AIPMTAIPMT 2009

Solution:

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