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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
$1.6\pi\ \mu V$
B
$3.2\pi\ \mu V$
C
$4.8\pi\ \mu V$
D
$0.8\pi\ \mu V$
Detailed Solution
Flux through the loop: $\phi = BA = B\pi r^2$
Induced emf: $|\varepsilon| = \frac{d\phi}{dt} = B\pi\times2r\frac{dr}{dt}$
B = 0.04 T, r = 2 cm = $2\times10^{-2}$ m, $\frac{dr}{dt}$ = 2 mm/s = $2\times10^{-3}$ m/s
$|\varepsilon| = 0.04\times\pi\times2\times2\times10^{-2}\times2\times10^{-3}$
$|\varepsilon| = 3.2\pi\times10^{-6}$ V
$|\varepsilon| = 3.2\pi\ \mu V$
Induced emf: $|\varepsilon| = \frac{d\phi}{dt} = B\pi\times2r\frac{dr}{dt}$
B = 0.04 T, r = 2 cm = $2\times10^{-2}$ m, $\frac{dr}{dt}$ = 2 mm/s = $2\times10^{-3}$ m/s
$|\varepsilon| = 0.04\times\pi\times2\times2\times10^{-2}\times2\times10^{-3}$
$|\varepsilon| = 3.2\pi\times10^{-6}$ V
$|\varepsilon| = 3.2\pi\ \mu V$