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A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T with its plane perpendicular to the field. The radius of the loop is made to shrink at a constant rate of 1 mm $s^{-1}$. The induced emf when the radius is 2 cm is
A
$2\ \mu V$
B
$2\pi\ \mu V$
C
$\pi\ \mu V$
D
$\frac{\pi}{2}\ \mu V$
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 = 0.025 T, r = 2 cm = $2\times10^{-2}$ m, $\frac{dr}{dt} = 1$ mm/s = $1\times10^{-3}$ m/s
$|\varepsilon| = 0.025\times\pi\times2\times2\times10^{-2}\times1\times10^{-3}$
$|\varepsilon| = \pi\times10^{-6}$ V = $\pi\ \mu V$
Note: the source prints 'plane perpendicular to the loop'; it means the plane of the loop is perpendicular to the field.
Induced emf: $|\varepsilon| = \frac{d\phi}{dt} = B\pi\times2r\frac{dr}{dt}$
B = 0.025 T, r = 2 cm = $2\times10^{-2}$ m, $\frac{dr}{dt} = 1$ mm/s = $1\times10^{-3}$ m/s
$|\varepsilon| = 0.025\times\pi\times2\times2\times10^{-2}\times1\times10^{-3}$
$|\varepsilon| = \pi\times10^{-6}$ V = $\pi\ \mu V$
Note: the source prints 'plane perpendicular to the loop'; it means the plane of the loop is perpendicular to the field.