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Q)

A conducting circular loop is placed in a uniform magnetic field B = 0.020 T with its plane perpendicular to the field. The radius of the loop starts shrinking at a constant rate of 1.0 mm/s. Find the induced e.m.f in the loop at an instant when the radius is 2cm?


(a) $ 25 \mu V$
(b) $ 2.5 \mu V$
(c) $ 0.25 \mu V$
(d) $ 0.025 \mu V$

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A)
$\phi = \pi r^2 B$
$ \frac {d\phi}{dt} = 2 \pi r . \frac {db}{dt}$
when $ r = 2 \times 10 ^{-2} m \;\; and\; \frac {dr}{dt} = 10 ^{-3} m/s$
$ e = \frac {d\phi}{dt} = 2 \times \frac {22}{7} \times (2 \times 10^{-2}) (0.02) \times 10^{-3}$
$ = 2.5 \times 10^{-6} V$
$ = 2.5 \mu V$
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