Electromagnetic Induction Ques 4
4. A conducting circular loop is placed in a uniform magnetic field of $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
[2009]
(a) $4.8 \pi $ $\mu V$
(b) $0.8 \pi $ $\mu V$
(c) $1.6 \pi $ $\mu V$
(d) $3.2 \pi $ $\mu V$
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Answer:
Correct Answer: 4.(d)
Solution:
- (d) Induced emf in the loop is given by
$e=-B \cdot \frac{dA}{dt}$ where $A$ is the area of the loop.
$e=-B \cdot \frac{d}{dt}(\pi r^{2})=-B \pi 2 r \frac{dr}{dt}$
$r=2 cm=2 \times 10^{-2} $ $m$
$dr=2 mm=2 \times 10^{-3}$ $ m$
$dt=1 $ $s$
$e=-0.04 \times 3.14 \times 2 \times 2 \times 10^{-2} \times \frac{2 \times 10^{-3}}{1} V$
$=0.32 \pi \times 10^{-5} $ $V$
$=3.2 \pi \times 10^{-6}$ $ V$
$=3.2 \pi $ $\mu V$
BETA
