Electromagnetic Induction - Result Question 12
12. 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
(a) $4.8 \pi \mu V$
(b) $0.8 \pi \mu V$
(c) $1.6 \pi \mu V$
(d) $3.2 \pi \mu V$
[2009]
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Answer:
Correct Answer: 12. (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.
$e=-B \cdot \frac{d}{dt}(\pi r^{2})=-B \pi 2 r \frac{dr}{dt}$
$r=2 cm=2 \times 10^{-2} m$
$dr=2 mm=2 \times 10^{-3} m$
$dt=1 s$
$e=-0.04 \times 3.14 \times 2 \times 2 \times 10^{-2} \times \frac{2 \times 10^{-3}}{1} V$
$=0.32 \pi \times 10^{-5} V$
$=3.2 \pi \times 10^{-6} V$
$=3.2 \pi \mu V$
