Electromagnetic Induction - Result Question 10
10. A conducting circular loop is placed in a uniform magnetic field, $B=0.025 T$ with its plane perpendicular to the loop.
[2010]
The radius of the loop is made to shrink at a constant rate of $1 mm s^{-1}$. The induced e.m.f. when the radius is $2 cm$, is
(a) $2 \pi \mu V$
(b) $\pi \mu V$
(c) $\frac{\pi}{2} \mu V$
(d) $2 \mu V$
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Answer:
Correct Answer: 10. (b)
Solution:
- (b) Magnetic flux linked with the loop is $\phi=B \pi r^{2}$
$ |e|=\frac{d \phi}{d t}=B \pi \cdot 2 r \frac{d r}{d t} $
When $r=2 cm, \frac{d r}{d t}=1 mm s^{-1}$
$e=0.025 \times \pi \times 2 \times 2 \times 10^{-2} \times 10^{-3}$
$=0.100 \times \pi \times 10^{-5}=\pi \times 10^{-6} V=\pi \mu V$
