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Q.

A conducting circular loop placed in a uniform magnetic field B = 0.02 T with plane perpendicular to the field, somehow the radius of the loop starts shrinking at a const rate of $1. \frac{m m}{\sec}$ . The induced emf in the loop at an instant when the radius is 2 cm is

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a

5.5 $μ V$

b

4.5 $μ V$

c

3.5 $μ V$

d

2.5 $μ V$

answer is C.

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Detailed Solution

Flux $ϕ = B . A = B . π r^{2}$
$\frac{d ϕ}{d t} = 2 π r . B \frac{d r}{d t} e m f e = \frac{d ϕ}{d t} = 2 π r . B \frac{d r}{d t} e = 2 \times 3.14 \times 2 \times 10^{- 2} \times 2 \times 10^{- 2} \times 1 \times 10^{- 3} = 2.5 \times 10^{- 6} V = 2.5 μ V$

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