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Q.

A conducting circular loop is placed in a uniform magnetic field B = 40 mT with its plane perpendicular to the field. If the radius of the loop starts shrinking at a constant rate 0.2 mm/s, then the induced emf in the loop at an instant when its radius is 1.0 cm is:

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a

$0.1 π μ V$

b

$0.2 π μ V$

c

$1.0 π μ V$

d

$0.16 π μ V$

answer is D.

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Detailed Solution

$\begin{array}{l} e = - B \frac{d A}{d t} = - B \frac{d}{d t} (π r^{2}) \\ = - B (2 π r \frac{d r}{d t}) = 2 π B r (- \frac{d r}{d t}) \\ e = 2 \times π \times 40 \times 10^{- 3} \times 10^{- 2} \times (0.2 \times 10^{- 3}) = 0.16 π μ V \end{array}$

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