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  4. A rectangular coil of metallic wire is placed in a uniform field 20 mT with its plane perpendicular to the field. If area of loop is shrinking at a constant rate of 0.4 m 2 / sec. Find the induced e.m.f. in the coil is

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Q. A rectangular coil of metallic wire is placed in a uniform field $20 \,mT$ with its plane perpendicular to the field. If area of loop is shrinking at a constant rate of $0.4\, m ^{2} / sec$. Find the induced e.m.f. in the coil is

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Solution:

$\phi=B A $
$\therefore \frac{d \phi}{d t}=\frac{d}{d t}(B A)=B \frac{d A}{d t}$ as $B$ is given constant.
$\therefore|\varepsilon|=\frac{d \phi}{d t} =20 \times 10^{-3} \times 0.4 \,V $
$=+8 \times 10^{-3} V$
$=8 \,mV$