A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field B = 0 . 8 T . When released the radius of the loop starts

Question

A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field B = 0 . 8 T . When released the radius of the loop starts shrinking at a constant rate of 2 cm s – 1 . The induced emf in the loop at an instant when the radius of the loop is 10 cm will be ______ mV .

TestHub · Accepted Answer

According to the Faraday's law of electromagnetic induction, the emf induced in a conducting loop is given by, $e = - \frac{d ϕ}{d t}$ , here, $t$ is time and $ϕ = B A$ is magnetic flux.

Here, $e = |\frac{d ϕ}{d t}| = \frac{d (B A)}{d t} = B \frac{d (π r^{2})}{d t}$

$= B π (2 r \frac{d r}{d t}) = 2 \times π \times 0.1 \times 0.8 \times 2 \times 10^{- 2}$

$\approx 10 mV$ (rounded off)

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