In a region of magnetic induction B = 10⁻² tesla, a circular coil of… | NEET 1988 (AIPMT)

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AC Generator & Transformer

In a region of magnetic induction $B = 10^{-2}$ tesla, a circular coil of radius 30 cm and resistance $\pi^2$ ohm is rotated about an axis which is perpendicular to the direction of $B$ and which forms a diameter of the coil. If the coil rotates at 200 rpm the amplitude of the alternating current induced in the coil is

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Answer: (c)

Peak emf $e_0 = NBA\omega$ with $N = 1$ .
$A = \pi(0.3)^2 = 0.09\pi\text{ m}^2$ , $\omega = \dfrac{2\pi \times 200}{60} = \dfrac{20\pi}{3}\text{ rad/s}$
$e_0 = 10^{-2} \times 0.09\pi \times \dfrac{20\pi}{3} = 6\pi^2 \times 10^{-3}\text{ V}$
$I_0 = \dfrac{e_0}{R} = \dfrac{6\pi^2 \times 10^{-3}}{\pi^2} = 6\text{ mA}$
So the answer is (c) 6 mA.

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