29. 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 (1988)
Solution:
The maximum induced emf is $e_0 = B A \omega = B (\pi r^2) (2\pi f)$.
Here $B = 10^{-2} T$, $r = 0.3 m$, $f = \frac{200}{60} = \frac{10}{3} s^{-1}$, and $R = \pi^2 \Omega$.
Amplitude of induced current is $I_0 = \frac{e_0}{R} = \frac{10^{-2} \times \pi(0.3)^2 \times 2\pi \times \frac{10}{3}}{\pi^2} = 10^{-2} \times 0.09 \times \frac{20}{3} = 6 \times 10^{-3} A = 6 mA$.
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