Question

In a region of uniform 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

• A. $4 \pi^{2} mA$
• B. $30\, mA$
• C. $6\, mA$
• D. $200\, mA$

Answer 1

Answer: (C)

Amplitude of the current,
$i_{0}=\frac{e_{0}}{R}=\frac{\omega N B A}{R}=\frac{2 \pi v N B\left(\pi r^{2}\right)}{R}$
$i_{0}=\frac{2 \pi \times \frac{200}{60} \times 1 \times 10^{-2} \times \pi(0.3)^{2}}{\pi^{2}}$
$=6 \times 10^{-3} A =6\, mA$