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A rectangular coil of 300 turns has an average area of $10\times25\,\text{cm}^2$. The coil rotates with a speed of 50 cycles per second in a uniform magnetic field of strength $2\times10^{-4}$ T about an axis perpendicular to the field. The peak value of the induced e.m.f. is (in volt)

1. $30\pi$
2. $300\pi$
3. $3\pi$
4. $\pi$

Correct answer: $30\pi$

Solution

The peak emf of a rotating coil is $E_0 = NBA\omega$. With $N=300$, $B=2\times10^{-4}$ T, area $=10\times25\,\text{cm}^2=2.5\times10^{-3}\,\text{m}^2$, and $\omega=2\pi(50)$, the result is $30\pi$ V. Hence the correct answer is $30\pi$.

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