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A coil of area 80 cm$^2$ and 50 turns is rotating at 2000 revolutions per minute about an axis perpendicular to a magnetic field of 0.05 T. The maximum value of the e.m.f. developed in it is

1. $200\pi$ volt
2. $3\pi\times10$ volt
3. $4\pi\times10^3$ volt
4. $2\sqrt{3}$ volt

Correct answer: $4\pi\times10^3$ volt

Solution

For a coil rotating in a uniform magnetic field, the peak emf is $E_0 = NBA\omega$. Using the given values gives a large emf because of the high number of turns and high angular speed. The correct option is the one matching this calculation.

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