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A rectangular coil of single turn, having area A, rotates in a uniform magnetic field B with an angular velocity $ω$ about an axis perpendicular to the field. If initially the plane of coil is perpendicular to the field, then the average induced e.m.f. when it has rotated through $90^{0}$ is

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$\frac{ω B A}{4 π}$

$\frac{ω B A}{π}$

$\frac{2 ω B A}{π}$

$\frac{ω B A}{2 π}$

answer is D.

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Detailed Solution

$e = \frac{∆ φ}{∆ t} \frac{B A}{t} a n d ω = \frac{2 π}{T}$

$T = \frac{2 π}{ω}$

Time taken for the coil to rotate through

$90^{0} = t = T / 4 = \frac{2 π}{4 ω} = \frac{π}{2 ω}$

$e = \frac{B A}{t} = \frac{B A}{π / 2 ω} = \frac{2 B A ω}{π}$

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