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° is

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$\frac{ωBA}{2 π}$

$\frac{2 ωBA}{π}$

$\frac{ωBA}{4 π}$

$\frac{ωBA}{π}$

answer is D.

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Detailed Solution

$\begin{array}{l} E = \frac{dϕ}{dt} = \frac{BA}{(T / 4)}; E = \frac{4 BA}{T} = (\frac{4 BA}{(\frac{2 π}{ω})}) \\ E = \frac{2 BAω}{π} \end{array}$

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