#### A square shaped coil of area$70\; cm^{2}$ having 600 turns rotates in a magnetic field of $0.4 \mathrm{wbm}^{-2}$, about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes 500 revolution in a minute, the instantaneous emf when the plane of the coil is inclined at $60^{\circ}$ with the field, will be ________ V.$\left(\text { Take } \pi=\frac{22}{7}\right)$Option: 1 44Option: 2 __Option: 3 __Option: 4 __

$\text { Area (A) }=70 \mathrm{~cm}^2=70 \times 10^{-4} \mathrm{~m}^2$

\begin{aligned} & \mathrm{B}=0.4 \mathrm{~T} \\ & \mathrm{f}=\frac{500 \text { revolution }}{60 \text { minute }}=\frac{500}{60} \frac{\mathrm{rev} .}{\mathrm{sec} .} \end{aligned}

Induced emf in rotating coil is given by

\begin{aligned} & \mathrm{e}=\mathrm{N} \omega \mathrm{BA} \sin \theta \\ & =600 \times 2 \times \frac{22}{7} \times \frac{500}{60} \times 0.4 \times 70 \times 10^{-4} \sin 30^{\circ} \\ & =600 \times 2 \times \frac{22}{7} \times \frac{500}{6} \times 0.4 \times 70 \times 10^{-4} \times \frac{1}{2} \\ & =44 \text { Volt } \end{aligned}

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