A square shaped coil of area 70 cm² having 600 turns rotates in a… | JEE Main 2023 (1 Feb, Shift 2)

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AC Generator & Transformer

A square shaped coil of area $70\text{ cm}^2$ having 600 turns rotates in a magnetic field of $0.4\text{ wbm}^{-2}$ , about an axis which is parallel to one of the sides of the coil and perpendicular to the direction of field. If the coil completes 500 revolutions in a minute, the instantaneous emf when the plane of the coil is inclined at $60^\circ$ with the field, will be ____________ V. (Take $\pi = \frac{22}{7}$ )

Numerical answer type. Work it out, then open the answer.

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Answer: 44

$e = NBA\omega\sin\theta$ , where $\theta$ is the angle between the coil's normal and $B$ .
Plane at $60^\circ$ to the field, so the normal is at $\theta = 30^\circ$ .
$\omega = \dfrac{2\pi \times 500}{60} = \dfrac{50\pi}{3} = \dfrac{1100}{21}\text{ rad/s}$
$NBA = 600 \times 0.4 \times 70 \times 10^{-4} = 1.68$
$e = 1.68 \times \dfrac{1100}{21} \times \dfrac{1}{2} = 44\text{ V}$

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