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  4. A square shaped coil of area 70 cm 2 having 600 turns rotates in a magnetic field of 0.4 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° with the field, will be V .(. Take .π=(22/7))

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Q. A square shaped coil of area $70\, cm ^2$ having $600$ turns rotates in a magnetic field of $0.4$ 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 ___ $V .\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$

JEE MainJEE Main 2023Alternating Current

Solution:

$N =600, A =70 \times 10^{-4} m ^2, B =0.4 T $
$ \omega=\frac{500 \times 2 \pi}{60}=\frac{100 \pi}{6} rad / s $
$ E = NAB \omega \sin \omega t $
$\omega t \text { is angle } b / w \vec{ A } \,\& \,\vec{ B } $
$ =600 \times 70 \times 10^{-4} \times 0.4 \times \frac{100 \pi}{6} \times \frac{1}{2} $
$=44\, V $