1. Tardigrade
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  3. Physics
  4. A rectangular coil of two turns having area A rotates in a uniform magnetic field B with angular speed ω about an axis perpendicular to the field and in plane of the coil. If initially the plane of the coil is perpendicular to the field, then the average induced emf when it has rotated through (π/2) is

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Q. A rectangular coil of two turns having area A rotates in a uniform magnetic field B with angular speed $\omega$ about an axis perpendicular to the field and in plane of the coil. If initially the plane of the coil is perpendicular to the field, then the average induced emf when it has rotated through $\frac {\pi}{2}$ is

Solution:

$\varepsilon = NBA\omega \,sin\omega t$
$\varepsilon = 2\, BA\omega \,sin\omega t$
$\varepsilon_{avg} = \frac{2BA\omega\int^{\frac{t}{4}}_{0}sin\omega t dt }{\frac{T}{4}} = \frac{8BA\omega}{2\pi} \frac{\left[-cos \omega t\right]_{o^{\frac{T}{4}}}}{\omega}$
$= \frac{8BA\omega}{\omega\,T}.[1-0]=\frac{8BA\omega}{2\pi}$
$\epsilon_{avg} = \frac{4BA\omega}{\pi}$