A rectangular coil ABCD is rotated anticlockw | vedclass

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Question

(A) The magnetic flux $\phi$ linked with the coil is given by $\phi = BA \cos 	heta$,where $	heta$ is the angle between the area vector of the coil

Vedclass · Accepted Answer

The plane of the coil is horizontal

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(A) The magnetic flux $\phi$ linked with the coil is given by $\phi = BA \cos 	heta$,where $	heta$ is the angle between the area vector of the coil and the magnetic field $B$.According to Faraday's law of electromagnetic induction,the induced $e.m.f.$ is $e = -\frac{d\phi}{dt}$.Substituting $\phi = BA \cos(\omega t)$,we get $e = -\frac{d}{dt}(BA \cos(\omega t)) = BA\omega \sin(\omega t)$.Thus,the induced $e.m.f.$ is $e = e_0 \sin(\omega t)$,where $e_0 = BA\omega$ is the maximum $e.m.f.$The $e.m.f.$ is maximum when $\sin(\omega t) = 1$,which occurs when $\omega t = 90^o$.At this position,the area vector is at $90^o$ to the magnetic field,meaning the plane of the coil is parallel to the magnetic field lines.Since the magnetic field is horizontal,the plane of the coil must be horizontal for the induced $e.m.f.$ to be maximum.

$A$ rectangular coil $ABCD$ is rotated anticlockwise with a uniform angular velocity about the axis shown in the diagram below. The axis of rotation of the coil as well as the magnetic field $B$ are horizontal. The induced $e.m.f.$ in the coil would be maximum when

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