Question
A rectangular coil $ABCD$ is rotated in uniform magnetic field with constant angular velocity about its one of the diameter as shown in figure.The induced $emf$ will be maximum, when the plane of the coil is
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Answer
Let the angle between magnetic field and the line perpendicular to the surface of rectangular coil be $\theta$
Hence the flux through the coil is $\phi=\vec{B} . \vec{A}=B A \cos \theta$
Hence the induced emf $=$ Rate of change of flux $=-\frac{d \phi}{d t}=B A \sin \theta \frac{d \theta}{d t}=B A \omega \sin \theta$
Hence it is minimum when $\theta=0^{\circ}, 180^{\circ}$
Which means when the plane of coil is at right angle to the magnetic field.
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