Question

When a rectangular coil is rotated in a uniform magnetic field about an axis passing through its centre and perpendicular to the field, the induced emf in the coil is maximum when the plane of the coil is
(A) Perpendicular to the field
(B) Parallel to the field
(C) Inclined at $60$ with the field direction
(D) Inclined at $45$ with the field direction

Answer 1

Hint : Here to find the induced emf in the rectangular coil in the magnetic field we will use the law of Faraday’s. Also, we will use the cosine function to be maximum.

Complete Step By Step Answer:
According to the law of Faraday’s that when the magnetic flux is linked with the circuit changes, an electromagnetic force is induced in the circuit which is proportional to the rate of the change of the flux linkage.
So, when the rectangular coil about an axis passing through its centre and the perpendicular to the direction of the field in the uniform magnetic field then the induced voltage in the coil is $= \dfrac{{d\phi }}{{dt}}$
Now, e.m.f. $= \dfrac{{d(NAB\sin \theta )}}{{dt}}$
$\Rightarrow emf = NAB\omega \cos \theta$
Where $\theta$ can be defined as the angle between the plane of the coil and the lines of force.
Hence, the induced emf in the coil is maximum when cosine angle is maximum or when angle is equal to zero when the plane of the coil is parallel to the field.
From the given multiple choices, the option B is the correct answer.

Note :
Remember the difference between the Lenz’s and Faraday's law. Lenz’s law states the direction of the current flow. Faraday’s law relates to the rate of change of the magnetic flux through the magnitude of the electromagnetic force induced in the loop.