Question

When a rectangular coil is rotated about an axis in the plane of coil and perpendicular to magnetic field with steady speed then

• A. periodical emf is induced
• B. no emf induced
• C. unidirectional emf is induced
• D. multi directional emf is induced

Answer 1

The correct option is A periodical emf is induced

$Given:$ A rectangular coil is rotated about an axis in the plane of coil and perpendicular to magnetic field.

$Solution:$ The magnetic flux $\varphi$ linked with a coil is given by

$\varphi =BA\cos \theta \dots \dots \left(1\right)$

Here, $B$ is the magnetic field, $A$ is the area of the coil and $\theta$ is

the angle between the direction of the magnetic field and area

vector.

The expression for Lenz's law is given by

$e=-\frac{d\varphi }{dt}\dots \dots$ (2)

Here, $e$ is the emf induced in the coil and $d\varphi$ is the change in

the magnetic flux linked with the coil in time $dt$

according to equation (1), the

magnetic flux linked with $N$ turns of the coil is given by

$\varphi =NBA\cos \theta$

Let now calculate the emf induced in the coil.

Substitute $NBA\cos \theta$ for $\varphi$ in equation (2).

$e=-\frac{d\left(NBA\cos \theta \right)}{dt}$

$\Rightarrow e=-NBA\frac{d\left(\cos \theta \right)}{dt}$

$\therefore e=-NBA(-\sin \theta )$

Due to this term, the induced emf in the coil is

period.Therefore, the emf induced in the coil changes

periodically.

$So,the$ $correct$ $option:A$