Question

A circular coil is held in a magnetic field, which is directed normally outwards, from the plane of the paper. The initial situation is shown in the figure. How many times the induced current becomes zero, in one complete rotation of the coil.

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

Initially, the angle $\theta$ between the $\overrightarrow{B}$ and $\overrightarrow{A}$ is $0^{\circ }$.

When the coil is rotated in clockwise sense, the angle $\theta$ changes.

The flux through the coil decreases, as $\theta$ increases, so $\cos \theta$ decreases.

Clearly, the induced current is zero, when induced e.m.f is zero.

Now, $E_{ind}=0$, when $\theta ={90}^{\circ },{270}^{\circ }$

In one complete rotation, ie $0^{\circ }\le \theta \le {360}^{\circ }$, the permissible values of $\theta$ is $0^{\circ }$ and ${270}^{\circ }$

Hence, option $\left(B\right)$ is the correct answer.