Question

A circular coil of mean radius $r$ and having $N$ turns is kept in a horizontal plane. A magnetic field $B$ exists in the vertical direction, as shown in the figure. In which of the following cases, an emf will be induced?

• A. If the coil is held stationary and the magnetic field is non-uniform
• B. If the coil is held stationary and the magnetic field is varying.
• C. If the coil is rotated with an angular velocity $\omega$ about an axis passing through the centre and perpendicular to its plane and the magnetic field is uniform.
• D. If the coil is rotated with an angular velocity $\omega$ about an axis passing through the diameter and the magnetic field is uniform.

Answer 1

Answer: (B), (D)

If the coil is rotated with an angular velocity $\omega$ about an axis passing through the diameter and the magnetic field is uniform.

The emf is induced in the circular coil when the magnetic flux through the coil changes with time.

The magnetic flux linked with a coil is,
$\varphi =BA\cos \theta$

Where, $B$ is the magnitude of the magnetic field, $A$ is the area of the plane on which it exists, and $\theta$ is the angle between the magnetic field lines and the normal (perpendicular) to $A$.

$\text{Option A}:$ $B$ and $A$ are constant, so the magnetic flux through the coil does not change with time, hence no emf induced.

$\text{Option B}:$ As magnetic field, $B$ varies, so magnetic flux also varies, thus an emf will be induced.

$\text{Option C}:$ As the number of field lines through the coil does not change with time, hence the magnetic flux does not change with time. So no emf is induced in the coil.

$\text{Option D}:$ If the coil is rotated about a diameter, $\theta$ changes, hence change in magnetic flux with time. Thus, emf will be induced in the coil.

Hence, options $\left(\text{B}\right)$ and $\left(\text{D}\right)$ are correct.