Question

A square conducting loop is in a region of uniform, constant magnetic field. Can the loop be rotated about an axis along one side and no emf be induced in the loop? Discuss, in terms of the orientation of the rotation axis relative to the magnetic-field direction.

Short answer

This can occur when the rotation axis is parallel to the magnetic field $\overrightarrow{\mathrm{B}}$. This makes the magnetic field $\overrightarrow{\mathrm{B}}$ is always perpendicular to the vector area$\overrightarrow{\mathrm{A}}$ of the loop.

Step-by-step solution

Important Concepts

The entire magnetic field that travels across a particular region is measured by magnetic flux.

Magnetic flux is given by

$\mathbf{\varphi }\mathbf{=}\overrightarrow{\mathbf{B}}\mathbf{.}\overrightarrow{\mathbf{A}}$

Where, $\overrightarrow{\mathrm{B}}$is the magnetic field and $\overrightarrow{\mathrm{A}}$is the area vector.

Application

This occurs when the rotation axis is parallel to the magnetic field .

This makes the magnetic field always perpendicular to the area vector .

Thus, the magnetic flux through the loop is constant and by faradays law, since there is no change in the magnetic field, there is no induced emf.