Question

A metal rod moves at a constant velocity in a direction perpendicular to its length. A constant, uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement(s) from the following.

• A. The entire rod is at the same electric potential.
• B. There is an electric field in the rod.
• C. Point $\text{P}$ will be at higher potential and point $\text{Q}$ will be at lower potential.
• D. The electric potential is lowest at the center of the rod and increase towards its ends

Answer 1

Answer: (B), (C)

Point $\text{P}$ will be at higher potential and point $\text{Q}$ will be at lower potential.

Since the rod is moving in a magnetic field, an emf $E=Bvl$ will induce across its ends.

As we know that, when we apply right- hand thumb rule for $(\overrightarrow{v}\times \overrightarrow{B})$, thumb is directed from lower potential to higher potential terminals of an imaginary battery or induced emf in a conductor. So here, point $\text{P}$ will be at higher potential and point $\text{Q}$ will be at lower potential.

Also, due to this potential difference, there is an electric field in the rod.

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

Note: If there is a potential difference between two points then an electric field also exists between the given points.