Question

A metal road moves at a constant velocity in a direction perpendicular to its length \& a constant uniform magnetic field too. Select the correct statement (s) from the following. (a) The entire rod is at the same electrical potential (b) There is an electric field in the rod (c) The electric potential is highest at the centre of the rod. (d) The electric potential is lowest at the centre of the rod.

Short answer

The correct statements are (a) "The entire rod is at the same electrical potential" and (b) "There is an electric field in the rod". This is because the metal rod experiences an electromotive force (emf) when moving in a magnetic field, which leads to the creation of an electric field inside the rod. Additionally, the entire rod is an equipotential surface, as the electric field is always perpendicular to the equipotential surface in a conductor.

Step-by-step solution

Understand the situation

The metal rod is moving in a magnetic field, and because of this, it will experience an electromotive force (emf). This emf will cause charges to redistribute inside the rod, creating an electric field and a difference in electric potential.

Determine the electric field in the rod

Due to the movement of the rod, an emf is induced, causing electrons to move in a direction opposite to the magnetic force. This creates an electric field inside the rod. Thus, (b) "There is an electric field in the rod" is a correct statement.

Determine the electric potential across the rod

In a conductor, the electric field is always perpendicular to the equipotential surface, which means that the electric potential remains constant along the equipotential surface. Since the rod is moving perpendicular to its length, the entire rod would be an equipotential surface. Hence, (a) "The entire rod is at the same electrical potential" is correct.

Analyze electric potential at the center of the rod

As we already determined that the entire rod is at the same electrical potential, the electric potential is neither highest nor lowest at the center of the rod. Thus, the statements (c) "The electric potential is highest at the centre of the rod" and (d) "The electric potential is lowest at the centre of the rod" are not correct. In conclusion, the correct statements are (a) "The entire rod is at the same electrical potential" and (b) "There is an electric field in the rod".