Question

Which of the following is a property of equipotential surfaces?

$[$0.77 Mark$]$

• A. The direction of electrostatic field will be perpendicular to the equipotential surface
• B. The potential difference between any two points on an equipotential surface is zero
• C. For a point charge, the equipotential surfaces will be concentric spheres
• D. All the statements above are correct.

Answer 1

The correct option is D All the statements above are correct.

An equipotential surface is a surface with a constant value of potential at all points on the surface. So the potential difference between any two points in an equipotential surface will be zero.

From the expression $dV=\overrightarrow{E}$ . $\overrightarrow{dr}$

The change in potential $dV$ will be zero when $\overrightarrow{E}$ is perpendicular to $\overrightarrow{dr}$,

Where $\overrightarrow{dr}$ is the displacement vector in the surface. So, Electrostatic field will be always perpendicular to an equipotential surface.

As the electrostatic field due to a point charge is radial in direction, the equipotential surfaces has to be concentric spheres.