Question

What is an equipotential surface?

Hint:

Constant potential everywhere means zero work along it and the electric field is perpendicular to the surface.

Answer 1

Step 1: Definition.
An equipotential surface is a surface on which the electric potential is the same at every point.

Step 2: Key property (no work is done).
Since the potential is constant over the surface, the potential difference between any two points on it is zero. Hence the work done in moving a charge \( q \) from one point to another on the surface is
\[ W = q\,(V_1 - V_2) = q\times 0 = 0 \]

Step 3: Relation with electric field.
Because no work is done along the surface, the electric field \( \vec{E} \) is always perpendicular to the equipotential surface at every point. For example, the equipotential surfaces around a point charge are concentric spheres.

\[\boxed{\text{Surface of constant potential; } \vec{E} \perp \text{surface, } W = 0}\]