Equipotential surfaces cannot ________.

Equipotential surfaces:

1. An Equipotential surface is a group of points in space that all have the same potential.
2. Equipotential lines represent equipotential surfaces in two dimensions.
3. Two equipotential surfaces cannot intersect each other because two different equipotential surfaces have different electric potentials, so if they intersect then the point of intersection will have two different potentials at the same point which is not possible. Now, if both surfaces have the same potential, then they will be considered a single surface, not two surfaces. Then, there is no meaning of intersection as both are the same surfaces.
4. Electric field lines are always perpendicular to equipotential surfaces.
5. If equipotential surfaces intersect at that point then electric field lines will also intersect which is not possible.
6. The electric field lines are perpendicular to the equipotential surface.
7. Because the electric force can’t have two directions at the same time, the field lines can’t cross each other. As a result, two equipotential surfaces do not have to be parallel.

In the above diagram, A and B are at the same potential as the equipotential surface is a surface that has equal potential at every point on it. Equipotential surfaces due to single point charge are concentric spheres having a charge at the center. The electric field due to a positive point charge is directed radially outwards as shown in the diagram above.

Hence, equipotential surfaces cannot intersect.