Which statement best defines an equipotential surface?

Which statement best defines an equipotential surface?

• A. A surface where the electric potential is the same at every point; E is perpendicular to equipotential surfaces
• B. A surface where the electric potential varies; E is parallel to the surface
• C. A surface where the potential is zero at all points
• D. A surface with constant electric field along it

Answer: (A)

Equipotential surfaces are surfaces where the electric potential is the same at every point. Because the potential does not change along such a surface, the potential gradient points normal to the surface, and the electric field, which is E = -∇V, points perpendicular to it. That makes the statement that best describes an equipotential surface one where the potential is constant and the electric field is perpendicular to the surface. If the potential varied along the surface, it wouldn’t be equipotential, and the electric field would have a component along the surface. Saying the potential is zero everywhere is just a special case of an equipotential surface, not the general definition. And claiming the surface has a constant electric field along it conflicts with the relation E = -∇V, since the field direction is perpendicular to the surface of constant potential.

Equipotential surfaces are surfaces where the electric potential is the same at every point. Because the potential does not change along such a surface, the potential gradient points normal to the surface, and the electric field, which is E = -∇V, points perpendicular to it. That makes the statement that best describes an equipotential surface one where the potential is constant and the electric field is perpendicular to the surface.

If the potential varied along the surface, it wouldn’t be equipotential, and the electric field would have a component along the surface. Saying the potential is zero everywhere is just a special case of an equipotential surface, not the general definition. And claiming the surface has a constant electric field along it conflicts with the relation E = -∇V, since the field direction is perpendicular to the surface of constant potential.