24.8: Equipotential Surfaces and Field Lines
Electric potential can be pictorially represented as a three-dimensional surface. On such a surface, the electric potential is constant everywhere. The equipotential surface is always perpendicular to the electric field lines, and while it is three-dimensional, it can be treated as an equipotential line in a two-dimensional case. These equipotential lines are also always perpendicular to electric field lines. The term equipotential is often used as a noun, referring to an equipotential line or surface.
No work is required to move a charge along an equipotential since there is no change in electric potential on such a surface. This is because the direction of the force is perpendicular to the displacement. Still, the force is in the same direction as the electric field, so motion along an equipotential must be perpendicular to the electric field.
For oppositely charged parallel plates, the equipotential lines are parallel to the plates in the space between them and evenly spaced. For a positive point charge, the electric field is radially outward. The potential corresponding to this point charge is the same anywhere on an imaginary sphere of radius r surrounding the charge. This is because the potential for a point charge varies inversely with distance and thus has the same value at any point that is a given distance r from the charge. An equipotential sphere is a circle in a two-dimensional view. Because the electric field lines point radially away from the charge, they are perpendicular to the equipotential lines.
The electric potential can be found for a known electric field by drawing perpendicular lines to the electric field lines. Similarly, for a known electric potential, electric field lines can be drawn by drawing them perpendicular to the electric potential lines.
