24.8:
Equipotential Surfaces and Field Lines
An equipotential surface is a 3-dimensional surface on which all the points have the same potential. If a test charge Q is moved on such a surface, its potential energy remains constant.
Therefore the work done to move from one point to another on equipotential surfaces is zero. The equipotential surface is always perpendicular to the electric field lines.
For a uniform electric field, parallel and equally spaced lines, equipotential surfaces are parallel planes perpendicular to the electric field.
The equipotential lines are the 2-dimensional representation of equipotential surfaces.
For an isolated charge, the electric field is radial and equipotential surfaces are concentrated spheres of different potentials with charge being at the center.
The equipotential lines are closely spaced where the electric field magnitude is higher and farther apart where the electric field is weaker.
For an electric dipole, the potential will be higher near the positive charge and lower near the negative charge.
For two positive charges, equipotential surfaces show a single 8-shaped surface where two equipotential surfaces intersect.
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.
Suggested Reading
- OpenStax. (2019). University Physics Vol. 2. [Web version]. Section 7.5; pages 320–323. Retrieved from https://openstax.org/details/books/university-physics-volume-2