Electric Potential

E-fields and Electric Potential

What is the connection between electric fields and the electric potential. We can measure the electric potential with a volt meter. How can we measure the electric field?

An equipotential line or an equipotential surface is a line (in 2D) or a surface (in 3D) on which every point has the same potential. Moving a charge along such an equipotential requires no work. That means the electric force must be perpendicular to the equipotential -- or the electric field is perpendicular to the equipotential.

The electric field is always perpendicular to an equipotential surface. The surface of a conductor is an equipotential surface so this means the electric field is perpendicular to a conductor.

For a uniform electric field, we can write

E = - V/x

A more general form of this is

E = - dV/dx

Point Charges

Continuous Charges

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(c) Doug Davis, 2002; all rights reserved