2.7 Conductors and Electric Potential

Conductors are equipotential surfaces

In electrostatic equilibrium, the electric field inside a conductor is zero, so no work is done moving charge within or on its surface. This means every point on and inside a conductor is at the same electric potential. The entire conductor, including its surface, forms an equipotential region.

Field is perpendicular to the surface

Since the surface of a conductor is equipotential, the electric field just outside must be perpendicular to the surface. Any tangential component would do work moving charges along the surface, contradicting equilibrium. Field lines meet conducting surfaces at 90°.

Charge distribution and curvature

Excess charge on a conductor resides entirely on its outer surface. Charge density (and thus field strength) is greater where the surface curvature is higher — sharp points accumulate more charge than flat or gently curved regions, which is why lightning rods use pointed tips to concentrate field and induce discharge.

Key terms

Why is a conductor's surface equipotential?

Because the internal electric field is zero in equilibrium, no work is done moving charge along the surface, making potential constant everywhere on it.

Direction of E just outside a conductor

Perpendicular to the surface; any tangential component would violate the equipotential condition.

Location of excess charge on a conductor

Resides entirely on the outer surface due to mutual repulsion of like charges.

Charge density and curvature relationship

Charge density (and field strength) is greatest at points of high curvature, like sharp tips or edges.

Potential inside a hollow conductor cavity (no enclosed charge)

Equal to the potential of the conductor's surface, since E = 0 throughout the interior and cavity.

Try an AP-style question

What is the potential throughout a conductor in electrostatic equilibrium?

1. The same everywhere
2. Highest at the center
3. Zero everywhere
4. Lowest at the surface