2.8 Conductors in Electrostatic Equilibrium

Electric field inside a conductor is zero

In electrostatic equilibrium, free charges in a conductor rearrange until the net electric field inside is zero. If a field existed, it would push charges further, so charge keeps moving until it cancels the internal field. This is a defining property of conductors at equilibrium.

Excess charge lives on the surface

Because the interior field is zero, any excess charge resides entirely on the conductor's surface. Charges spread out to minimize repulsion, distributing themselves so the field inside stays zero and the conductor's surface becomes an equipotential.

Field is perpendicular to the surface

Just outside a conductor's surface, the electric field is perpendicular to the surface. Any parallel component would push surface charges sideways until equilibrium is restored, so at equilibrium no tangential field component can remain. Field strength is often greater where curvature (charge density) is higher.

Key terms

Electric field inside a conductor at equilibrium

Zero — free charges rearrange to cancel any internal field.

Where excess charge resides on a conductor

Entirely on the surface, since the interior field must be zero.

Direction of field just outside a conductor's surface

Perpendicular to the surface; no tangential component exists at equilibrium.

Conductor surface at electrostatic equilibrium

An equipotential surface — no work is done moving charge along it.

Effect of surface curvature on field strength

Sharper points (higher curvature) have higher charge density and stronger local electric fields.

Try an AP-style question

What is the electric field inside a conductor in electrostatic equilibrium?

1. Maximum at the center
2. Equal to kQ/r²
3. Zero
4. The same as outside