1.7 Conductors in Electrostatic Equilibrium

Conductors in Electrostatic Equilibrium

In electrostatic equilibrium, charges in a conductor stop moving, so the electric field inside the conductor is zero. Any excess charge resides entirely on the surface of the conductor. If the field were nonzero inside, free electrons would keep accelerating, contradicting equilibrium.

Field at the Conductor's Surface

Just outside a conductor's surface, the electric field is perpendicular to the surface. If there were a tangential component, charges would slide along the surface, violating equilibrium. Using Gauss's Law with a thin pillbox straddling the surface gives E = σ/ε₀, where σ is the local surface charge density.

Cavities and Shielding

If a conductor has an internal cavity with no charge inside, the field within the cavity is zero, and any charge on the conductor resides only on outer surfaces — this is electrostatic shielding. If a charge is placed inside the cavity, an equal and opposite induced charge appears on the cavity wall, and equal charge appears on the outer surface.

Key terms

Electric field inside a conductor (equilibrium)

Zero — free charges rearrange until the internal field cancels.

Location of excess charge on a conductor

Entirely on the outer surface, due to mutual repulsion of like charges.

Direction of E just outside a conductor's surface

Perpendicular to the surface; a tangential component would move surface charges.

Field magnitude at a conductor's surface

E = σ/ε₀, derived from Gauss's Law using a pillbox at the surface.

Electrostatic shielding

A conductor with an empty cavity has zero field inside the cavity, shielding it from external charges (Faraday cage effect).

Try an AP-style question

What is the field just outside the surface of a conductor with surface charge density σ?

1. 0
2. σε₀
3. σ/(2ε₀)
4. σ/ε₀