3.1 Electrostatics with Conductors

Conductors in electrostatic equilibrium

In a conductor, free charges move until the net electric field inside is zero. This means the conductor's interior has constant potential, and any excess charge resides entirely on the surface. Just outside, the field is perpendicular to the surface.

Field at a conductor's surface

The electric field just outside a charged conductor's surface is E = σ/ε₀, where σ is the local surface charge density. This differs from the field near an infinite sheet (σ/2ε₀) because the conductor's own field cancels the interior field, doubling the exterior contribution.

Cavities and shielding

A conductor with a hollow cavity and no enclosed charge has zero field inside the cavity, regardless of external fields — this is electrostatic shielding (Faraday cage). If a charge is placed inside the cavity, an equal and opposite induced charge appears on the cavity wall, and the same charge appears on the outer surface.

Key terms

Electric field inside a conductor (equilibrium)

Zero — free charges rearrange until internal field cancels.

Where does excess charge live on a conductor?

Entirely on the outer surface.

Field just outside a conductor's surface

E = σ/ε₀, perpendicular to the surface.

Electrostatic shielding

A conductor's cavity has zero field inside if no charge is enclosed, blocking external fields (Faraday cage).

Charge in a cavity of a neutral conductor

Induces -Q on the cavity wall and +Q on the outer surface.

Try an AP-style question

A neutral conducting shell surrounds a +5 μC point charge at its center. What is the field outside the shell?

1. Double that of the point charge
2. Zero
3. Same as a −5 μC charge
4. Same as a +5 μC point charge