Electric Field at the Surface of a Conductor

In electrostatic equilibrium, free charges within a conductor redistribute until the net electric field inside becomes zero. This occurs because any internal electric field would cause charges to move, violating equilibrium. The electric field due to induced surface charges exactly cancels any external field, creating a field-free interior.

The ice pail experiment uses an electroscope to detect charge movement when a charged ball is lowered into an uncharged conducting container. Negative charges move to the inner surface, attracted to the positive ball, while positive charges move outward. When the ball touches the inner wall, all charge flows out, proving charges reside only on the conductor's outer surface.

The electric field magnitude at a conductor's surface is directly proportional to the surface charge density. Using a cylindrical Gaussian surface and applying Gauss's law, the field strength depends only on local surface charge density, not on the conductor's shape or other charges nearby.

If the electric field had a component parallel to the conductor's surface, free charges would move along that surface, contradicting electrostatic equilibrium. Therefore, the field must be perpendicular to the surface. Any parallel component would cause charge redistribution until equilibrium is restored with a purely perpendicular field.

An infinitesimal cylindrical Gaussian surface is positioned through the conductor surface. Flux through the curved sides is zero; flux through the flat end equals field times area. With constant surface charge density, Gauss's law gives total flux as charge enclosed divided by permittivity, yielding the surface field magnitude.

Induced charges always reside on the outer surface of a conductor, regardless of where they originate or how the conductor is shaped. Negative charges are attracted toward positive external charges and move to the nearest outer surface, while positive charges are repelled outward, establishing electrostatic equilibrium.

When a charged cloud approaches a transmission tower, the metallic earth wire develops induced surface charges. The conductor reaches electrostatic equilibrium with charges distributed on its surface, creating a perpendicular electric field that depends on surface charge density, protecting the tower from electrical damage.