In a conductor, mobile charges can move through the material. If a conductor is left undisturbed in an electrostatic situation, those charges rearrange until there is no further net motion. The conductor is then in electrostatic equilibrium.

Electric field inside

If a nonzero electric field remained inside the conducting material, mobile charges would continue to accelerate. Therefore, in electrostatic equilibrium,

$$\mathbf E=\mathbf0$$

inside the conductor.

Constant potential

Because the electric field vanishes inside, the conductor is an equipotential:

$$V=\text{constant}$$

throughout its interior and surface.

Excess charge lies on the surface

Any excess net charge resides on the conductor's surface. Otherwise charges within the material would continue to repel one another and move.

Just outside the surface, the electric field has no tangential component in equilibrium; it points normal to the surface.

Cavities and shielding

A closed conducting shell can shield its interior from external electrostatic fields under appropriate conditions. This behavior follows from charge rearrangement and the requirement that the field inside the conducting material vanish.

These equilibrium properties make conductors natural building blocks for capacitors and electrostatic shielding.