Charge Penetration into a Conductor in Equilibrium

Statistical mechanics is used to show that the electric charge on a conductor in equilibrium is not restricted to its surface but penetrates into the interior in the form of a space charge density, the effective penetration depth being of the order of a few atomic distances. Similarly, the electric potential in a charged conductor is not strictly constant but varies in space which results in a small but finite potential difference between the interior and the surface layers.