In electrostatics, the charge distribution on the surface of a conductor at electrostatic equilibrium is such that the electric field inside the conductor is zero. This means that charges redistribute themselves on the surface in a manner that cancels out any electric field within the conductor.
Specifically, the charges on a conductor will distribute themselves in such a way that they create an electric field that is perpendicular to the surface and has a magnitude of zero inside the conductor. This is achieved through the phenomenon known as "electrostatic shielding." Any excess charge on a conductor will accumulate on its outer surface and will redistribute itself so that the electric field due to these charges cancels out the external electric field (if present) within the conductor.
In summary, the charge distribution on the surface of a conductor in electrostatic equilibrium is such that it neutralizes any electric field within the conductor, resulting in a net zero electric field inside. This behavior is a consequence of the properties of conductors and the nature of electrostatic interactions.