field at the surface of a charged conductor must be normal to the surface at every point . (For a conductor without any surface charge density, field is zero even at the surface.) See result . . The interior of a conductor can have no excess charge in the static situation A neutral conductor has equal amounts of positive and negative charges in every small volume or surface element.
When the conductor is charged, the excess charge can reside only on the surface in the static situation. This follows from the Gauss’s law. Consider any arbitrary volume element v inside a conductor. On the closed surface S bounding the volume element v, electrostatic field is zero.
Thus the total electric flux through S is zero. Hence, by Gauss’s law, there is no net charge enclosed by S . But the surface S can be made as small as you like, i.e., the volume v can be made vanishingly small. This means there is no net charge at any point inside the conductor , and any excess charge must reside at the surface .
. Electrostatic potential is constant throughout the volume of the conductor and has the same value (as inside) on its surface This follows from results and above. Since E = inside the conductor and has no tangential component on the surface, no work is done in moving a small test charge within the conductor and on its surface. That is, there is no potential difference between any two points inside or on the surface of the conductor.
Hence, the result. If the conductor is charged,