Potential and Conductors

  1. Equipotentials are perpendicular to field lines. Since field lines come in perpendicular to the surface of a conductor, the surface must be an equipotential.

  2. Since there's no field inside a conductor at equilibrium, and the potential difference between two points separated by a distance Dr is given by:
    DV = -E Dr cosq
    EVERY point in a conductor at equilibrium must be at the same potential.

    q is the angle between the electric field E and the displacement Dr.