Physics 202 Electric Potential Application of Gauss' Law to Conductors Repulsion between excess charges on a conductor forces the charge to distribute on the surface of the conductor where an effective normal surface force prevents escape.
Equilibrium occurs when E vanishes inside the conductor so no bulk currents are generated.
E is normal to the surface just outside, else surface currents would flow. A small patch of the surface of a conductor is essentially planar. The electric field is normal to the surface and its magnitude is proportional to the surface charge density. The potential vanishes along the line bisecting the dipole. Potential of a continuous charge distribution Consider a line charge on the z- axis.