# Confused by surface charge and voltages

1. Oct 1, 2012

### bingbong

How can a conducting sphere have no voltage at the surface, and yet have a surface charge when there's a charge outside of the sphere? Wouldn't the surface charge create voltage at the surface?

2. Oct 2, 2012

### vanhees71

A conducting sphere means that it consists of a material, where charges are (quasi-)free to move around. Thus, if you bring a charge distribution outside of the sphere, their electromagnetic field acts on the free-moving charges such that in the stationary limit the sphere becomes a surface of constant electric potential, because then and only then the tangent components of the electric field vanish along the sphere, and this they have to, because in the stationary limit there must be no current along the surface, and there was a current, if the tangent components of the electric field were not vanishing because of Ohm's Law $\vec{j}=\sigma \vec{E}.$