Overview
A conductor is defined to be a material where the charges in the conductor are free to move around.
- {% \vec{E} = 0 %} inside the conductor - if this were not true, the charges within the conductor, being free to move, would move to new locations, thus altering the field. If the conductor is at equilibrium (i.e. the charges are not moving), this implies that the field must be zero
- {% \vec{E} %} outside the conductor is perpendicular to the surface of the conductor, otherwise a component of the field parallel to the surface will move charges around.
- {% \rho = 0 %} inside the conductor - this true because {% \nabla \cdot \vec{E} = \rho/ \epsilon_0 %}