Conductors

Ideal

Electrons can freely move, i.e. $\vec{F} = - e \vec{E} = 0$
Hence, no electric fields in conductors, thus they form an equipotential.
Additionally, the charge density inside a solid conductor must be zero.
Charge accumulates on the surface of the conductor.
Right above the surface, the electric field must be perpendicular to the surface, i.e. parallel to the surface normal.
$\vec{E} = \frac{σ}{ε_{0}} \hat{n}$ just above the field. Thus, we can get the charge density from the electric field just above the surface