Given a charged conducting body with a flat side, can the charge density (and hence the normal electric field) be constant on the flat part? According to physics lore, the charge density is greater on projecting bumps, and there are various hand-waving explanations. In the case of a charged conducting disk, the density is least at the centre and becomes infinite at the edge (Eqn. 29).
This question arose while thinking about Is there a 3D shape with a flat face throughout which one would experience constant “downward” acceleration?