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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? enter image description here 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?

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  • $\begingroup$ As a quick thought, I believe that unless the flat surface is infinite there is always going to be a gradient that tends to increase density by the edges. $\endgroup$ – Niki Di Giano Aug 1 '18 at 8:37
  • $\begingroup$ Just spit balling. But, it would seem that with the area-density of the capacitive disk in hand, you could try for some estimate of the volume-density for a thin cylinder, from which you could consider a "thin cylinder" where the height tapers from the center to the edge to exacerbate the repulsion between patches at the high density edges. Perhaps you might then adjust things so that some small but flat portion (a smaller circle or thinner ring along the axis of symmetry?) still approximately solves the boundary conditions. $\endgroup$ – entprise Sep 30 '18 at 16:13

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