Is there a way to make the charges of a charged conductor evenly distributed over the surface? I know the charges of a charged insulator are evenly distributed but I want to know that if there is a way to make the charges of a charged conductor evenly distributed too.
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The only way to have the charges on a charged conductor evenly spread is to make sure that there is no horizontal component of electric field in the case of "evenly spread". The only two solutions for that are
- things with infinite dimensions: planes, cylinders
- spheres
For any other shape of conductor, there comes a point where the evenly distributed charge would feel an asymmetrical force - more charge on one side than on the other. The charge, which can flow freely because it's in a conductor, will respond to this by moving - until the forces even out. At that point you have the usual boundary condition (electric field perpendicular to the conductor surface) but no longer a uniform charge distribution.
update I just found a relevant earlier answer - this shows a bit of the mathematics of the above, but otherwise agrees exactly.
