I recently came across this problem, in David Morin's weekly problem set. The solution to which I figured, as explained here. But I also came across the solution explained in this report. Here the author solves the problem in n dimensions too and concludes that in 2-dimensional space, the object that gives maximum field would a thin circular plate, and not the planar cross-section of the 3D object found to give maximal field before.
I tried to verify this by calculating fields for the 2 different candidates, but I found the field for a uniform circular plate on a point on the circumference diverges to infinity. Same is the case for various objects, like a uniform semicircular plate at the centre. Why does this happen? Why is it that the field does not diverge for a uniform sphere at the surface of the sphere but it does for other objects? Also, will this be practically experienced?
