The following potential is given The question is what the charge distribution is. The middle part is a charged dielectric. The two discontinuous points are the result of a charge accumulated in one point. And after that point the potential doesn't vary. So my thoughts are that the physical situation is a charged dielectric between two charged plated, with the charges of the dielectric oposite to the charge on the plate it faces. I think I'm right so far. But now I want to calculate the charge distribution. The hint was to use delta-function and I can see why, but I don't know how. Can any of you help me? PS: My paint skills suck, but I hope it's clear that the middle parabolic and the left potential is higher than the right one.