Thanks for the kind words, friend. I really tried to make the science happen in this piece.



As to your solution being different, that's kinda sorta weird. The Poisson equation is two steps away from Gauss's law (you get it by substituting E = -gradφ into divE = 4πρ, and the latter is basically just a differential form of Gauss's law, if we apply the divergence theorem to it). And there's only a single physically meaningful solution for problems like these. I'd actually fancy taking a look at what you came up with.