I have asked this question before in another section of the forum but I still don’t have an answer so I thought I would try here. Ok…here goes.. In three dimensions, Poissons equation can be used to model an electrostatic problem in which there is a single point charge at the origin. The right hand side of the equation would be represented by the three dimensional Dirac delta function. The solution for this equation gives a the potential function u = 1/(4 Pi r). Taking the gradient of this produces the vector function for the electric field which as expected is an inverse square of the distance. Ok…so here is the real part of the question. If we do this in two dimensions the solution now is u = 1/ (2 Pi Log(r) ). What bothers me about this is taking the gradient of this function now produces a field that is no longer an inverse square. Is there some physical explanation for the fact that in two dimensions the field decays as 1 over r or is the reason because electrostatics problems really should only be thought of as three dimensional problems?