How does, for example, the field of a single point charge arise as the solution of a wave equation? I tried solving the wave equation that arises from Maxwell's equations with a source, that is rho = q delta(0) (I cant get Latex to work), but it got too complicated for me. I think it might be necessary to approximate the charge distribution of a single charge as a gaussian and then take the limit in which it becomes a delta function at some point to solve this. Anyways, when you solve the equation in a vacuum you get perpendicular E and B fields oscillating in phase with one another. My question is, do you get the same thing when you solve in the presence of a source, and if so how does this lead to the 1/r^2 coulomb field?