Comment by praptak
What I never got about the simple symmetry-based solution is "if we accept the idea that we can treat the current fields for the positive and negative nodes separately".
Why are the currents in the two node solution (not symmetric) a simple sum of the currents of two single node solutions (symmetric)?
Obviously the 2 node solution still has some symmetries but not the original ones that let us infer same current in every direction.
the Maxwell Equations are linear in the electric and magnetic fields, then you can add Up and subtract fields and Potentials from each other. It's the same Argument for why interfernce works or optical gratings