I had one curiosity regarding maxwell equations in 3-D
From the curl equations, you get 6 unknowns, with 6 equations. The divergence equations add 2 additional equations. When these are combined, we have 6 unknowns and 8 equations. I was curious if someone could give insight for why this is the case? More equations than unknowns makes me think that the solution is not unique.
What happens is that the two equations involving divergences are redundant provided that they are satisfied at any given specific time (that is, with this last assumption the two equations follow from the other six). This was shown by Stratton in the 1940's.