Elegance

Here is the derivation of some fairly well known (aka - know them or die) physics equations from electricity and magnetism as derived using the variational principle. I skipped a few steps here and there, mainly with the first couple lines of the variational principle, but the blanks can be filled in if necessary. I am posting this because I found this derivation so elegant and absolutely wonderful. We derived it for General Relativity in order to get familiar with some mathematical tricks; but still, it's beautiful.