Even if you don't have a physics background, you should catch these two episodes, both of which discuss Maxwell's equations: "Maxwell's Equations" and "Gravity, Electricity, Magnetism."

Although the equations for the gravitational, electric and magnetic force constants had been known for at least 50 years, and all were known to be eerily similar in form, it wasn't until James Clerk Maxwell decided to play around with the formulas for electricity and magnetism that he revealed something beautiful and profound, leading to the combining of the electric and magnetic forces into the electromagnetic force. Here are the equations (you'll have to use Google/Wikipedia to get the meaning of the terms in the equations, which isn't really necessary for making my point, below):

For the electric force constant: Ke = 9x10⁹ Nm² /c²

For the magnetic force constant: Km=1x10^-7 Ns² /c²

When we divide the electric force constant by the magnetic force constant, we get 9x10¹⁶ m² /s² and this is obviously the square of something. So if we take the square root of this quantity, we get 3x10⁸ m/s. This happens to be the speed of light. How elegant and beautiful!

I am reminded of something that the great historian of science Jacob Bronowski said of Albert Einstein, which might also apply to Maxwell: "Einstein had the ability to ask immensely simple questions. And what his life showed, and his work, is that when the answers are simple, too, then you hear God thinking."