## The basis of radio

Maxwell’s Equations & Light demonstrates the path from Maxwell’s equations to a wave equation that the propagation of radio waves (and light) in space.

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To a physicist, I imagine being the first human to see that equation must have been like being struck by lightning. This equation is just the old and venerable wave equation. Maxwell’s equations imply that the electric field can travel along in space as a wave. The same steps lightly modified give the exact same expression for the magnetic field. The two waves are intimately interleaved, creating each other and traveling outward. There’s more. The wave equation says that the speed of the wave is 1 divided by the square root of the constants in front of the time derivative. Plugging in (and feel free to try it yourself!), Maxwell saw that the speed of these electromagnetic waves matched the value of the speed of light.

OK. you need to figure out grad and curl and some other calculus type stuff but, still, E&M like this has a pleasing ethic all its own.

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