# Electromagnetism/Talk

Holy moly there's a lot more. Next, there's how to transform the electric field under relativity, then there's defining and calculating B (an extremely long section since it turns out to be a combination of relativity and E), then how B and E transform under relativity, and finally a derivation of the wave equation for electromagnetic waves. So much to do, so little time. The vector potential is probably also worth mentioning...

Some technical points: The magnetic field due to a wire is stationary only if the wire is at rest in an inertial frame and carries a stationary current. The electric field between the plates of a capacitor is stationary only if the plates are at rest in an inertial frame and have a stationary charge distribution.

The formatting of many equations in the text did not work (on my computer).

I think the derivation of the wave equation should go under electromagnetic wave or under wave equation, maybe even under electromagnetic wave equation. Otherwise, this article is going to get too long. I may take a crack at deriving the WE soon, since I want to refer to it for nonlinear optics. As for the equations, I can't find a font with &nabla; in it. Perhaps curl and div would be better, though this won't match the rest of the Wikipedia -- DrBob

Ok, right about the article's length. You may want to try Mozilla as a browser, and from what I've heard the special characters used in Wikipedia are an HTML standard. At any rate, the wave equation isn't that tough to derive (now that I have my notes to look at), just take the curl of the two Maxwell's equations that have the curl in them, and use the mathematical identity:

∇×∇×A = -∇2A + ∇(∇·A)

for any vector field A (there may be some caveats, but I'm fairly sure that they don't apply to actual magnetic and electric fields). Then use the fact that you want speed of light in a vacuum to say that div(E) = 0 and curl(j) = 0. It gets considerably more sticky in matter since those last two are no longer true and they're tied to particles that have mass and their own electric fields. --BlackGriffen