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).

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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 ∇ in it. Perhaps curl and div would be better, though this won't match the rest of the Wikipedia -- DrBob

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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