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OK, we'll start out with the nursing, math-light discussion, and then we'll add some more math if desired.
At its heart, electromagnetism is about fields. The electric field is denoted E, and the magnetic field is denoted B. At every point in space, a magnetic or electric field will have a particular strength and a particular direction. See what happens when you scatter iron filings on a sheet of paper above a bar magnet:
The orientation of the iron filings is parallel to the direction of the magnetic field at those points, and the density of the filings is related to its relative strength. The electric field works in pretty much the same way, except it is created by charges. You can see the electric field in a similar manner by rubbing a balloon on your head and holding it away from your hair.
Now, we can figure out what the electric and magnetic fields are. There are four fundamental equations that describe how they work, known as Maxwell's equations. Interestingly, he didn't develop them. All he did was make a small correction to one of them, and then he got his name on all of them. He did, however, show that the interaction of these equations demonstrates the necessary existance of electromagnetic radiation, which is what we're talking about here. The first of the two equations we're be most concerned with is Faraday's law. Faraday showed with this law, to the suprise of everyone, that the electric fields and magnetic fields were linked. He showed that a changing magnetic field (either strength or direction of the field can be changing) will generate a current in a coil of wire. This is how a generator works. Steam, water, or a zealous person on a bicycle can spin a coil of wire in the middle of a magnetic field, and the changing magnetic field (relative to the coil) generate a current in that coil. The current is caused by an electric field that wasn't there when the coil was still, but is created when the coil starts spinning. No balloons necessary. Pretty cool, eh?
The second equation we care about is Ampere's law, and this is the one that was corrected by Maxwell. Ampere originally developed his law to describe the magnetic field that's formed by current flowing in a wire. This law describes how one can use a nail to pick up paper clips by wrapping a coil of wire around it and connecting the wire to a battery. Here's what Maxwell saw. Let's say that we put a small break in our wire, and on each end of the break, we put two parallel metal plates close together, but not touching. This creates a basic capacitor. If we keep running current through the wire, the moving charges (electrons) in the wire that make up our current will get stuck on our plates and start accumulating. Well, we know what happens when we have charges built up. We get an electric field, just like our balloon, but since we're constantly increasing the charge in our capacitor, our electric field is increasing. Now, we already know that our wire with its current is generating a magnetic field. What about the space between the plates? Does the magnetic field suddenly just vanish since we have no more current? No! Instead, what Maxwell showed is that this increasing electric field will generate a magnetic field in exactly the same as the wire. Pretty cool how that works out, huh?
But wait a minute. Doesn't that sound familiar? We already knew that a changing magnetic field will generate an electric field, and now we have a changing electric field generating a magnetic field. Hmmm. That sounds a little circular, doesn't it? Couldn't a changing electric field generate a changing magnetic field that creates a changing magnetic field that creates a changing electric field right back again? Yes! And that's why Maxwell got his name on all the equations. Right after he made his correction to Ampere's law, he saw this very connection. He tied these two equations together and showed that the electric and magnetic fields can, and must, be able to oscillate together in a wave. Just as in the ocean, the water will move with crests and troughs, the electric and magnetic field strengths will cycle from strongly up to strongly down and so on. What's even more amazing is that Maxwell worked out exactly how fast these electromagnetic waves travel based on the collection of constants in his equations, and it worked out to be exactly equal to the speed of light. No one, up to that point, had any idea that light was at all related to electromagnetism, or even waves! Newton even thought that light was just a collection of particles, something like atoms. And yet here we see that light, unequivocally, behaves just like a wave, just like sound, or water, or sending a series of whiplashes down your garden hose. But not only that. We saw that the same stuff that picks up paper clips, that makes your hair stand up, that makes current in wire, and the stuff that lets you see it all, all of which were thought to be radially different phenomena at one point, are in fact all unified. Demonstrating the existence of electromagnetic radiation, its relation to light, and the beautiful elegance behind it is one of the greatest conquests in physics.
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tl;dr
So, anyway, have you played any NL tournies? If so, what was your ROI? If not, would you consider playing donkaments?