Classical electromagnetism; acceleration; momentum; energy?

Man, you ask good questions. Let's see what I can do. I'll use qualitative descriptions instead of math because I'm rusty.

Look at Maxwell's equations (I recommend the point form, not the integral form. Also, you have to know vector calculus fairly well first, and picture the fields in space and what the vector calculus equations are saying about them):

I. Electric flux comes out of any point in space in proportion to the charge density at that point, so at points with no charge, the flux ("amount of field") pointing into that point equals the amount coming out.

II. The magnetic flux into any point equals the amount coming out.

III. An electric field increasing/decreasing in intensity at a point generates a magnetic field in circles around that point such that those circles are perpendicular to the direction of increase/decrease. A moving charge also does. This magnetic field is proportional to the rate of increase/decrease/motion.

IV. A magnetic field increasing/decreasing in intensity at a point generates an electric field in circles around that point such that those circles are perpendicular to the direction of increase/decrease. This electric field is proportional to the rate of increase/decrease.

1. A charge moving at a changing speed would produce a changing magnetic field intensity, which in turn produces a changing electric field, which produces a changing magnetic field, and so on out into the universe. That is an electromagnetic wave. Your electron will radiate its wave in all directions. It's not a sinusoidal wave, though, because you're not moving the electron back and forth. It's just a short little one-time wave in the shape of the way you moved the charge. (In fact, one way to look at it is that this wave basically tells the rest of the universe to adjust the electric and magnetic field at every point to correspond to the electron's new position and velocity.)

2. Constant motion of a _stream_ of charges produces a constant magnetic field, which does not produce an electric field (because only a changing (increasing/decreasing) magnetic field generates an electric field around it). So it stops there; no wave propagates. For a single charge instead of a stream of charges, the picture is a bit more complicated, but it's essentially for the same reason as the stream of charges: because everything is eventually constant, and you need change at every level to get something that propagates out.

3.

a. Yes. Otherwise there would be nothing to update the field in the universe due to that charge, and we know the field must track the position of the charge, so there must be.

b. Yes. Or maglev trains wouldn't work.

c. Only if the other charge isn't moving in some way that exactly cancels out that wave. But generally yes, that's how electronic circuits work. Each electron is moved by a moving field/wave from the previous electron and then its wave/field in turn moves the next one.

d. (Did I mention these are awesomely good questions?) Sort of. The charge DOES always radiate a wave in the strictest technical sense, but it happens to be precisely the right shape and phase of wave to partially (or sometimes fully) cancel out the wave that moved it, at least in the space "after" that charge along the wave's path. In fact, that is the mechanism by which it absorbs some of the incoming wave's energy and thus prevents that wave from moving infinitely many particles as it propagates onward through the universe (and thus doing infinite work, which is obviously impossible). So this is how your wall blocks sunlight. (I hope I'm making sense.) Now, it doesn't necessarily _just_ cancel out some of the wave that moved it. It can also propagate out the sides a little in addition to partially cancelling the incoming wave, so in those cases the answer is a more definite and obvious yes. (In fact, the electrons in an antenna that transmit a radio wave are themselves being moved by an electric wave in the wire, so obviously this must happen.)

e. Yes. That's where sunlight comes from.

f. Yes. That's why the flame of a candle or the exhaust from a rocket engine emits light.

g. No different.

4.

a. When a charge moves, it emits a wave, and the push back from the rear end of that wave stops its motion, thus reducing the particle's momentum. The wave has the ability to move charges when it hits them, and in doing so it increases their momentum. So it is reasonable to say the wave "carries momentum" from the first charge to the second.

b. This is neat because this is the part where you really start seeing out how it is possible for particles to "attract each other by exchanging photons", something you've probably heard before. Unfortunately, it's too hard to explain and I'm out of allowed characters.

Sorry for the sloppy answers. You might want to talk to folks at www.physicsforums.com or even email me if you want any clarification and I'll see what I can do.

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