Do two parallel electron beams attract?

Electron beams left to themselves diverge.

Google cathode ray tube and electrostatic repulsion.

The answer is found from the theory of special relativity. First. assume that all electrons have the same velocity vector. Then, if you are in a coordinate system with the ame velocity, the electrons appear stationary and all the electrons repel each other mutually. In that coordinate system, there is no magnetic field.

If the beams travel at different velocities, assume that you (the coordinate system) ride along with the slow beam. That slow beam produces no magnetic field. The other beam does produce a magnetic field. An electron in your beam sees a force on it that looks like an electric field according to how the combination of electric and magnetic fields transform under motion.

Bill

Like repels.

Inside an X-ray tube, two opposite polarity 90kV DC sources meet (opposite attracts). A huge electron beam jumps from one node, into the target element, usually Palladium. Off of that Palladium face splashes a pretty thick X-ray flux where the electron beam enters the Palladium target mass. Pretty cool stuff. Some German Doctor (SGD) ;-] made the one I described. They run about $950.00 each. About ten inches long and nearly three inches in diameter. Used in airport X-ray conveyor systems.

180kV Power Supplies is fun stuff to make. :-] X-ray stuff too. Lead lined cases. Oil filled cases (tanks). We were making one with a brass case, which also stops X-rays. That would also be oil filled, but end up slightly lighter than the lead lined solution. Everything sits on thick G-10 slabs, down in the tank of oil, and has big G-10 blocks and such used for various construction elements of the supplies. We had a couple of Delrin bobbins in a couple of the transformer locations.

Want to feel old? When was the last time you looked at a periodic table? I saw several that I didn't recognize.

I should have also mentioned that many people believe that there is sufficient residual gas in vacuum tubes so that a plasma of positive ions builds up around an electron beam to neutralize the electrons. If that is true, and I have not read any papers to verify it, there will be no dc forces between electron beams. Positive ions move slowly compared to electrons. Thus, one can expect electrostatic forces from the fluctuations of electron density but not from steady state beams.

Bill

...

Interesting. So, if I understand this correctly, if we have two observers, one moving at the same velocity as the electron and the other moving at a different velocity, then the first observer doesn't see a magnetic field, but the second one does. In fact, in the first case there actually isn't a magnetic field, but in the second case there is one.

This makes my head hurt. Is this right? How could this be...? Once the field is generated, doesn't it propagate on it's own independent of what its source electron is doing? And independent of what any particular observer is doing?...

Ouch, it hurts again.

Many people believe Elvis is alive.

Both "theories" are equally dumb.

I don't know how "dumb" these theories are but I verify that the first one isn't correct. In Freshman physics lab there was this experiment we all did. It was to measure e/m for electrons. I forget the details but an electron beam was accelerated into an almost evacuated bulb which was placed between a pair of Helmholtz coils. The idea was that when you adjusted the magnetic field and the acceleration voltage just right the beam made a perfect circle back to it's starting point and you could calculate e/m from that.

OK. But all that isn't the point. The point is that we were told that the bulb was not totally evacuated so that there was sufficient residual gas in the bulb so that a plasma of positive ions built up around the electron beam. (remind you of anything?) In this case the purpose was so you could see the electron beam in the dark from the ionization. I can say for sure that this beam very definitely got wider and more fuzzy as it proceeded through the tube. Clearly there WERE DC forces defocusing the beam. I suppose one could argue it was collisions with ions doing it, but I don't think there was a great density in the tube.

As for Elvis.... I swear I saw him over at a Burger King near here... MAN, did he look OLD! :-)

OK. That makes sense. So let me ask you this. I've seen it said on a number of websites discussing the issue of whether or not a magnetic field rotates with a magnet that according to Einstein, a magnetic field MUST rotate with the magnet for SR to be correct. Your above argument seems to say the same thing in that if the magnetic field did NOT travel with the electron then in the moving coordinate system there WOULD be a magnetic field because it would have a velocity different from the electrons. Do you think this is what they meant when they say a magnetic field must rotate with the magnet according to SR?

Benj

It may make your head hurt, but you are getting it.

It turns out that there is a tensor (maybe a new buzz word for you) that is a combination of the electric and magnetic fields called the electromagnetic field. This tensor is an invariant. That is, it is an entity that represents the EM field that does not change as you look at it in from various "laboratories" moving at various uniform velocities. It is analogous to representing a vector by its x, y, and z components. If you look at a vector from a rotated coordinate system, it still is the same vector, but the x, y, and z components have changed.

In a moving coordinate system, the EM field is the same, but the various measured electric field and magnetic field components describing the fields have been changed the same way as the x, y, and z components of an unchanged vector have changed in a rotating coordinate system.

Another place tensors show up is in stress and strain. The stress tensor is a combination of shear and tensile stress, depending upon how you pick a coordinate system.

These days, EEs probably learn more about tensors and how to use them than they used to. In my day, tensors were left to mathematicians. Engineers got a poor man's version of tensor analysis for stress and strain by using Mohr's circle to show how materials could fail in tension when undergoing tensile stress.

Bill

I fail to follow your logic as to why the magnetic field, say of long cylindrical magnet rotates if you rotate the magnet along the cylindrical axis. In fact, experiment has shown that the field does not rotate with the magnet. It does not induce an emf in a loop of wire connected to the ends of the magnet with a conducting brush.

Bill

This is the kind of confused thinking that arises from the invention of mathematical intermediaries that are then considered real, such as E & M "fields". There are only electrons & they move relative to each other. Work out the problem in terms of charges & potentials (see C. J. Carpenter) & determine the observable motion - all the rest is just math.

A few points:

The term "vacuum tubes" has a specific meaning. A vacuum tube with gas in it (other than say mercury vapor rectifiers) is a failed tube.

Anything that gets in the path of a stream will diverge the stream. Vegetation will diverge a stream of machine gun bullets. Electron streams are not exempt.

This question is doomed to remain hypothetical, since there seems to exist no set up allowing to focus two separate parallel electron beams withing the same guiding E and B fields.

If you calibrate your fields to have an electron stream to be correctly focussed, then you can have only one beam in the fields.

Ref: "Principles of Charged Particle Acceleration", Wiley & Sons, by S. Humphries.

Andr=E9 Michaud

Do you mean that there are no entities such as protons, neutrons, molecules, ions, etc?

Observations leading to the theory of relativity were being made before and during the establishment of the existence of electrons. Maxwell had no knowledge of the existence of electrons. Nevertheless, his equations fitted in very well with the theory of relativity when it was expounded. Faraday himself noted that there was something wron with understanding when induced emf in coils of wire did not depend upon whether the coil was moved or whether the magnet was moved.

There is good reason for relying on "just math' if you understand what you are doing. Mathematical physics is not an exercise of picking equations out of your mathematical cookbook.

Bill

-- Support the troops. Impeach Bush. Oh, I forgot about Cheney.

Let's see. A mole of air is about 6E23 molecules in a volume of 24200 cc. A really good vacuum would be 1E-9torr. That is about 1E-12 atmosphere pressure. If I do my arithmetic correctly that is about 25 million molecules of air per mL (cubic centimeter). Hardly a perfect vacuum.

Remember however, for engineering purposes, good enough is perfect.

Bill

Which is why tubes have getters.

True.

My logic would be that if a magnetic field moves with an electron at a certain velocity (which the electron beam considerations seem to show) then doesn't it follow that a magnet made up of charged particles and generating a magnetic field from say circulating currents of some kind would of necessity move with the charged particles giving rise to the the permanent field?

I think this is the big argument! Because a rotating magnet doesn't induce emf in a coil (or Faraday generator disk) people have assumed that the field does not rotate. But then another group of people answer that, no, the first group failed to consider the induced emf in the WIRING which cancels the emf in the disk so it only "appears" that there is no emf generated. People looking at this have concluded that nobody seems to have come up with an experiment that definitively shows which of these two alternatives is the correct one and the argument seems to rage on.

What I therefore asked was to go back a step to first principles and ask if a magnetic field moves with an electron (idea came from data that said that one gets the same results from a permanent magnet as you do from rotating a coil of wire). We seem to agree here that the field MUST move with the electron (other wise e-beams would self-focus and magnetic fields would appear out of nowhere in a reference frame attached to the electrons).

So I don't think that anyone has really settled the question (Raging since the days of Faraday) of whether the magnetic field rotates. Seems to me like someone ought to be clever enough to find an experimental arrangement that could separate the effects of induction in the test loop from that in the wiring. Apparently nobody has. The last was A.G. Kelly of Ireland who thought he'd shown proof that the field rotates with the magnet, but then others tore apart his data showing that once again BOTH explanations (Field rotates or field does not rotate) gave identical results in his setup. (Nice list of references on the topic at end)

Benj

I could kind of handle tensors, at least in a vague sense as to how the explanation you give here works, but when the physics instructor brought up spinors, I changed majors.

But can you explain magnetism without relativistic effects, or do you just have to accept it as a given and do the math? You certainly can't "explain" it in terms of charges and potentials.