Lorentz force question

EvilTesla

The lorentz foce has been bothering me. Becouse it seems to sugest an abosolute velocity.


Say you have tw parrellel wires, with equal current running in the same direction. According to Lorrentz force, they attract.

Now, the two wires are plasma. The curents are running side by side, at equal velocity (equal current).

Everthing is the same. The electrons should still attraced.

A little wierd, but not too bad.

NOW. Simply remove the plasma. Two streams of electrons, in space. The Lorentz force should still attracked, as the only thing that has changed between these experements is the medium. EXCEPT in space, there is no medium, which means that there is NOTHING to compare the speeds to. THe electrons are still traveling at the same velocity (which no longer makes sence) And they are still atrackting.

See what I am getting at?

Anyone know where my thinking is wrong?

Thanks!

CompuChip

You are talking about a force.
Force induces acceleration of the wires.
And special relativity doesn't work for accelerated frames.

If you want, attach an accelerometer to some electrons in both wires, and measure it. However, this will still only give you information about the change in velocity of the wires, starting from some arbitrary reference. In other words, about the relative velocity of the wires.

EvilTesla

The Lorentz force is perpendicular to velocity, so in the case of wires, the lorentz force wont change the velocity that is generating the lorentz force.


Where did special relitivity come into this?

Cryxic

I'm not quite sure I fully understand your scenario, but even if we took it at face-value, it does not seem to imply absolute velocity. Under all of those circumstances (electrons in wire or in space), you only compare the relative velocities. You can't say that the electrons have an absolute speed in space any more than you can say they had absolute speeds when you did the experiment with wires on Earth.

EvilTesla

I guess what I am asking is

in F=QVB. What is the "V" relitive too?

It can't be the relitive speed between the two electrons. Becouse the lorentz force exists when electrons are traveling in the same direction, with the same velocity.

It can't be the relitive speed of the medium, becouse the lorentz force works without a medium.

so what else can V be relitive too?

berkeman

This is actually a pretty interesting question. If an observer moves at the same constant velocity of a charged particle, he must not see (be able to measure) the B-field being generated by that particle? Hmmm...

Dick

Plasmas are overall neutral. The 'current' is a difference in the velocities of the negative and positive components of your plasma. If you remove the positive component the situation is completely different. Now you also have an electrostatic force between the two streams. They will repel. And yes, if are travelling at the same speed as a moving charge you don't see any B field. The mix of E and B fields an observer sees generated by a charge is completely dependent on the motion of the observer.

berkeman

Awesome. Thanks, Dick.

EvilTesla

How does that work in a wire??

If you have two parrell wires, with equal current flowing in the same direction

Do they not repel despite the charges having equivalent velocities?

Dick

Wires are like plasma. You have a population of free electrons, but you have an equally large population of metal atoms that are missing an electron. Wires are overall neutral. The only difference with a plasma is that the atoms aren't mobile. Just the electrons.

Phrak

To add to Dick's remarks, there are a few things at work for beams of charged particles moving in parallel. Moving right along with the beams, the electrons will only experience electric repulsion as he says--just Coulomb repulsion.

Changing to the frame of reference where the charged particles are in motion: There is the introduction of a magnet field, an increase in mass, and time dilation. These are all effects explained by relativity. All contribute to a slower percieved divergence of the constituent particles of the beams

Bob S

I believe that if you have two extremely relativistic electron beams side by side, there is no net force, because the attractive Lorentz force is exactly cancelled by the repulsive Coulomb force. If the beams are less than relativistic, the repulsive Coulomb force is dominant. This one of the problems in trying to combine low-velocity heavy-ion beams.
Bob S

Dick

Really? Parallel beams? Same velocity? In a vacuum? This is a pretty idealized question. What Lorentz force are you talking about? I'm kind of a believer that absolute velocity doesn't matter. I've had arguments with accelerator people about issues like this and they never really made their objections clear. Can you?

berkeman

Actually, this brings up an interesting follow-up question. The electrons in parallel wires carring the same current have the same drift velocity in the same direction. But we still generally in EE problems calculate the B-field from one wire, and apply that B-field to the other wire to calculate the attractive force. But this must be wrong, if the electrons in one wire are moving with the same drift velocity as the other wire, they must not experience any measureable B-field? I can see how we can get a repulsive force for opposing currents in parallel wires, but is the attractive force zero for equal parallel wire currents?

Dang, time for an experiment!

Dick

Hi berkeman, there is no B field between the electrons in the two wires. There is a B field between the electrons in each wire and the stationary charges in the other wire. Being KI6EGL, I think you know what the result will be. Put away the experimental apparatus. It's RELATIVE velocity of ALL charges. Not just the electrons.

Phrak

When you say extremely, this is a little fuzzy. That is, how extreme?

In the limit as v-->c, mass goes to infinity, so any finite applied force results in an acceleration that goes to zero.

Other than that, I'm equally currious. In the limit, does the magnetic force equally cancel the electric force? It seems it should, but I couldn't demonstrate it.

Dick, and Bob. I think were looking for this condition: F = 0 = Bv +E

berkeman

Hah! I'm beginning to see that the simplistic way of understanding (and teaching and tutoring) this case needs a bit of modifying. This is great.

But, now that I see that the electrons in one parallel wire don't experience any Lorentz force from the electrons in the other wire, it would seem that the force from the passing + atoms in my own wire would be much larger than the passing + atoms in the other wire. The Biot-Savart force from such nearby passing charges would be quite large! Is it not an issue because of perceived local charge neutrality? And if so, how is that different from the passing + charges in the other parallel wire? Thanks.