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Dale
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Just standard electrostatic induction.Subplotsville said:How would this interaction be described from the point of view of the electron?
http://en.wikipedia.org/wiki/Electrostatic_induction
Just standard electrostatic induction.Subplotsville said:How would this interaction be described from the point of view of the electron?
DaleSpam said:Just standard electrostatic induction.
http://en.wikipedia.org/wiki/Electrostatic_induction
All that is important is the total force on the charge. The fact that the electric and magnetic forces are in different directions in one frame is not important. In the frame of the electron there is no magnetic force and the total force is just the electrostatic force. The total force in one frame maps to the total force in the other frame, even if the individual electric and magnetic forces do not.Subplotsville said:Care to explain what you mean? The forces caused by the electric and magnetic fields of the moving electron are in different directions. They are at right angles to each other. How does the electron, which sees itself at rest and therefore without a magnetic field, account for its magnetically directed effect on the (incidentally electrically neutral) piece of iron?
DaleSpam said:All that is important is the total force on the charge. The fact that the electric and magnetic forces are in different directions in one frame is not important. In the frame of the electron there is no magnetic force and the total force is just the electrostatic force. The total force in one frame maps to the total force in the other frame, even if the individual electric and magnetic forces do not.
I don't feel up to it. It seems like a lot of effort for little benefit.Subplotsville said:I gathered that you meant something like this. What I'm asking is for you to show your work, if you feel up to it.
I already said that in the electrons frame it doesn't produce a magnetic force, just an electric force. As you said, the iron is electrically neutral so there is no net force on the iron, but there are net forces on the free conduction electrons, so they move so as to maintain a 0 E field inside (neglecting resistance).Subplotsville said:How does the moving electron explain its electric field producing a force of any sort on the electrically neutral piece of iron, much less a magnetic force?
DaleSpam said:I don't feel up to it. It seems like a lot of effort for little benefit.
I already said that in the electrons frame it doesn't produce a magnetic force, just an electric force. As you said, the iron is electrically neutral so there is no net force on the iron, but there are net forces on the free conduction electrons, so they move so as to maintain a 0 E field inside (neglecting resistance).
A good electrodynamics book or special relativity book should explain how the magnetic field arises from the electric field and relativity. I think Purcell has a good treatment of that.Subplotsville said:Well yeah, this is what an electric field is expected to do. What needs explanation is how this amounts to a magnetic-like effect just because the source is motion, despite the formal differences between the two fields. Thanks anyway.
The physical dynamic is Maxwells equations and the Lorentz force law, as always.Subplotsville said:That's up to you, of course. The thing is, without some sort of explanation in terms of a physical dynamic, you might as well claim the Great Pumpkin causes it.
there is no "magnetic like effect" in the electrons frame.Subplotsville said:Well yeah, this is what an electric field is expected to do. What needs explanation is how this amounts to a magnetic-like effect just because the source is motion, despite the formal differences between the two fields. Thanks anyway.
lugita15 said:A good electrodynamics book or special relativity book should explain how the magnetic field arises from the electric field and relativity. I think Purcell has a good treatment of that.
DaleSpam said:The physical dynamic is Maxwells equations and the Lorentz force law, as always.
there is no "magnetic like effect" in the electrons frame.
DaleSpam said:I am not 100% sure what you are asking, but you seem to be ascribing to the electrostatic force something that it cannot do. The electrostatic force can only move charges around, it cannot make charges appear or disappear. If the wire is charged then it is charged and there is no amount of electrostatic force that can make it otherwise.
Also, the charges are not static, so you need to think in terms of electrodynamics, not electrostatics. Fundamentally it is Maxwell's equations and the Lorentz force law that must be satisfied, not Coulomb's law except as an approximation to Maxwell and Lorentz.
As I said, back in post 106, there is only an E-field and therefore you get only electrostatic induction:Subplotsville said:Again, an electron moves past an electrically neutral piece of iron and so causes a current in it. What is the step-by-step description of how this happens through the electric field alone in the electron's frame of reference?
No, electroSTATIC induction. That is why I even included a link, so that there would be no confusion as to which induction concept I was referring to.Subplotsville said:Electromagnetic induction seems pretty magnetic-like to me.
It has a different number of electrons and protons on it at any given time. That is what it means to be charged.chingel said:I guess what I mean is that considering only one wire, what forces the wire to be charged in the electron's frame?
Because that is not self-consistent. Those values are all frame-dependent, so they cannot be the same in the electron's frame. In particular, any wire (even one with no resistance) has some capacitance wrt ground. The same field that drives the current through the wire in the lab frame also charges the capacitance of the wire in the electron's frame. I.e. it is not just a potential across the wire, but the whole wire is at an elevated potential.chingel said:Since the wire has no resistance, the voltage, charge and the overall electric field is zero at least in the lab frame, but why couldn't the electron say the same thing in its own frame?
Hmm, that makes sense, I will have to think about that a bit.chingel said:Is it that the electric field of the protons is contracted in the electron's frame and allows more proton density while the electrons don't feel an extra force from it?
DaleSpam said:As I said, back in post 106, there is only an E-field and therefore you get only electrostatic induction:
http://en.wikipedia.org/wiki/Electrostatic_induction
No, electroSTATIC induction. That is why I even included a link, so that there would be no confusion as to which induction concept I was referring to.
See Figure 1.1 here:Subplotsville said:Then, in post 107, I asked you to explain how that works. Namely how "only an E-field" could be responsible for what is otherwise known as electromagnetic induction in a piece of iron by a moving electron. I'm still waiting for an explanation.
Yes, you are referring to electrostatic induction. The problem is, the question is about electromagnetic induction. You claim they are equivalent. Okay, demonstrate the equivalence. Merely claiming this or that and calling a question resolved is not satisfactory in science.
If you are willing to work the problem out in the conductor's frame and post it then I can transform it to the electron's frame and post how it also works there.Subplotsville said:What I'm asking is for you to show your work, if you feel up to it.
OK, I've uploaded it to Google Docs here.Subplotsville said:I can't open PDFs on this computer.
DaleSpam said:If you are willing to work the problem out in the conductor's frame and post it then I can transform it to the electron's frame and post how it also works there.
lugita15 said:OK, I've uploaded it to Google Docs here.
This is a fine scenario, and I agree it captures all of the essential elements. My offer still stands, work the problem in one frame and post your work then I will transform it to the other frame and show how it works there.Subplotsville said:There are two electrons in close proximity. They are stationary to each other and in parallel motion -- in a direction perpendicular to the line that joins them -- with respect to an observer. This observer sees them as having two mutual interactions: 1) electrostatic and 2) magnetic on account of their being moving charges. Yet each electron sees the other as having only an electric field. How is this reconciled?
chingel said:Not an expert on this subject by any means, but since the electrons are moving with respect to the lab frame, they would experience time dilation, making them accelerate less in the same amount of time as measured by a clock in the lab frame, resulting in a conclusion that they feel less force, since they accelerated less. So in the lab frame they would seem to repel each other with less force, as the magnetic fields and forces would predict.
Subplotsville said:Thanks, though I'm looking for an in-thread explanation, if possible. More forum readers will benefit from it that way.
That is a very specific claim, can you prove it?Subplotsville said:Time dilation would cancel some of the electrostatic repulsion in this case, but not nearly enough to account for the magnetic attraction which increases linearly with speed and so becomes a significant factor even at slow speeds.
DaleSpam said:That is a very specific claim, can you prove it?
Your logic would be sound if the magnetic field were linear in time dilation. Can you prove that it is?Subplotsville said:The proof is implicit in what you quoted. The magnetic field is linear with speed, whereas time dilation is not and in fact increases negligibly at low speeds. Therefore, the magnetic attraction canceling the repulsion between the two electrons in parallel motion is not accounted for by time dilation. This is sufficient to refute the proposition without going into quantitative details.
DaleSpam said:Your logic would be sound if the magnetic field were linear in time dilation. Can you prove that it is?
Btw, I think that your overall point is probably correct, i.e. I think that you need all of relativity, not just time dilation. But your reasoning is unsound.
Agreed. I was talking about small speeds.Subplotsville said:Proof at relativistic speeds is unnecessary.
You are assuming that the relativistic effects can be ignored. You cannot assume the very point in question, that is a logical fallacy called begging the question.Subplotsville said:It is only necessary to look at the linearity of the magnetic field with changing speed at the low end of speed: where relativistic effects are close to flat and can thus be ignored over small changes in speed. Meaning, the two (mutually at rest) electrons exchange magnetic forces that vary linearly (to the observer) even where relativistic effects vary negligibly.
The excerpt I gave before was about how the magnetic force arises from the elecrostatic force and relativity, which is what I thought you were asking about. If you want to know about electromagnetic induction, here is another excerpt from Purcell, both in PDF format (attached) and in Google Docs, containing a relativistic analysis of Faraday's law. It may not be possible for me to copy and paste from it. Why exactly are you not able to view the Google Docs version?Subplotsville said:Maybe you could copy and paste the part where he addresses electromagnetic induction by an isolated charge, since this forum has a format we know everyone's computers, including mine, can actually read.
DaleSpam said:Agreed. I was talking about small speeds.
You are assuming that the relativistic effects can be ignored. You cannot assume the very point in question, that is a logical fallacy called begging the question.
In your argument above you started with three correct premises:
1) that the time dilation would cancel some of the electrostatic force
2) that the magnetic force is linear in v
3) that time dilation is not linear in v
But the fact that time dilation is not linear in v is not relevant. Time dilation is not force. What we are interested in is not whether or not time dilation is linear in v but whether or not the force canceled out by time dilation is linear in v.
Again, I think your conclusion is likely to be sound, but your argument is invalid.
Tantalos said:What about length contraction? Why do we not take into account the fact that the charge is length contracted on the lines when they move?
Tantalos said:What about length contraction? Why do we not take into account the fact that the charge is length contracted on the lines when they move?
DaleSpam said:Yes, that is why I suspect that the conclusion is probably correct. I don't think time dilation alone can explain it in all cases, I suspect that all relativistic effects are required.
DaleSpam said:But the fact that time dilation is not linear in v is not relevant. Time dilation is not force. What we are interested in is not whether or not time dilation is linear in v but whether or not the force canceled out by time dilation is linear in v.
lugita15 said:Why exactly are you not able to view the Google Docs version?
Tantalos said:What about length contraction? Why do we not take into account the fact that the charge is length contracted on the lines when they move?
No, at low speeds the gamma factor is virtually flat, that does not imply that the less acceleration effect is virtually flat. That is the part which you have not proved and which is not implied by the comments you have made. You are simply assuming your conclusion, aka begging the question.Subplotsville said:The idea being that the electrons have a slower clock and therefore measure less acceleration by the electrostatic repulsion between them. At low speeds this effect is virtually flat with a change in speed, while the magnetic force goes up in proportion to speed. On this basis alone, the two effects are not equivalent.
The integral of charge density over all of space is invariant. Charge density itself is part of the four-current.rbj said:so the question is, is charge invariant under special relativity? i think i was told it was, but it is curious that mass is affected but charge is not, both intrinsic properties of a particle like an electron.