Magnetism seems absolute despite being relativistic effect of electrostatics

[Dale]

How would this interaction be described from the point of view of the electron?

Just standard electrostatic induction.
http://en.wikipedia.org/wiki/Electrostatic_induction

 

[Subplotsville]

Just standard electrostatic induction.
http://en.wikipedia.org/wiki/Electrostatic_induction

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?

 

[Dale]

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?

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]

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 gathered that you meant something like this. What I'm asking is for you to show your work, if you feel up to it. If not, maybe someone else would like to. 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? The fact that electric and magnetic effects occur in different directions is only one of several discrepancies.

 

[Dale]

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 don't feel up to it. It seems like a lot of effort for little benefit.

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?

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]

I don't feel up to it. It seems like a lot of effort for little benefit.

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.

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).

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]

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.

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.

 

[Dale]

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.

The physical dynamic is Maxwells equations and the Lorentz force law, as always.

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.

there is no "magnetic like effect" in the electrons frame.

 

[Subplotsville]

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.

Thanks, though I'm looking for an in-thread explanation, if possible. More forum readers will benefit from it that way.

The physical dynamic is Maxwells equations and the Lorentz force law, as always.

These are general principles. How do they lead us to expect the claimed result in this particular instance? 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?

there is no "magnetic like effect" in the electrons frame.

Electromagnetic induction seems pretty magnetic-like to me. If you are repeating your claim that this is reducible to electric forces alone, I am repeating my request for a physical description of how this takes place.

 

[lugita15]

Thanks, though I'm looking for an in-thread explanation, if possible. More forum readers will benefit from it that way.

OK, attached is an excerpt from Purcell describing how the magnetic force arises.

 

[Subplotsville]

I can't open PDFs on this computer. Maybe you could copy and paste the part where he addresses electromagnetic induction by an isolated charge.

 

[chingel]

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.

I guess what I mean is that considering only one wire, what forces the wire to be charged in the electron's frame? 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? What forces the electrons to be spaced wider, shouldn't they feel an electrostatic force from the increased density of positively charged particles between them? Why don't more electrons come in from the source of the electrons, since the electrostatic force of the protons should be pulling them?

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?

 

[Dale]

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?

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

Electromagnetic induction seems pretty magnetic-like to me.

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.

 

[Dale]

I guess what I mean is that considering only one wire, what forces the wire to be charged in the electron's frame?

It has a different number of electrons and protons on it at any given time. That is what it means to be charged.

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?

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.

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?

Hmm, that makes sense, I will have to think about that a bit.

 

[Subplotsville]

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

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.

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.

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.

 

[Dale]

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.

See Figure 1.1 here:
http://www.ece.drexel.edu/courses/ece-e304/e3042/CLICK_HERE_TO_VIEW.htm

It describes the scenario as seen in the electron's frame, with the additional complication that the field from the electron is spatially non-uniform, but as the conductor moves through the spatially non-uniform field the charges and currents re-distribute along the principles sketched out there. I hope it is clear now how an E-field in the electron's frame can produce the currents and charges that would be expected in the conductor's frame where there is an E- and a B-field.

 

[Dale]

What I'm asking is for you to show your work, if you feel up to it.

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]

I can't open PDFs on this computer.

OK, I've uploaded it to Google Docs here.

 

[Subplotsville]

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.

Since you like to reduce things to electrostatics, in the interest of clarity and to avoid more of the same inconclusive back-and-forth, let's get rid of the conductor and rephrase the problem with only essential elements remaining.

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?

OK, I've uploaded it to Google Docs here.

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.

 

[chingel]

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.

 

[Dale]

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?

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]

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.

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. Also, there's the situation where the two electrons are passing each other going in opposite directions, in which case their magnetism causes an increase rather than a decrease in their mutual repulsion.

 

[rbj]

Thanks, though I'm looking for an in-thread explanation, if possible. More forum readers will benefit from it that way.

The classical electromagnetic effect is perfectly consistent with the lone electrostatic effect but with special relativity taken into consideration. The simplest hypothetical experiment would be two identical parallel infinite lines of charge (with charge per unit length of $\lambda$ and some non-zero mass per unit length of $\rho$ separated by some distance $R$. If the lineal mass density is small enough that gravitational forces can be neglected in comparison to the electrostatic forces, the static non-relativistic repulsive (outward) acceleration (at the instance of time that the lines of charge are separated by distance $R$) for each infinite parallel line of charge would be:

$$a = \frac{F}{m} = \frac{ \frac{1}{4 \pi \epsilon_0} \frac{2 \lambda^2}{R} }{\rho}$$

If the lines of charge are moving together past the observer at some velocity, $v$, the non-relativistic electrostatic force would appear to be unchanged and that would be the acceleration an observer traveling along with the lines of charge would observe.

Now, if special relativity is considered, the in-motion observer's clock would be ticking at a relative rate (ticks per unit time or 1/time) of $\sqrt{1 - v^2/c^2}$ from the point-of-view of the stationary observer because of time dilation. Since acceleration is proportional to (1/time)², the at-rest observer would observe an acceleration scaled by the square of that rate, or by ${1 - v^2/c^2}$, compared to what the moving observer sees. Then the observed outward acceleration of the two infinite lines as viewed by the stationary observer would be:

$$a = \left(1 - v^2 / c^2 \right) \frac{ \frac{1}{4 \pi \epsilon_0} \frac{2 \lambda^2}{R} }{\rho}$$

or

$$a = \frac{F}{m} = \frac{ \frac{1}{4 \pi \epsilon_0} \frac{2 \lambda^2}{R} - \frac{v^2}{c^2} \frac{1}{4 \pi \epsilon_0} \frac{2 \lambda^2}{R} }{\rho} = \frac{ F_e - F_m }{\rho}$$

The first term in the numerator, $F_e$, is the electrostatic force (per unit length) outward and is reduced by the second term, $F_m$, which with a little manipulation, can be shown to be the classical magnetic force between two lines of charge (or conductors).

The electric current, $i_0$, in each conductor is

$$i_0 = v \lambda$$

and the magnetic permeability is

$$\mu_0 = \frac{1}{\epsilon_0 c^2}$$

because $c^2 = \frac{1}{ \mu_0 \epsilon_0 }$ so you get for the 2^nd force term:

$$F_m = \frac{v^2}{c^2} \frac{1}{4 \pi \epsilon_0} \frac{2 \lambda^2}{R} = \frac{\mu_0}{4 \pi} \frac{2 i_0^2}{R}$$

which is precisely what the classical E&M textbooks say is the magnetic force (per unit length) between two parallel conductors, separated by $R$, with identical current $i_0$.

 

[Dale]

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.

That is a very specific claim, can you prove it?

 

[Subplotsville]

That is a very specific claim, can you prove it?

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.

 

[Dale]

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.

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.

 

[Subplotsville]

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.

Proof at relativistic speeds is unnecessary. 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.

 

[Dale]

Proof at relativistic speeds is unnecessary.

Agreed. I was talking about small speeds.

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.

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.

 

[lugita15]

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.

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?

 

[Tantalos]

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.

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?

 

[Dale]

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?

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.

 

[rbj]

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?

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.

the simple analysis i did that also got to the correct conclusion, but used nothing other than time-dilation. the mass per unit length $\rho$ gets bumped up by a factor of $\gamma = \left(1-\frac{v^2}{c^2}\right)^{-1/2}$ because of length contraction. and it gets bumped up by another factor of $\gamma$ because of relativistic mass. that's in the denominator.

in the numerator there is the charge per unit length gets bumped up by $\gamma$ because of length contraction. the question is should the quantity of charge itself be affected by $\gamma$? if not, there is $\gamma^2$ in the numerator and $\gamma^2$ in the denominator and it comes out in the wash. 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.

 

[Subplotsville]

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.

The logical step connecting time dilation and a change in force was omitted because it was already described in someone's post. 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. This leaves the lab observer unable to account for the two electrons not seeing the decreased net repulsion between themselves which he attributes to the magnetic attraction caused by their parallel motion.

BTW, I'm not sure a slower clock would measure less acceleration. Since the time variable is in the denominator, less time means more acceleration. But this doesn't matter since the non-linearity problem disqualifies it anyway.

Why exactly are you not able to view the Google Docs version?

This computer is restricted as to what online file types it can access, for security reasons. Pretty much only html, images and a few others. Sorry about that.

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?

Length contraction shouldn't be a factor in this case. It is only in the direction of motion. The electric and magnetic forces between the two electrons are perpendicular to the direction of their motion. The lab sees the electrons with a velocity perpendicular to the line joining the electrons, which see each other as at rest.

 

[Dale]

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.

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.

Btw, there is another way to resolve this issue, simply take me up on my offer from above.

 

[Dale]

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.

The integral of charge density over all of space is invariant. Charge density itself is part of the four-current.

The idea of relativistic mass is not in much use today, so most people wouldn't say that mass is affected. They would just use the invariant mass which is obviously invariant. Using relativistic mass can be particularly problematic in this kind of problem when you are doing accelerations in directions perpendicular to the motion.