# Length-contraction-magnetic-force between arbitrary currents

Discussion in 'Physics & Math' started by PengKuan, May 12, 2017.

1. ### Q-reeusValued Senior Member

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3,172
Not quite. There will be an uneven force density profile along the 'central lead' owing to that the out-of-plane B field component, generated by the circular coil, is not uniform as a function of radius from coil axis to periphery. All that matters is that the in-plane center of force acting on 'central lead' is offset from the coil axis of rotation. It's that offset that generates the torque.
Doesn't have to. By simply applying principle of superposition, change from one 'central lead' to two or more evenly spaced such, and likewise for external feed wires, torque on the 'central leads' + circular coil is maintained - now without any resultant linear forces on that assembly. Likewise for the immobile exterior feed circuitry + emf source. This is blindingly obvious by inspection alone! Why is there any continued issue to discuss here?
Directly acting on it as in Lorentz force sum from any B fields acting on it - yes zero. As I have stated over and over. Torque is mechanically transferred to the coil via the 'central lead(s). Obviously. And by symmetry, it's easily found the net interaction between symmetrically disposed 'central leads' generates zero torque. Are we done here?
Not directly. But it's necessarily part and parcel of the overall circuit. Only the coil B field has the correct orientations to induce azimuthal forces & thence torques on the rest of the circuit. Which must sum to zero for the overall circuit. I seem to remember stating that quite a few times already.
No. See above.
Provided 'entire circuit' means 'entire rest of circuit, exclusive of coil + 'central leads', then yes. See above.
No - you have jumped the rails again. Just read again carefully what I wrote above.
OK - a brief summary: circular coil never experience a direct torque on it - it's mechanically transferred via in-plane Lorentz forces acting directly on the 'central leads'. Similarly, the exterior immobile feed circuitry experiences a counter-torque. The B field generating both torque and counter-torque is supplied by the circular coil only.
Let's keep it short! As per that earlier quote in blue, Lorentz forces are a direct consequence of applying SR to charges in arbitrary relative motion. Consequently, if your Amperian force law were true, Lorentz force law is false. Therefore SR has it wrong. However, there has never been an experiment disagreeing with SR. Draw your own conclusion!

Last edited: Apr 2, 2018

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3. ### PengKuanRegistered Member

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Thank you for your patience. I see that you are fed up with my arguing. Let us stop at this conclusion:
While Lorentz force law is balanced on the whole circuit, it has not provided a satisfactory explanation to this rotating coil which is a part of this circuit.

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5. ### Q-reeusValued Senior Member

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Well unfortunately we have not had a satisfactory overall convergence - just on a few points. Sadly there remains a fundamental disagreement.....
Just how you can make that last conclusion, after all the foregoing discussion, escapes me. There were a number of issues covered in #34 never subsequently responded to.
However, given your final line above, I'd say there is no point bringing those up now.
My conclusion is you are so certain in your own outlook, based as it is on the need, shared by Ampere, to have Newtonian action & reaction preserved at the isolated current element level.
It's not how modern physics sees it.

Despite what I have written and argued here, purely within the context of steady current loops, there are other situations that call into question whether overall action and reaction always hold true. But to expand on that here would only lead to unnecessary diversion.

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7. ### PengKuanRegistered Member

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Fundamental disagreement is not unfortunate, but a good thing, because it is where new knowledge comes from. I can tell that our disagreement will be settle down very soon.

I have decided not to answer many issues because that would divert the discussion from the main point. Now that this is over, if there is any other point you want to talk about. Please raise it.

8. ### Q-reeusValued Senior Member

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Only this. We agree that Ampere force law disagrees with SR derived Lorentz force law. Have you worked out what replacement for SR is needed to be compatible with Ampere force law? Do you think any such 'new SR' will be generally self-consistent in all situations? I'm willing to wager any amount it would not.

9. ### PengKuanRegistered Member

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Plasma under Coulomb magnetic force
Nuclear fusion reactors use strong magnetic field to confine plasma in reaction chambers. The magnetic field is so designed that plasma should follow field lines which do not encounter the chambers’ wall. But it seems that a mysterious force pushes plasma off its track. For explaining this force, Coulomb magnetic force law for plasma is derived.
Plasma under Coulomb magnetic force
PDF http://pengkuanem.blogspot.com/2018/04/plasma-under-coulomb-magnetic-force.html
or

10. ### PengKuanRegistered Member

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Sorry Q-reeus, I have just seen your reply. I did not receive notification in my email.

I have propose a law that is Lorentz + a term, which I think agree with SR, here #28 http://www.sciforums.com/threads/length-contraction-magnetic-force-between-arbitrary-currents.159343/page-2#post-3511346
But I do not know why Ampere force law disagrees with SR. SR is ok, not Lorentz force law.

11. ### Q-reeusValued Senior Member

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3,172
By now it's clear the conversation just goes in meandering circles. That above link to earlier post #28 was in turn answered by my #34. Remember? In particular, my itemized point 1 there dealt with your incorrect assumption that moving conduction charges Lorentz contracted to a higher density within a conductor as seen in the conductor (not moving charges) rest frame.
It doesn't work that way for the reasons I gave then. Invalidating your subsequent derivation of 'Coulomb magnetic force'. What's new on the table?

12. ### PengKuanRegistered Member

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32

If you do not accept the increase of density is wrong, then, why do you propose that “local electron density actually decreases by 1/γ”?

13. ### Q-reeusValued Senior Member

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3,172
A confusing double negative there. I think you meant to write: "If you do not accept the increase of density is correct..."
Which is true, within the context I gave (rest frame of conductor) - and for the reasons set out back in #34.
As explained back then. To repeat; electron number density in circuit rest frame must be independent of charge flow speed. You can't have charges vanishing or popping into existence - conservation of charge is sacrosanct. Combined with charge invariance, charge density is fixed there - indifferent to charge speed. You have probably confused the situation for a closed circuit to that applying for an unrestrained infinite line current. Where moving charges are presumed free to maintain their number density constant in their own rest frame. The two cases are fundamentally different. SR applies equally to both, but the differing restraints/boundary conditions modifies the net results.
There is still a Lorentz contraction going on in the closed circuit case, but from a base, in the moving charge local rest frame, where charge density there has been stretched to 1/γ of that when the charges are at rest in the conductor rest frame i.e. when there is zero current.

I emphasized local rest frame and local charge density because charges moving in different parts of the circuit will have different relative velocities. And will see each other's number densities as variously Lorentz contracted or dilated wrt the zero current case. Which btw works out overall to be perfectly equivalent re forces acting, to just applying Lorentz force expression between such current elements.
All the above is perfectly consistent with an observer moving relative to the circuit, observing net negative or positive charge densities in various parts of the circuit. The total however always adds to zero.
Try studying that article I linked to back in #25.

Last edited: Apr 12, 2018
14. ### PengKuanRegistered Member

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Yes, I have done a typo.
Yes. Conservation of charge is sacrosanct. I know this.
I take this one, local charge density increases.
I have looked at this article. It is about linking classical EM and SR, which explains magnetic force as non reducible.
What I’m doing is to explain how magnetic force comes to live from Coulomb force.

15. ### Q-reeusValued Senior Member

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Are you contradicting what I wrote above - local conduction charge density necessarily dilates by factor 1/γ - by virtue of closed circuit constraints?
That guarantees charge neutrality in loop rest frame regardless of flow speed since conduction charge density wrt zero current case is there always γ(1/γ) = 1.
Good luck with finding some experiment that can unequivocally distinguish your Amperian aka Weber-Ampere force expression from the universally accepted Lorentz one.
A Peter Graneau persisted with your self-same conviction. Even managed to get one or two papers published in a few respectable journals back in the 80's, at a time when rail gun research was a hot topic. Also performed numerous experiments claimed to 'prove' existence of tensions in conductors only Amperian forces could explain. In each such case, it was rebutted as being perfectly in accord with Lorentz forces acting only.
Your choice to carry on his legacy - and finish up frustrated.

16. ### PengKuanRegistered Member

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Let’s talk SR later.

Peter Graneau have seen longitudinal magnetic force at work in railgun recoil. It is a pity no one want to believe him. If longitudinal magnetic force does not exist, how can you explain the Bucking of steel rails of the railgun? See image below.

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17. ### Q-reeusValued Senior Member

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Would be nice to have a link to the accompanying article. Regardless though, when an object, forming also one of the two short-leg transverse current paths in a closed circuit, is accelerated rapidly owing to Lorentz forces acting, there is necessarily a reaction back on the rest of the structure.
OK I had better not be contradicting myself here. Back in #34 I gave in point 2 an example of a slender rectangular coil, and stated the two parallel long legs felt no equal and opposite force to the ones tending to expel each short leg outwards. However they do experience Lorentz forces acting normal to their own axes - owing to the currents in those transverse short legs. In a rail gun, such transverse forces acting on the rails will be huge and will be impulsive owing to the traveling nature of projectile-come-transverse-current-path. Unless great care is taken in the mechanical stabilization of those current rails, it's entirely possible the impulsive transverse forces will lead to rail buckling. One thing is for sure - rail buckling will not amount to evidence Lorentz force law thus SR is somehow wrong.

Last edited: Apr 14, 2018
18. ### PengKuanRegistered Member

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Here is the link
https://dflund.se/~snorkelf/Longitudinal/node3.html
Search for Railgun recoil
I'm not searching for evidence that SR is somehow wrong. I think that the rail suffers strong longitudinal force that made them to fold.

19. ### Q-reeusValued Senior Member

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Nice article - brings back a few memories. As you are no doubt aware, most of those listed experiments have alternate explanations consistent with only Lorentz forces acting. Seemingly simple and clear cut evidence for longitudinal forces is not so when considering all the complex fine details.
One example that does seem clear cut I will comment on further: Under 'The multi-arc generator', it reads:

"In Nasi tex2html_wrap2971 owski's experiment a longitudinal stress, or repulsion, was observed in the interior of a conductor. The question now arose if this repulsion could be observed more directly. This was studied by Ruscak and Bruce [62]. A 6.4mm copper rod was cut into 1cm pieces and stacked to 1m length in a glass tube in vertical position. A light spring kept the pieces close together. When current pulses of 3-30kA were discharged through the column the pieces separated and arcs formed in between them, Figure 2.6. Some pieces spotwelded together by the arcs. Clearly, the rod pieces seemed to repel each other."

It would take enormous pressure - enough to generate plastic yield in the metal pieces - to create a more-or-less truly uniform current distribution across the interfaces between each copper rod piece. And that assumes perfectly clean surfaces of contact. That was not the case. Close up, very non-uniform flow through asperity contact patches will be the case. That will yield two effects:

1: Local hot spots where current densities are far above average.
2: Large radial components of current in the vicinity of such asperity contact regions.

2 all by itself will generate resultant Lorentz forces acting longitudinally - and of the right sign to yield repulsion between segments.
Additionally, 1 above will give rise to local ablating thus thermally induced gas pressure also tending to part the segments.
[Further thought - local melting at asperities will allow pinch forces to act longitudinally by reason of hydrostatic quasi-equilibrium in the melt regions. Possibly the greatest contributor to parting forces.]

Seemingly clear cut cases are not really clear cut if looked at closely.

Last edited: Apr 14, 2018
20. ### PengKuanRegistered Member

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Do you mean that these alternate explanation exclude longitudinal force?

But what about the railgun recoil force that I have posted photo of?

21. ### Q-reeusValued Senior Member

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They don't require longitudinal forces.
I gave one tentative explanation. But once again, when e.g. extremely high current densities are in play, you need to consider the fine details of what is actually going on.
There is arcing between the rails and projectile conductor surfaces. That means a plasma under pinch pressure that can be quasi-hydrostatically transferred to the rails.
The actual current distributions in that portion of the rails, in and near sliding contact with the accelerating projectile's conducting surfaces, will be highly non-uniform. There is then every chance of locally generated forces having components along the rail axes.

Just ss for that 'Multi Arc Generator' case, what seems naively to be clear-cut is anything but when under the microscope.
If Weber-Ampere theory of longitudinal forces were correct - SR has been overthrown. Something stated numerous times by now. Lorentz forces are the unique outcome of applying SR to charges in relative motion. Period. [Exclusive of radiation reaction which is totally negligible or entirely absent for current loop cases considered here] As I wrote much earlier - what is your alternative to SR that yields Weber-Ampere law for charges in relative motion?
Would it also work for other situations (basically, everything) where it's known SR is correct?

Last edited: Apr 15, 2018
22. ### PengKuanRegistered Member

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“They do not require” means “They have other alternatives”. But this leaves the chance for longitudinal forces intact. “They don't require longitudinal forces” does not mean longitudinal force is wrong.

Arcing, plasma, pinch pressure… These are not formal explanations, but possible factors that could be overlooked. You use “can be”, “every chance” which mean possible and these explanations have the same probability for being correct then longitudinal force.

For 'Multi Arc Generator', you cited 1: Local hot spots, 2: Large radial components of current. You also cited local ablating/gas pressure. For railgun rail buckling, you have also 3: arcing, plasma, pinch pressure. And for the other experiments in https://dflund.se/~snorkelf/Longitudinal/node3.html? They are 8:
1 Nasi owski's wire fragmentation,
2 The multi-arc generator,
3 Railgun recoil,
4 Ampère's hairpin experiment,
5 Agitation and wave formation,
6 Movement due to asymmetry,
7 Conductor stretching,
8 Electrodynamic explosions in water

Each experiment has the need of Ad hoc explanation. So, we need least 8 independent explanations, more than 10 if yours are counted. But longitudinal force is the one that is possible in all of them. If you see the group of 8 experiments as one phenomenon, is it better to explain them with longitudinal force at once or with the more than 10 ad hoc ones?

Occam's razor "Entities are not to be multiplied without necessity" explains why Copernican system wins against geocentric model. Future positions of the sun, moon and other solar system bodies can be calculated using a geocentric model or heliocentric model. Both work, but the geocentric model arrives at the same conclusions through a much more complex system of calculations than the heliocentric model, that is, each planet needs a different model for geocentric model, but heliocentric is the only one for all the planets.

Longitudinal force is the alternative for all the 8 experiments, but classical theory needs multiple. Before these experiments, the correct attitude should be: the best fitted alternative for the experiments is longitudinal force, but it is out of the classical domain. Let’s find how to include longitudinal force in a theory with a bigger domain. Rather than saying, classical theory is complete and nothing can be out of its explanative power.

I think Weber-Ampere law is wrong. The fact that Lorentz force fits SR does not exclude the possibility that other law conforms SR. My Coulomb magnetic force law is derived from SR, thus does not overthrow SR.

23. ### Q-reeusValued Senior Member

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Do you not agree there are indeed details needing to be considered - over and above what a simple 2D CAD drawing of any given setup would naively imply?
You say ad hoc. Better wording would be particular complexities. The reason for rejecting longitudinal forces is perfectly straightforward. Only Lorentz forces - as expressed in Grassmann's expression for forces between current elements, are compatible with SR.
So your longitudinal forces are not identical to their's? Whatever, both predict longitudinal forces contrary to uniquely SR derived Lorentz forces.
But it would if true. You really need to go right back and tackle what I wrote in #34 - itemized point 1.

I glanced through the 'Analysis of experiments' section of Lars Johansson's article: https://dflund.se/~snorkelf/Longitudinal/node5.html#SECTION00500000000000000000
He has considered the details from a Maxwell stresses pov mainly, and finds it adequately explains the observed behavour with maybe a question mark around details of NasiLowski's exploding wire situation needing cleaning up. I was not aware of how flimsy and prone to buckling Graneaus' rail gun setup was till reading that.
Have you corresponded with Johansson? Given his experience and focus on this issue, that would seem a logical thing to do.