Length-contraction-magnetic-force between arbitrary currents

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

1. PengKuanRegistered Senior Member

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Tangential magnetic force experiment with circular coil

If magnetic force is to respect Newton’s third law, there should be a recoil force on the vertical current which is Ft. This force is tangent to the current I1 and called tangential magnetic force. Some physicists claim that tangential magnetic force exists, this claim is supported by some experiments such as the rail gun recoil force shown by Peter Graneau and Ampère's hairpin experiment, see Lars Johansson’s paper. But these experiments did not convince the main stream physicists and tangential magnetic force is rejected. I have carried out an experiment to show tangential magnetic force acting on a circular coil.

PDF Tangential magnetic force experiment with circular coil http://pengkuanem.blogspot.com/2017/06/tangential-magnetic-force-experiment.html

3. Q-reeusValued Senior Member

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I remember discussing Graneau et. al.'s claims re Amperian forces back sometime in the 80's. It was being taken seriously by one researcher at a local defense establishment looking into rail-gun design. Apart from the obvious conflict with SR implied by Ampere's formulation, I pointed out any purported longitudinal forces could be made vanishingly small by applying a simple scaling argument. All agree that for separate current circuits, the correct inter-circuit forces result always agrees with the standard magnetic Lorentz force law. Therefore any 'longitudinal forces' must be found between current elements within any given circuit. But any given circuit can be sub-divided up into a bundle of an arbitrarily large number of arbitrarily fine filamentary circuits. Apply the supposed Amperian longitudinal force expressions between current elements within each such filamentary circuit, and it soon becomes evident the longitudinal force densities i.e. stresses vanish in the limit of infinitesimal filament radii. Consequently, for the undivided circuit also. If you doubt that, do your own sums!

The impulses observed in that YouTube vid with suspended coil will for sure follow from a thorough application of the magnetic Lorentz force law. As for the example of unequal action and reaction between a transverse current element and an infinitely long current, the standard reply is it neglects momentum changes occurring in the fields. You can't just have an isolated, electrically neutral current element. It forms part of a larger circuit. Even so, the active part of any such an element is just the moving electrons, and they generate an electric and magnetic field, which together with the magnetic field of the infinitely long current, formally at least will contain precisely the 'missing' momentum change you get by looking at only the magnetic forces between the currents.

There are situations where no such simple resolution is evident, but I'm not going there here!

5. danshawenValued Senior Member

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Ha. Think about a permanent magnet, or for that matter, a magnetar. It has a magnetic field in the rest frame. That should not even be possible, should it? Okay, so I should watch the other video.

Why doesn't a magnetar simply break up itself up into billions of smaller magnets and spontaneously flip half of them to the opposite polarity / orientation to cancel out its own magnetic field? Atomic bonds are not strong enough to prevent this, really, are they? Or is it full of magnetic monopoles or something? Pretty sure that won't be explained in the video.

Last edited: Jun 7, 2017

7. PengKuanRegistered Senior Member

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Why is Ampere's formulation in conflict with SR?

The force that lies on the radial vector is not necessarily instantaneous. Gravitational force is not instantaneous.

The splitting of a circuit into filamentary circuits does not change the total force on a part of the circuit. Let A and B be 2 part of the same circuit. We split them into A1, A2… An and B1, B2…Bn. The total force on B1+ B2+…+Bn stays the same.

Lorentz force is perpendicular to current. So, the torque on the coil due to Lorentz force is zero.

8. Q-reeusValued Senior Member

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Check any textbook on EM that includes SR. Lorentz force follows directly from a relativistic treatment of charges in relative motion. Plenty of online resources too, e.g.:
http://www.physics.udel.edu/~bnikolic/teaching/phys208/lectures/em_special_relativity.pdf
And? This permits Amperes 'longitudinal forces' how exactly?
Strawman argument. I nowhere suggest otherwise, and it misses my argument entirely. You seem to be like another poster who endlessly argues but never gets down to doing the sums to prove it one way or the other. My claim is correct. Do the sums!!
A correct analysis taking all the circuit into account will for sure be consistent with Lorentz forces only.

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9. exchemistValued Senior Member

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10. PengKuanRegistered Senior Member

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Continuous rotation of a circular coil experiment
There is a long standing debate about whether tangential magnetic force exists. In «Tangential magnetic force experiment with circular coil» I discussed this force and presented an experiment that showed the action of this force. But, as the rotation of the coil in that experiment was limited to a small angle, it does not show that tangential force exists all over the coil. So, I have carried out the present experiment that shows continuous rotation of the coil to make clear that tangential force has the same value around the coil

PDF Continuous rotation of a circular coil experiment http://pengkuanem.blogspot.com/2017/06/continuous-rotation-of-circular-coil.html

11. PengKuanRegistered Senior Member

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Coulomb magnetic force
The relativistic length contraction effect and changing distance effect produce 2 different magnetic forces. Together they form complete magnetic force.
I have derived 2 magnetic forces with Coulomb’s law and charges’ velocity. The first force dFlc is derived in «Length-contraction magnetic-force between arbitrary currents». The second force dFcd is derived in «Changing distance effect». dFlc and dFcd are added together to give the expression for complete magnetic force dFcm.
Coulomb magnetic force
PDF http://pengkuanem.blogspot.com/2018/03/coulomb-magnetic-force.html
or
PDF Changing distance effect http://pengkuanem.blogspot.com/2018/03/changing-distance-effect.html or

12. NotEinsteinValued Senior Member

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PengKuan, are you here to discuss your work (in that case, please respond to post #25), or just to advertise (which is against the rules)?

13. PengKuanRegistered Senior Member

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I want to discuss my subject. I answer all the replies.

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15. PengKuanRegistered Senior Member

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There was no direct reply to #25. It was one year ago. Jun 8, 2017

In fact, my post #27 titled Continuous rotation of a circular coil experiment is a reply to #25 and his objection in #22. He objected about 'longitudinal forces' and I thought it would be more convincing to make a coil rotate continuously and I did my experiment #27 Continuous rotation of a circular coil experiment to show the 'longitudinal forces' at work. But he did not reply to me. Should I reply to Q-reeus’ #25 for him to see my post?

And in #25, he said
To this objection, my post #28 titled Coulomb magnetic force is an answer which explain how in theory 'longitudinal forces' arises. I had not this theory at the time of his post #25. So, I couldn’t answer right then.

I will give him a reply now.

16. PengKuanRegistered Senior Member

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Sorry for replying you 1 year too late. But the Administrator reminds me that I should keep discussing with you. Please read the post #27 which is an answer to your objection about 'longitudinal forces'. I think it is more convincing to make a coil rotate continuously and I did my experiment #27 titled Continuous rotation of a circular coil experiment to show the 'longitudinal forces' at work.

which explains how in theory 'longitudinal forces' arises. I had not this theory at the time of your post #25. So, I couldn’t answer right then.

17. Q-reeusValued Senior Member

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Thanks for apology but not needed given your situation.
As you state in first part of that vid, it's a Homopolar motor. The further claim only longitudinal forces can explain it's motion is false. The lead labelled 'central lead' clearly runs radially from coil periphery to central axis. That portion is subject to an out-of-plane B field generated by the coil. The resulting Lorentz force will obviously act in the plane of the coil but whose center is offset from the coil rotational axis. Thus a Lorentz force generated torque acts to spin the coil as shown.
An industrial version would have axially symmetric radial current feeds to avoid the unbalanced wobble inherent in your setup. And btw it's by contemplating the field symmetries existing in a balanced radial currents design, one can see the radial currents do not act reciprocally on the coil. But this is not overall violating Newtonian mechanics - a counter-torque will be experienced in the exterior feed portions of the circuit. In any overall analysis the entire circuit must be evaluated.
With so many links to further articles it's a big overall read. I'll try and itemize in no particular order:

1: First article linked to within 'https://pengkuanem.blogspot.com/2018/03/coulomb-magnetic-force.html' is 'Length-contraction-magnetic-force between arbitrary currents': http://pengkuanem.blogspot.com/2017/05/length-contraction-magnetic-force.html
Towards the top of p2, it claims:
"When a current circulates, the free electrons move at velocity v and their charge density ρ- increases according to equation (6) and becomes ρ'- of equation (7).
Note that the increase of charge density is a relativistic effect, the wires are neutral and not actually charged, that is, there is not excess of positive or negative charges."

The claimed increase in electron charge density - implicitly wrt lab frame - by the usual factor γ = 1/√(1-v²/c²) (eqn (7)), is wrong. And clearly inconsistent with the latter statement there is no overall charge imbalance. Cannot have it both ways! Fact is there must be conservation of charge number in a closed circuit, and coupled with charge invariance, charge density in lab frame is constrained to be independent of drift velocity.
In a frame where drifting conduction electrons are stationary, local electron density actually decreases by 1/γ. While it's the positive lattice charge density that increases by factor γ.
Thus conduction electrons in their own frame 'swim' in a positively charged 'sea', and feel a net radial inward force proportional to distance from the conducting wire axis (assuming a wire of circular x-section). It's a bit laborious to do but readily found this inward radial force is precisely that given by the magnetic Lorentz force - owing to motion wrt the azimuthal B field generated by the wire current. There are no net longitudinal forces anywhere in that scenario. The correct picture is nicely given in that article I linked to back in #25.

That above initial conceptual error invalidates essentially everything that follows. But, moving down to part 6 'Annex' in:
https://pengkuanem.blogspot.com/2018/03/coulomb-magnetic-force.html
, let's look at a few other linked articles given there:

2: http://pengkuanem.blogspot.com/2012/03/lorentz-forces-internal-to-equilateral.html
Various assumptions are made about the magnitude of the reaction forces - all without doing a somewhat tricky actual integration over the entire lengths involved.
At any rate your finding of a 'violation of Newton's 3rd Law' is moot. All that matters is the net force on the entire loop. Which just by symmetry alone will be zero. That action does not generally equal reaction between given parts of a loop current could have been more convincingly demonstrated in the case of a large aspect ratio rectangular loop current. Pick any given short end. The two long legs on either side act on the short length to produce an outward Lorentz force on the short leg - acting along the long legs common axis. Yet the short leg induces only lateral forces on each of the long legs!!!!!!! But again that is not a crisis for Newtonian mechanics - there is an opposite outward thrust on the other short leg. Overall - zero self-force on the loop. That's what matters.

That one is particularly easy to dismiss. Sorry but there is no such creature as that magnetic shield. In particular because there is no way to shield the azimuthal B field created by leg s3, via that cylinder presumably of ferromagnetic material. All you will have is an internal circulating B within the 'shield'. The sole means to neutralize the field of that 'shielded' leg is via a coaxial current there of equal magnitude and opposite sense. Such 'shielding current' must continue somewhere to form a closed circuit. All you then have in effect is a new overall circuit with the two common legs effectively not there.

4: http://pengkuanem.blogspot.com/2012/03/lorentzforce-internal-to-coil-analyze.html
Now you have unsymmetric shapes and an actual double integration over the entire loop in each case is needed. [But see 6 below!]

Basically, a bent short dipole antenna. Owing to the L shape, there will be an unsymmetric radiation pattern. Thus a net momentum flow in the radiation field. Which you have not accounted for. Furthermore, the assumption that only magnetic Lorentz forces need be considered is wrong. Net electrical forces owing to non-electrostatic -dA/dt E fields also exist and will in general act counter to the magnetic forces. A thorough analysis taking all contributing factors into account is needed before claiming a violation is real.
A great place to study the separate and net contributions of E and B fields & forces within conical cavity resonators is: http://www.gregegan.net/SCIENCE/Cavity/Cavity.html
The advantage there being the systems are entirely closed so external radiation of momentum is not present to complicate analysis.

6: http://pengkuanem.blogspot.com/2014/11/self-force-of-3d-coil.html -> https://pengkuanem.blogspot.com/2012/04/analyze-of-lorentz-forces-internal-to.html

A hard slog to work through. Assuming the un-numbered final expression, following (9) on p7 there is mathematically correct, and yields the claimed force imbalance....

It means either your numerical evaluation has failed to adequately capture the tendency for 'blow-up' of forces close to the corners (assuming idealized infinitely thin currents), or....

There is a mathematical crisis at hand. That's because, going back to my post #22, it's been long known the net magnetic Lorentz forces between any two steady and stationary loop currents are equal and opposite: http://physicspages.com/pdf/Griffiths EM/Griffiths Problems 05.49.pdf
Well obviously use of your version guaranteeing equal and opposite forces won't change that outcome.

But here's the rub. We all agree any possible net self-force on the original undivided loop will go as I^2, where I is the current in that loop.
Now Subdivide your triangular loop equally into n filamentary loops all having the same overall shape. The current in each such filamentary loop is now I/n. Taken in isolation the assumed self-force is therefore ~ to (I/n)^2. Summing for n such loops we arrive at a net self force ~ to n(I/n)^2 = I/n - recalling that the inter-loop forces are equal and opposite.
Obviously this is a logical contradiction. Unless of course there is precisely zero net force on the original loop thus for any subdivided filamentary loop also.
[There is one proviso re above finding: Neither the original nor subdivided loops can be allowed to have infinitely sharp corners. By stipulating corner radius of curvatures r >> than wire x-sectional dimensions of either the original or subdivided loops, no mathematical singularity issues will arise to cause anomalies.]

Last edited: Mar 30, 2018
18. Q-reeusValued Senior Member

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Erratum: 4th last line in #34, last term should have been (I^2)/n not I/n.

19. PengKuanRegistered Senior Member

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Thanks for your reply with so much comments. But I cannot manage so many points at once. I think it would be great enough if we can arrive at one agreement, at least agree about our difference.

My point is that magnetic force must respect Newton’s third law at the current element level. That is, the forces on 2 interacting elements must sum to zero.

Your point is different. You believe that Lorentz force law respects already Newton’s third law, at the coil level. It does not have to on the current element level. This is why you always emphasize:
But my experiment is meant to show the contrary. You said:
This means that you think that the force on the 'central lead' is made by the “B field generated by the coil”. So, this force is acted by the coil.

Then you said:
So, for you it is the force on the 'central lead' that makes the coil rotate, that is, the force made by the coil pushes the 'central lead' which makes the coil to rotate.

But the coil and the 'central lead' are parts of the same solid structure. If the force made by the coil on the 'central lead' can make the coil to rotate, it is a self force of this structure. This is like asserting that someone can make him to fly upward by pulling his hair. This is of cause impossible. So, the explanation using Lorentz force law is inconsistent, which is because of the non respect of Newton’s third law at the current element level by Lorentz force.

20. Q-reeusValued Senior Member

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You're welcome.
Given only the negative conduction charges are in relative motion, we can ignore the positive lattice charges and consider two electrons in relative motion. Then it's apparent there is not just forces acting between the charges, but also time-changing EM field configurations. Formally a momentum density P = (E x B)/c is stored in those fields, and is changing with time - viz a formal force density dP/dt exists in the crossed time-changing fields. Turns out the mechanical force imbalance i.e. Lorentz force sum is exactly compensated by the time rate of change of 'stored field momentum'. There are many articles on that topic. It's worth noting the field momentum is mostly not associated with radiation, but is 'locally stored' in the quasi-static crossed fields.

So even for isolated current elements, an overall force balance exists - IF one is prepared to accept that real momentum exists in crossed static or quasi-static fields.
But this is getting away from your situation which deals with steady-state loop conduction currents. The above issue of field momentum doesn't then enter.
Yes. But see above.
And there is no such issue with your Homopolar generator. You failed to include my further comment:
"An industrial version would have axially symmetric radial current feeds to avoid the unbalanced wobble inherent in your setup. And btw it's by contemplating the field symmetries existing in a balanced radial currents design, one can see the radial currents do not act reciprocally on the coil. But this is not overall violating Newtonian mechanics - a counter-torque will be experienced in the exterior feed portions of the circuit. In any overall analysis the entire circuit must be evaluated."

Think about it afresh. In your setup, the coil B field reverses direction exterior to the coil periphery, and acts on that basically radial feed wire (and electrolytic path between feed wire tip and coil periphery), plus emf source e.g dry cell battery, plus any other electrical connecting wires not shown, to give an overall equal and opposite counter-torque. The entire circuit will experience zero net torque and linear force.
In some Homopolar motor designs, there is axially uniform radial current flow from periphery to center, and the B field of such radial current flow is entirely azimuthal thus generates zero torque on any azimuthal coil windings. Manifestly, no equal and opposite action between these parts of the overall circuit is possible.
If Newton's third law were respected at the current element level in the way you think, SR has been overthrown. Lorentz force law is the outcome of SR transformations applied to moving charges.
Yet I get the impression you believe in SR. Problem!

Last edited: Mar 31, 2018
21. PengKuanRegistered Senior Member

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I had noticed that you said “a counter-torque will be experienced in the exterior feed portions of the circuit.” I did not cite it because for me it is a confusion. The force on the central lead comes from the coil through its magnetic field, not from the exterior feed portions. You cannot say that the reaction force of the central lead acts on the exterior feed portions rather than on the coil. If Bob kicks Bill, Bill does not retaliate Tom who did nothing.
In reciting “a counter-torque will be experienced in the exterior feed portions of the circuit.” and also saying:
You maintain that the force making the coil to rotate is on the central lead. Let us add this force with the force on the exterior feed portions. When they are in front of each other, the force on the central lead points toward left to make the coil rotate. The force on the exterior feed portions points toward right so that the overall force is zero. In this case, the central lead is at 6 o’clock on the round clock represented by the coil.

When the central lead rotates 180°, pointing at 12 o’clock, the force on it points toward right to make the coil rotate. But the force on the exterior feed portions still points toward right. So, the overall force on the system is 2 times the force on the central lead. Do you agree with this ?
I complete agree. But this is not true in the second case.
I’m sorry to point out the error you make in logic. “Lorentz force law is the outcome of SR”. Lorentz force law is not equivalent to SR nor is it the father of SR. It is the child of SR. If one kills the son, the father does not die.

22. Q-reeusValued Senior Member

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Which is what I wrote! How did you get to wrongly interpret me as having claimed action and reaction was between 'central lead' and exterior feed wire? I nowhere claimed such.
A poor analogy here since it is a fact that current elements will in general unequally react on each other via Lorentz forces. To labor a point made many times now.
It's further true, as per my #2: itemized example of slender ratio rectangular circuit given in #34, there need be no equal and opposite reaction between any given current element and the entire rest of circuit. All that matters is that the net of loop self-forces and torques adds to zero. Which Lorentz forces correctly applied guarantees.
No. You have misinterpreted my argument. For the lopsided, unsymmetric arrangement in your setup. the single 'central lead' will be acting, via Lorentz forces, to some extent on both the circular coil and rest of circuit. Not action-reaction equally, but such that always the net force and torque on the entire circuit is zero.

Again, you have left out of your quotes a telling point I have made repeatedly - choose a symmetric arrangement where at least 2 equally spaced 'central leads' are used, likewise for the exterior feed wire(s), and your argument is manifestly moot. A torque still exists driving the coil to spin, but symmetry now guarantees there are no possible 'unbalanced linear forces'. Which in fact are never there in the overall circuit of your lopsided design, but is now manifestly impossible by symmetry alone.

Further, as stated last post, and earlier, multiply the 'central lead(s)' to become in effect a circular disc, uniformly fed from the periphery, and the B field generated by that radial current flow is purely azimuthal. Hence incapable of generating any Lorentz force on the circular coil whose current is also purely azimuthal.
The exterior, axially uniform feed currents - the entire rest of circuit - experience the equal and opposite torque to that acting on the coil via Lorentz forces on the radial acting 'central lead -> disk' current.
Which is fairly obvious by inspection - the generally upward say B field interior to the coil periphery, bends over and acts downwardly exterior to the periphery - where the exterior , radial feed currents are closest to that B field.
Sorry but the error is all yours. That in red is a complete misinterpretation of what you quoted in blue. Have another read, and a rethink of what I actually wrote.

23. PengKuanRegistered Senior Member

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For avoiding such misunderstanding, let me summarize the things upon which we agree you and me.
The Lorentz force the whole circuit acts on itself is zero. I agree.
The Lorentz force on the central lead is azimuthal. I agree. If I understand well the word, azimuthal means tangent to any circle centered at the axis.
The Lorentz force on the central lead is acted by the coil’s magnetic field. I agree.
The Lorentz force acts a counter torque on the exterior lead, contrary to the rotation of the coil. I agree.

So, we do not need to repeat these things anymore and concentrate our attention on the difference between us. The setup is split into 2 parts. One is immobile including exterior lead, other wire and so on. The other is the coil plus the central lead, which rotates. The question is: what is the force that drives the coil to rotate? You said in #34:
You think it is the torque on the central lead that drives the coil.
What you propose here is a rearrangement of the setup to make 'unbalanced linear forces' impossible. But this does not explain the driving torque.
The circular coil is already circular and has not azimuthal force on it. So, the torque on it is zero.
Yes. Agree.
Yes. Agree. But this is not the reaction force as you said here:
So, the force on the exterior feed wire has nothing to do with the driving torque. The torque on the central lead is acted by the entire circuit. So, there is a counter torque on the entire circuit to make the overall torque zero. The torque on the immobile part is not the reaction force as you said. By subtraction, the reaction force to the driving torque is on the coil. Is this correct?
The text in blue:
This is what I have understood:
You claim:“Lorentz force law is the outcome of SR transformations applied to moving charges.” For me this means “Lorentz force law is built on SR”. What you mean by this is: “Lorentz force law is as correct as SR”. So, you assert this deduction:
“If Newton's third law were respected at the current element level in the way you think”, for me this is equivalent to say “If Lorentz force law were wrong”. Your conclusion:“SR has been overthrown”. For me this means “Then, SR is wrong”. What you mean is “If Lorentz force law were wrong, then, SR is wrong”.

But you say “Lorentz force law is the outcome of SR”. So, Lorentz force law is a child of SR. If Lorentz force law were wrong, SR is not necessarily wrong because it is not the consequence of Lorentz force law.