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"Two different phenomena" in Maxwell-Ampere law; EM waves
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Joined: Fri May 19, 2017 6:20 am
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Post "Two different phenomena" in Maxwell-Ampere law; EM waves
Feynman notes that Faraday's law of induction "applies whether the flux changes because the field changes or because the circuit moves (or both). The two possibilities - 'circuit moves' or 'field changes' - are not distinguished in the statement of the rule."

He concludes: "We know of no other place in physics where such a simple and accurate general principle requires for its real understanding an analysis in terms of two different phenomena."

Really? The former case - "circuit moves" - could equally well be called "field moves" (relative to the circuit). Similarly, in the Maxwell-Ampere law (with no conduction current), the surface integral of D may change because the field moves or because the field changes, and the former case is easily quantified by analogy with the magnetic term in the Lorentz force law. Thus we obtain two equations describing the propagation of plane electromagnetic waves using no curls or circuit integrals, but only cross products. ("Look, Mom: no calculus!")

On that basis I have been able to reproduce the classical theory of double refraction and conical refraction of EM waves in non-isotropic media: http://vixra.org/pdf/1705.0276v1.pdf. So, while I might be missing something, I must also have done something right.

Moreover, it seems to me that the "field moves" case of the Maxwell-Ampere law must have a "circuit moves" form. Einstein famously wrote of Faraday's law:

Quote:
For if the magnet is in motion and the conductor at rest, there arises in the neighbourhood of the magnet an electric field with a certain definite energy, producing a current at the places where parts of the conductor are situated. But if the magnet is stationary and the conductor in motion, no electric field arises in the neighbourhood of the magnet. In the conductor, however, we find an electromotive force, to which in itself there is no corresponding energy, but which gives rise - assuming equality of relative motion in the two cases discussed - to electric currents of the same path and intensity as those produced by the electric forces in the former case.


The nearest analogy for the Maxwell-Ampere law would be:

Quote:
For if the charge is in motion and the magnetic core at rest, there arises in the neighbourhood of the charge an H field with a certain definite energy, producing a magnetic flux at the places where parts of the magnetic core are situated. But if the charge is stationary and the magnetic core in motion, no H field arises in the neighbourhood of the charge. In the magnetic core, however, we find a magnetomotive force, to which in itself there is no corresponding energy, but which gives rise - assuming equality of relative motion in the two cases discussed - to magnetic fluxes of the same path and intensity as those produced by the H field in the former case.


Fri May 19, 2017 9:40 am
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Post Re: "Two different phenomena" in Maxwell-Ampere law; EM wave

/edit/

see my next post, below :


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Last edited by quantumantigravity on Sat May 20, 2017 10:56 pm, edited 3 times in total.



Sat May 20, 2017 6:59 pm
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Post Re: "Two different phenomena" in Maxwell-Ampere law; EM wave
quantumantigravity wrote:
grputland wrote:

The nearest analogy for the Maxwell-Ampere law would be:

Quote:
For if the charge is in motion and the magnetic core at rest, there arises in the neighbourhood of the charge an H field with a certain definite energy, producing a magnetic flux at the places where parts of the magnetic core are situated. But if the charge is stationary and the magnetic core in motion, no H field arises in the neighbourhood of the charge. In the magnetic core, however, we find a magnetomotive force, to which in itself there is no corresponding energy, but which gives rise - assuming equality of relative motion in the two cases discussed - to magnetic fluxes of the same path and intensity as those produced by the H field in the former case.



Sounds logical, and clear enough for me.

If you are correct, I wonder if you could possibly try
to apply your hypothesis in order to find
the answer to "The Catt Question" :

http://www.ivorcatt.co.uk/x479.htm


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Sat May 20, 2017 7:02 pm
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Post Re: "Two different phenomena" in Maxwell-Ampere law; EM wave
Simply expressed, my suggestion is that the Maxwell-Ampere law, like Faraday's law, can be understood in terms of "lines of force" cutting a circuit. To me, this seems to follow from the similar mathematical forms of the two laws. To call it a "hypothesis" is to overrate it, methinks.

Concerning the Catt question, I don't think my "hypothesis" helps. I submit that whether the new charge in the bottom conductor comes from below ("south") or from the west depends on whether the ground conductor is grounded along its entire length or only at the western end. That distinction seems to have been ignored in the discussion. In neither case do individual electrons need to move at anything like the speed of light; only the change in concentration of electrons needs to move at that speed -- as McEwan and Josephson correctly note. It seems to me that Pepper interpreted the question as being broader than it was, and then concentrated his answer on the part that wasn't asked.

Disclosures: (1) By choosing viXra, I didn't intend to mark my idea as heterodox. (2) I hadn't heard of Catt before.

Thanks to "quantumantigravity" for the reply.


Sun May 21, 2017 6:41 am
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Post Re: "Two different phenomena" in Maxwell-Ampere law; EM wave
grputland wrote:
Simply expressed, my suggestion is that the Maxwell-Ampere law, like Faraday's law, can be understood in terms of "lines of force" cutting a circuit. To me, this seems to follow from the similar mathematical forms of the two laws. To call it a "hypothesis" is to overrate it, methinks.

Concerning the Catt question, I don't think my "hypothesis" helps. I submit that whether the new charge in the bottom conductor comes from below ("south") or from the west depends on whether the ground conductor is grounded along its entire length or only at the western end. That distinction seems to have been ignored in the discussion. In neither case do individual electrons need to move at anything like the speed of light; only the change in concentration of electrons needs to move at that speed -- as McEwan and Josephson correctly note. It seems to me that Pepper interpreted the question as being broader than it was, and then concentrated his answer on the part that wasn't asked.

Disclosures: (1) By choosing viXra, I didn't intend to mark my idea as heterodox. (2) I hadn't heard of Catt before.

Thanks to "quantumantigravity" for the reply.



Very good answer to the Catt question.

And I am still impressed by the logic and clarity of your conjecture (hypothesis).

If it really is an original idea, then you should put all your effort into designing and performing an experiment, which does not seem would be that difficult to do.

Please, keep us updated on any progress, even theoretical.

Looking forward to hear from you! :)

P. s.

In the meantime, you are very welcome to take a look
at my hypothesis : https://quantumantigravity.wordpress.com/





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Wed May 24, 2017 7:40 pm
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Post Re: "Two different phenomena" in Maxwell-Ampere law; EM wave
My claim is that an electric displacement field D moving at velocity r induces a magnetizing field

H = r×D.

This claim correctly predicts the ray-velocity and wave-slowness surfaces and polarization patterns for a biaxial birefringent crystal. That is probably more persuasive than any new experiment I could suggest. But:

If we consider the field to be stationary while a particle moves through it at velocity v, the velocity of the field relative to the particle is −v, so that (according to my claim) the particle "sees" a magnetizing field

H = −v×D,

hence a flux density

B = −μv×D.

Hence, if the "particle" is a magnetic dipole with moment M, it is subject to a torque

τ = M×B = −μM×(v×D),

whose associated potential energy is

U = −M.B = μM.v×D.

The restoring torque in combination with a moment of inertia gives a frequency of oscillation -- a testable prediction.

At the risk of getting out of my depth and/or spending too much time, the torque and potential energy could perhaps also be checked theoretically. If the dipole takes the form of a current loop, the fixed changes will have the same relativistic space contraction while the moving charges will not, causing different net electrical forces on different sides of the loop, hence a torque. And it is uncontroversial that a moving magnetic dipole will induce an electric field which will be superposed on the surrounding field, causing an orientation-dependent addition to the potential energy.

But perhaps what is really needed is a direct derivation of the initial claim. I'll comment again when I have something presentable.


Thu May 25, 2017 1:16 pm
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Post A Testable Prediction ???
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grputland wrote:

That is probably more persuasive than any new experiment I could suggest.




THERE IS NOTHING more persuasive than EXPERIMENTAL RESULTS. :)


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grputland wrote:

The restoring torque in combination with a moment of inertia gives a frequency of oscillation — a testable prediction.



IF YOU CAN MAKE A REALISTIC PREDICTION, THEN TEST IT !!! :)


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Fri May 26, 2017 1:14 am
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Post a testable prediction
grputland wrote:

The restoring torque in combination with a moment of inertia gives a frequency of oscillation -- a testable prediction.



Look, my Quantum Anti-gravity Hypothesis
makes easily testable Nobel Prize winning predictions :

https://quantumantigravity.wordpress.com/


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Sun May 28, 2017 1:56 am
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