I try my best to find deficiency in the PAPPAS experiment. Pappas inserted the Cupper wire into Mercury, but mercury dissolves the Cupper, formind amalgame. We know nothing, how this amalgame behaves inder initial DC current conditions. The process could lead to a polarization nerar Cu/Hg interface, leading to an Electrochemical Overpotential. Then, changing polarity, the Voltage is partially or in full is compensated by this overpotential, resulting to the assymmitry in the mecanical results.

The only metal, which is not dissoleved in Hg is IRION, which should be used as a CONDUCTOR - WIRE . But Electrochemistry was not addressed in the PAPPAS experimental work.

Demitris, your question came to me out of sky. As I don't have a General Physics book on hand, I answer from the top of my mind. Ampere and Biot-Savart forces belong to Electrical Engineering today. Only Lorentz force belongs to Physics.

I am sure, Biot-Savard force serves Engineers fine, so, they use it. Strictly speaking, the second Law of Newton fails Relativism, but by no way Engineers will switch to GENERAL RELATIVITY.

As this post, probably, will be seen by professional Theoretical Physicists, please, inform, whether Navier - Stockes Equation of Fluid Mechanics was ever rewritten within General Relativity Field. As it is, the N - S Equation is based on Newtonian Mechanics as well.

There is one Ampere's law that the circulation of the magnetic field is proportional to the current density; that's the one modified by Maxwell when he introduced the displacement current. There is another Ampere's law of force, giving the force on a correct loop, in the presence of a distribution of currents. To my knowledge this Ampere's law of force is no more than the magnetic force as follows from the law of Biot- Savart. There are, however arguments that there is a difference. (See for example http://www.21stcenturysciencetech.com/articles/spring01/Electrodynamics.html .) This article might sound as a conspiracy theory. However it has relevant information on Mossotti's proposal to explain gravity as an electromagnetic force. This possibility was explored by Weber, Heaviside, Ritz, and Lorentz. Lorentz gave up because he could not explain Mercury's orbit precession. I think this is a possibility to consider nowadays, despite the formulation of general relativity, because our knowledge of the Solar system and the structure of matter has improved. (There is a recent book by Jefimenko, relative to this subject.)

Exelent discussion, please, anyone who has access to the paper discussed for free, provide PDF file along with his post.

@Oscar, the paper refers, to your rank, to the second Ampere law:

dF_{1,2}=-r\frac{I_{1}I_{2}}{r^3}\left(2ds_{1}.ds_{2}-\frac{3}{r^2}(ds_{1}.r)(ds_{2}.r)\right)

This law is symmetrical under interchange of 12:

dF_{2,1}=-dF_{1,2}

The law of Biot-Savart IS NOT symmetrical and thus is violating the Newton's third law of action and reaction.

There exists also a great assumption in classical electromagnetic theory if we accept as true the Biot-Savart law:

All open circuits are supposed to be closed due to displacement currents (via aether? via billiard ball like particles? how?) in order for the Biot-Savart law to work properly.

That's the crucial point, I think.

I see. I did not get to the source because I would have to pay for it and that's too much for a school teacher in USA. It is interesting though. I will take a look to the sources I have. I can tell now that Biot-Savart is valid but only for closed, stationary loops, because isolated stationary linear elements of current will be in violation of conservation on charge. In this case, the expression can be made symmetrical (Inductance is a symmetrical matrix.) For electrodynamic situations Biot-Savart does not apply. It will be interesting to study its generalization and compare to Ampere's experimental law.

Thanks to Demetris, I finished my first reading of this paper. The author found different results for mechanical forces acting on conductors within close loop system, when direction of electric current is changed. . This experiment is not supported by Amper Formula, as the value of force depends on product of currents in different parts of closed system, and is proportional to I^2, and, just independent on the direction of the current.

Thus, the very formula the author advocates fails to support his results.

More to the point, the Lorentz force, acting on the moving charge by the external elictromagnetic field can be directly derived from the INDUCTION LAW of FARADAY, which preceded the MAXWELL Equetions. and formed their basis.

In short, I found the experimental results unsupported within classical works of either

FARADAY, MAXWELL, LORENTZ and EINSTEIN or by the AMPER FORMULA. .

Dear Alexander, your point is making situation more interesting. According to your study the experiment cannot be explained with the foundations of classical electromagnetic theory, thus arises a new question: why the Π (orthogonal frame) does not react with the same way when we altering the current direction?

Dear Demetris Christopoulos

Please send me your reference "http://link.springer.com/article/10.1007%2FBF02721552#

I am unable to download this.

I read all answers / comment and find very much interesting. Really, I am fully agreed with your nice comments.

Demetris, the PAPAS experimental result contradicts with Ampere formula, wich he wished to confirm. Thus, no result can be found within Classical Electromagnetism, which support the PAPPAS result. When such descipency is found, the second independent lab should confirm the claimed experiment. Please, provide results of confirmation in the case that is known to you. As it is, I am inclined to believe that an experimental error has been made. I can not indicate the reason for this error without actually seeing the equipment and running experiment by my own hands.

The classical Electromagnetism serves mankind fine, during last 150 + years. Any real flaw would be reported long before the PAPPAS experiment.

Regards, Alex

Here is PDF file of the paper Demetris is talking about.

Dear Alexander, I found it interesting and I posted it here in RG, I have not any further access to the original experimental data. Another relevant paper that claims the equivalence of the two laws is here:

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.176.6745&rep=rep1&type=pdf

@ Demetris. Oh, sure, I agree with the last paper you provided. The author politely indicated that no contradiction exist within the classical electromagnetism, and that the PAPPAS experiment proves nothing and, thus, is mistaken.

But you raised fine discussion on the subject, I, personally, had a good time. Thanks a lot.

I try my best to find deficiency in the PAPPAS experiment. Pappas inserted the Cupper wire into Mercury, but mercury dissolves the Cupper, formind amalgame. We know nothing, how this amalgame behaves inder initial DC current conditions. The process could lead to a polarization nerar Cu/Hg interface, leading to an Electrochemical Overpotential. Then, changing polarity, the Voltage is partially or in full is compensated by this overpotential, resulting to the assymmitry in the mecanical results.

The only metal, which is not dissoleved in Hg is IRION, which should be used as a CONDUCTOR - WIRE . But Electrochemistry was not addressed in the PAPPAS experimental work.

And, finally, I provide here the file of the paper, published in TOP Journal in Physics,

rejecting PAPPAS claim . They provide experimenta data and theoretical calculations,

supported by classival Electrodynamics.

There exists also:

http://www.physicsessays.org/doi/abs/10.4006/1.3033428?journalCode=phes

Demetris, you wrote:

"The law of Biot-Savart IS NOT symmetrical and thus is violating the Newton's third law of action and reaction."

The Newton's third law must fail at relativistic conditions. It may only work when the velocity of transferring interactions is infinite. Such approximation is OK in classical mechanics, but need not to work in electromagnetism, and, in fact it doesn't work. Thus the asymmetry in Biot-Savart law is not a sufficient reason to claim it is incorrect.

Accidentally, Newton is also remembered for his works on gravity - but that's completely different story.

Dear Marek Gutowski

As I know the both the laws are used for calculation of magnetic field due to flow of currnet in conductor.

I want to know which is much more preciously or eccurate.

Just a wild guess: Ampere's law, at least in its integral form, is unusable when the current line is knotted. This is no problem for Biot-Savart description.

Moon and Spencer have shown that only Ampére's force law is in accordance with present observations. Biot-Savart's law is obtained from Grassman's modification of Ampére's force law, which he made to prevent longitudinal forces. Biot-Savart´s law is the field part of Grassman's law. However, Grassman's law violates Newton's third law, i.e. momentum conservation, and surely cannot be taken seriously in case searching for interaction between single charges.

So why is Ampére's law suppressed by the modern society? This is because, from this law there is no way to define a magnetic field. It is the quest for a field that makes us do this severe mistake.

I have summarized the problems in my book Electrodynamics - The Field Free Approach

http://link.springer.com/book/10.1007%2F978-3-319-13171-9

See also Weber's Electrodynamics by AKT Assis, Kluewer