Internal Lorentz force paradox

[CaptainPanic]

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pengkuan,
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[pengkuan]

Rigorous proof of the flaw of the Lorentz force Law

Analyze of the Lorentz forces internal to an triangular coil

Personal information removed.

12 April 2012

The Lorentz force respects the third Newton's law. Is the Lorentz force internal to a coil consistent with the thirdNewton's law ? Let us analyze the triangular coil ABC in the Figure 1; the current is I . Each side feels a Lorentz force from the magnetic field of the coil itself. The resultant force of all the Lorentz forces on the 3 sides is the double integrated F in the Figure.

 

I have done a numerical computation for a triangular coil with base length of 1 and height of 10. The calculated force is dimensionless and the value of the overall resultant force is (see the Figure 2):

S= 35.21 e_y

This force is not 0, violating the third Newton's law. In general, this value suffices to prove that the Lorentz force law is flawed, because only one counter example is sufficient to topple a general law. However, to exclude any doubt about the accuracy of this numerical calculation, I have done a rigorous analytical proof, which gives the expression of the dimensionless resultant force for a isosceles triangular coil, F_res given in the Figure.

 

Thus, the analytical method proves without a doubt that the Lorentz force law is flawed. The mathematical derivation of the proof is given in the Mathematical Proof (see pdf link)

 

 

The mathematical proof is in the pdf document and the following jpeg

Analyze of the Lorentz forces internal to an triangular coil

https://docs.google....a0lsRlVfSXpYbWM

 

 

And the complete study

Paradoxes and solutions about Lorentz force law

https://docs.google....vcDlTMjdYMXMydw

Edited April 13, 2012 by hypervalent_iodine
Personal information removed.

[pengkuan]

Mathematical cause of the existence of the remaining resultant internal Lorentz force

 

19 avril 2012

 

I have given a rigorous proof of the existence of a remaining resultant Lorentz force internal to a triangular coil and a numerical computation that confirms this proof:

Proof of the remaining resultant Lorentz force internal to a triangular coil

https://docs.google....a0lsRlVfSXpYbWM

 

Why the Lorentz force law cannot respect the third Newton's law? What is the mathematical cause that leads to this inconsistency? Let us examine the effect of the characteristic perpendicularity of the Lorentz force with the current. Take a triangle with height h and base a+b (see the Figure 1).

 

Mechanism.pdf

[pengkuan]

Mathematical cause of the existence of the remaining resultant internal Lorentz force

 

19 avril 2012

 

 

 

 

Mathematical cause of the existence of the remaining resultant internal Lorentz force

https://docs.google....T0ZfaXdpenFvSjA

[pengkuan]

Synthesis of the inconsistency of theLorentz force law

I have given several proofs of an inconsistency of the Lorentz force law, for example, in "Mathematical cause of the existence of the remaining resultant internal Lorentz force"

 

In this article, I have proven mathematically that the Lorentz force internal to a triangle coil cannot sum to0, because the magnitude of the Lorentz force is approximately a parabola of the height whereas the force that makes 0 sum varies linearly with the height.

 

One of the objections to me is: "Your mathematics are wrong". This objection could be receivable if this were an unique mathematical proof. But this is not the case, for I have given an other mathematical proof, in "Proof of the remaining resultant Lorentz forceinternal to a triangular coil"

 

...........

 

 

Please read the attached document or the link

 

geometry.pdf

 

https://docs.google....d2ZMWUp0Slp6bmM

Edited April 24, 2012 by hypervalent_iodine
Personal information removed.

[studiot]

Hello pengkuan,

 

I am new to this forum and notice that you have posted a great deal of arithmetic to wade through in your quest for issues with the Lorenz force.

 

I would suggest a more fruitful area to visit would be to examine the Hall effect in semiconductors where streams of both positive and negative charge carriers are deflected in the same direction by a common Lorenz force and ask for/look at the physics behind that.

 

Hint there is a pseudovector involved.

 

go well

Edited April 23, 2012 by studiot

[pengkuan]

Hello pengkuan,

 

I am new to this forum and notice that you have posted a great deal of arithmetic to wade through in your quest for issues with the Lorenz force.

 

I would suggest a more fruitful area to visit would be to examine the Hall effect in semiconductors where streams of both positive and negative charge carriers are deflected in the same direction by a common Lorenz force and ask for/look at the physics behind that.

 

Hint there is a pseudovector involved.

 

go well

 

Thank you

[pengkuan]

Correct differential magnetic force law

Peng Kuan 彭宽

Tuesday, May 01, 2012

 

The Internal Lorentz force inconsistency is illustrated by the many contradictions I have provided (read the following documents)

Synthesis of the inconsistency of the Lorentz force law

Mathematical cause of the existence of the remaining resultant internal Lorentz force

Proof of the remaining resultant Lorentz force internal to a triangular coil

All Documents Links

 

These contradictions are sufficient evidences to break the Lorentz force law down. But how would physics be without the Lorentz force law? In fact, the correct magnetic force law is already there and the above contradictions were demonstrated to clear the way. Indeed, the Lorentz force law is so strong in the mind of physicists that no one accepts a new law without the old one proven to be false.

 

......

 

Please read

https://docs.google....SmNXLWNPYlBIQ1E

Differential.pdf

[pengkuan]

Calculation of the Lorentz' Torque and the Ampere's torque

Peng Kuan 彭宽

Thursday, May 03, 2012

In the article «The Lorentz torque experiment», I have proposed an experiment to test the Lorentz force law and the differential Ampere's force law. The theoretical predictions of the torque on a coil according to the Lorentz force law and the differential Ampere's force law give different values. The experimental measurement will confirm one law and refute the other. The curve of the Lorentz' torque and the Ampere's torque are drawn in the Figure 1. It is important for the experimenters to know how to do this calculation and why the values are so different. Below is the explanation..... Please read the document below

torque calculation.pdf

https://docs.google....aXJmWkdHLXdTMzQ

[pengkuan]

Comparison of the 2 magnetic force laws

Peng Kuan 彭宽

 

Saturday, May 05, 2012

 

I have given the correct magnetic force law in the article «Correct differential magnetic force law », named the differential Ampere's force law.

 

Is this law really correct? The unique way to certainty is experiment. However, we can still do theoretical analysis to get more confidence. For example, comparing the comportment of the 2 laws in some particular cases. Let us analyze the magnetic force internal to a triangular coil and near the summits (see the Figure 1).

 

......

 

Please read the following document.

https://docs.google....WEx2NjBPRU1HX3c

Comparaison.pdf

[pengkuan]

Curve shape of the magnetic torques

Peng Kuan 彭宽

Friday, May 11, 2012

 

In the article The Lorentz torque experiment, I have given the design of an experiment that tests the predictions of the Lorentz force law and the differential Ampere's force law. The predicted outcome of the experiment is a single-humped curve for the Lorentz force law and double-humped curve for the differential Ampere's force law. This difference of curve's shape is dependent on the coil's dimension. To avoid the confusion that the curve is always single-humped for the Lorentz force law and double-humped for the differential Ampere's force law, I give here the numerical results for coils of 4 different dimensions. The calculation method is described in the article Calculation of the Lorentz' Torque and the Ampere's torque ..........

 

Please read the following document

torque_curve.pdf

 

https://docs.google....dUFFUnNpak5IMkE

[pengkuan]

B-cutting paradox

Peng Kuan email removed

Tuesday, May 22, 2012

 

In several articles I have shown one inconsistency of the Lorentz force law, that Lorentz force internal to a coil violates the third Newton's law. Below are some links:

Synthesis of the inconsistency of the Lorentz force law

Mathematical cause of the existence of the remaining resultant internal Lorentz force

Proof of the remaining resultant Lorentz force internal to a triangular coil

 

The Lorentz force law is also used to interpret the generation of an electromotive force in a coil with a wire moving in a magnetic field. Let us look at the Figure 1 in which a rectangular coil with a movable wire is shown. The movable wire is the bar conductor of length l that is constrained to move at the velocity v. An electrical generator provides a current I in the coil that creates a magnetic field B. As the bar conductor moves, it cuts the force lines of the magnetic field B. This is the "B-cutting" action referred in the title

............

 

Please read the following document

B cutting.pdf

 

https://docs.google....RzRITFgtdzA5VHc

[pengkuan]

Lorentz' EMF paradox

Peng Kuan

Thursday, May 31, 2012

 

One basic notion in the electromagnetic theory is the generation of electromotive force (EMF) by a conductor moving in a magnetic field. This EMF is said to be created by Lorentz force. However, I have shown that the energy conservation law is violated by this explanation. The rigorous proof is in the article B-cutting paradox

https://docs.google....RzRITFgtdzA5VHc

 

So, there is a need to better understand the mechanism of EMF generation by Lorentz force.

 

 

Please read the following document.

Lorentz EMF.pdf

Lorentz' EMF paradox

https://docs.google....cTlqdS0wclkzTXc

[pengkuan]

Lorentz' EMF Experiment

 

 

I have explained the inconsistency of the theory of EMF generation by Lorentz force in the article Lorentz' EMF paradox

https://docs.google....cTlqdS0wclkzTXc

 

The last argument of this article is that the capacitor would not be charged by the bar moving in a magnetic field (see the Figure 3 of Lorentz' EMF paradox). This argument needs more explanation. Let us see how a capacitor is charged by an electrostatic field. In the Figure 1, a plate capacitor is charged by the charged rod nearby because free electrons are pushed by the electrostatic field and move into the top plate through the wire.

 

Please read the following document

Lorentz' EMF Experiment

Lorentz EMF experiment.pdf

https://docs.google....eXFqS1c5UnFMVWM

Edited June 7, 2012 by pengkuan

[Joatmon]

With reference to #1.

I hesitate to join in as I'm not mathematically inclined and haven't done more than glance through the thread. However, it seems to me that a very basic principle may not have been taken into account.

F=BIL.

Perhaps it's because the vectors haven't been drawn to scale, but length of the conductor segments doesn't seem to have been taken into account. Obviously current and orientation in space of every point has to be taken into account. If you think of dividing the coil into many equal length pieces and draw a force vector for each piece at right angles to that piece IMO they should add to zero.

If this point has been covered then please accept my apologies.

Edited June 7, 2012 by Joatmon

[pengkuan]

With reference to #1.

I hesitate to join in as I'm not mathematically inclined and haven't done more than glance through the thread. However, it seems to me that a very basic principle may not have been taken into account.

F=BIL.

Perhaps it's because the vectors haven't been drawn to scale, but length of the conductor segments doesn't seem to have been taken into account. Obviously current and orientation in space of every point has to be taken into account. If you think of dividing the coil into many equal length pieces and draw a force vector for each piece at right angles to that piece IMO they should add to zero.

If this point has been covered then please accept my apologies.

 

Thank you. The first post was about a numerical computation. I have done more analytical study. See below.

 

 

The resultant force of all internal force of an object must be 0. I have proven that the integral of the Lorentz force internal to a triangular coil is not 0. Please read

Mathematical cause of the existence of the remaining resultant internal Lorentz force

http://pengkuanem.bl...istence-of.html

Proof of the remaining resultant Lorentz force internal to a triangular coil

http://pengkuanem.bl...nternal-to.html

Synthesis of the inconsistency of the Lorentz force law

http://pengkuanem.bl.../synthesis.html

 

If this were right, this will violate the energy conservation law:

Make a triangular coil , let the coil move in the direction of the resultant force S. Since the magnetic flux passing through the coil is constant, the current will not do any work. But S would do a work in the movement, creating a quantity of energy.

 

Please read

Paradoxes and solutions about Lorentz force law

http://pengkuanem.bl...lete-study.html

[pengkuan]

B-Cutting Solution

 

Curiously, the Lorentz' EMF paradox permits to solve the B-cutting paradox. I have proven that EMF generation by cutting magnetic field line violated the energy conservation law and that a wire moving in a magnetic field did not create EMF.

.............

 

The energy conservation law is respected when the correct law of magnetic force and Faraday's law are applied instead of the Lorentz force law and Lorentz' EMF. This simple case illustrates the solution of the B-cutting paradox.

 

Please read the following document

B-Cutting Solution

http://pengkuanem.bl...g-solution.html

[pengkuan]

Non Loop EMF Experiment

 

In order to test EMF creation by Lorentz force, I have proposed an experiment in the article Lorentz' EMF Experiment. But, this experiment is difficult to implement because the process of measurement is complicated: put the bar in place, communicate it a speed, remove it, stop, measure the tension. One has to resume this again and again.

 

Here is a better design that permits continuous measurement of the EMF created by the bar in a non loop setup. This design uses 2 isolated metallic spheres as condensers, which is illustrated in the Figure 1 (a). In this figure a battery charges the 2 spheres that stock electrostatic charge.

 

.................

 

 

Please read the following document

Non Loop EMF Experiment

http://pengkuanem.bl...experiment.html

[pengkuan]

Displacement Current Paradox

8 July 2012

 

I have exposed 3 inconsistencies of the Lorentz force law in several articles, these inconsistencies are about Lorentz force, but they can also be about magnetic field. So, let us examine the Maxwell–Ampere equation.

 

 

Displacement current creates magnetic field in free space. For example, on a conductor sphere been charged by an alternate current (see the Figure 1), the electric charge varies, the electric displacement field D varies and the variation of D creates a magnetic field around the sphere. Let us calculate this magnetic field.

 

Please read the following document

Displacement Current Paradox http://pengkuanem.bl...nt-paradox.html

[pengkuan]

Phantom Lorentz force Paradox

16 July 2012

 

I have exposed an inconsistency of Ampere-Maxwell equation, in the article

"Displacement Current Paradox" http://pengkuanem.bl...nt-paradox.html

This equation states that displacement current creates magnetic field and EMF. However, "Displacement Current Paradox" shows that this EMF would violate the energy conservation law.

 

Magnetic field has 2 properties, EMF and Lorentz force. Let us study the Lorentz force created by magnetic field associated to displacement current. The Figure 1 shows a round plate capacitor charged by an alternate current Ic, and a wire loop in which circulates a constant Il. The varying charge of the capacitor creates a displacement current and then a magnetic field, which in turn, exerts a Lorentz force on the current loop.

 

Please read the following document

Phantom Lorentz force Paradox http://pengkuanem.bl...ce-paradox.html

[pengkuan]

Electromagnetic Wave Paradox

23 July 2012

 

In 2 previous articles, I have shown that the magnetic field generated by displacement current violated energy conservation law. But, this type of magnetic field was involved neither in Lorentz force nor in EMF. Its only use is for electromagnetic wave. Here, we will check the consistency of electromagnetic wave equation.

 

Please read the following document

Electromagnetic Wave Paradox http://pengkuanem.bl...ve-paradox.html

[studiot]

In post 56 I said hello and pointed out that the Lorenz force fails in the Hall effect in semiconductors.

 

You can find the theory in any good intermediate solid state physics book, such as Ashcroft and Mermin.

 

You thanked me in the following post.

 

However I have not seen further reference.

 

Did I waste my effort?

[pengkuan]

I am sorry. I did not well understood your post. I have not noticed that it was about semiconductor specifically and that the deflection of positive charges was the crux.

 

Now, if I have understood the problem, the deflection of streams of negative charge is correct, but that of positive charges is contrary to Lorentz force law. Is it right?

In post 56 I said hello and pointed out that the Lorenz force fails in the Hall effect in semiconductors.

 

You can find the theory in any good intermediate solid state physics book, such as Ashcroft and Mermin.

 

You thanked me in the following post.

 

However I have not seen further reference.

 

Did I waste my effort?

 

The positive charge carriers are holes, isn't it? They do not move, but it is the departure of electrons that leaves the hole.

Hello pengkuan,

 

I am new to this forum and notice that you have posted a great deal of arithmetic to wade through in your quest for issues with the Lorenz force.

 

I would suggest a more fruitful area to visit would be to examine the Hall effect in semiconductors where streams of both positive and negative charge carriers are deflected in the same direction by a common Lorenz force and ask for/look at the physics behind that.

 

Hint there is a pseudovector involved.

 

go well

[studiot]

The positive charge carriers are holes, isn't it? They do not move, but it is the departure of electrons that leaves the hole.

 

That's the whole point of it.

 

If both holes and real electrons apparently move in the same direction, what drives the electrons that move in the opposite direction to vacate the hole sites?

[Joatmon]

That's the whole point of it.

 

If both holes and real electrons apparently move in the same direction, what drives the electrons that move in the opposite direction to vacate the hole sites?

 

When I was a lecturer this is how I convinced my students that the hole apparently moves in the opposite direction to the electron flow. I used to line up a few students as in the diagram leaving a space. The students were electrons and the space a hole. As the students shuffled to the left the class could see the "hole" moving to the right. Electrons have a negative charge and as the hole is attractive to electrons it has a positive charge.