Electromagnetic wave energy flux

Lorentz perpendicular action experiment

Faraday’s torque experiment

Partial EMF measurement

Crux of the controversy about Faraday’s law

Can EMF distribution be known

Current loop inside a thin wire

This figure is used for discussion here

https://groups.google.com/forum/?hl=fr&fromgroups=#!topic/sci.physics.electromag/su7Jfa9yNEQ

Talk about torque with Roman

here

http://pengkuanem.blogspot.fr/2013/02/success-of-modified-lorentz.html

Erratum in Faraday's law paradox

Erratum: I forgot to precise an important condition in "Faraday's law paradox": the wire is cut between A and D and there is not current flowing in the wire. This is why the free electrons must stay still. I have corrected this error.

Faraday’s Law Paradox

Lorentz force on open circuit

A wave that is out of phase with itself

Used Links

Deformation of EM wave signals

http://independent.academia.edu/KuanPeng/Papers/1868601/Deformation_of_EM_wave_signals

Displacement magnetism experiment design

http://independent.academia.edu/KuanPeng/Papers/1868993/Displacement_magnetism_experiment_design

Non Loop EMF Experiment

http://independent.academia.edu/KuanPeng/Papers/1869004/Non_Loop_EMF_Experiment

Lorentz torque experiment

http://independent.academia.edu/KuanPeng/Papers/1869001/Lorentz_torque_experiment

Why EM wave equation does not conform torelativity?

http://independent.academia.edu/KuanPeng/Papers/1869009/Why_EM_wave_equation_does_not_conform_to_relativity

Can EM wave go forward back?

http://independent.academia.edu/KuanPeng/Papers/1875721/Can_EM_wave_go_forward_back

Summary

Can EM wave go forward back?

Deformation of EM wave signals

Peng Kuan 彭宽                                titang78@gmail.com                           https://twitter.com/pengkuanem

Deformation of EM wave signals

14 August 2012

Electromagnetic wave carries signals emitted by antenna into space. The EM field of a wave is mathematically defined by the EM wave equation whose monochromatic solution is the equation (1). A signal is a time varying EM field that can be expressed by Fourier series which is the sum of monochromatic wave functions, that is, a sum of equation (1) of different amplitudes and wave lengths.

We notice that the amplitude and phase of the equation (1) vary with distance and frequency, that is, monochromatic EM waves of different frequencies evolve differently in space. In consequence, the form of the Fourier series is distorted, the traveling signal is deformed. What is the extent of the deformation of EM signal in space? 

Please read the following document

Used documents links

Why EM wave equation does not conform to relativity? http://pengkuanem.blogspot.com/2012/08/why-em-wave-equation-does-not-conform.html

Why EM wave equation does not conform to relativity?

Peng Kuan 彭宽                               titang78@gmail.com                       https://twitter.com/pengkuanem

Why EM wave equation does not conform to relativity?

1 August 2012

This question is not about real electromagnetic wave. Physical wave does not violate relativity principle and always travel at constant speed c. It is the electromagnetic wave equation that does not conform to relativity. By computing the speed of the solution of the wave equation, we find that its velocity is faster than that of light and varies with distance and frequency. This result proves that the wave equation does not faithfully describe the physical phenomenon of electromagnetic wave.

A rigorous mathematical proof is given below. The annex is provided just in case where someone wants to check the validity of the used equations and is not necessary to the proof.

We study the spherical wave sent by an element of antenna of length dl which carries a current I (see the Figure 1). As the magnetic field of this element is only in the phi direction, in spherical coordinates, the general wave equation simplifies to the polar wave equation for the phi component. The polar wave equation admits the an analytical solution (ref. Clayton R. Paul, Keith W. Whites and Syed A. Nasar, Introduction to Electromagnetic Fields, Mcgraw-Hill College; 3 Sub edition (December 9, 1997), p.590). We call this solution “antenna wave”. 

Please read the following document

Displacement magnetism experiment design

Peng Kuan 彭宽                                titang78@gmail.com                           https://twitter.com/pengkuanem

Displacement magnetism experiment design

31 July 2012

According to Ampere-Maxwell equation, displacement current creates magnetic field. I call this theory displacement magnetism. I have proven that displacement magnetism violates energy conservation law and as a consequence, the wave equation is inconsistent ^(1,2,3).

The above conclusions need experimental test. I propose an experiment whose design is shown in the Figure 1. A round plate capacitor is charged by an alternate current, I_c. In the circuit a long rectangular loop is connected in series. The magnetic field variation in the space between the plates and outside the capacitor is measure by an EMF sensor. Another EMF sensor measures the magnetic field near the long side of the loop. 

Please read the following document

Used documents links
1)      Displacement Current Paradox http://pengkuanem.blogspot.com/2012/07/displacement-current-paradox.html
2)      Phantom Lorentz force Paradox http://pengkuanem.blogspot.com/2012/07/phantom-lorentz-force-paradox.html
3)      Electromagnetic Wave Paradox http://pengkuanem.blogspot.com/2012/07/electromagnetic-wave-paradox.html

Documents Links http://pengkuanem.blogspot.com/2012/04/documents-links.html

Electromagnetic Wave Paradox

Peng Kuan 彭宽                                titang78@gmail.com                           https://twitter.com/pengkuanem

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. 

Used documents links

Phantom Lorentz force Paradox http://pengkuanem.blogspot.com/2012/07/phantom-lorentz-force-paradox.html
Displacement Current Paradox http://pengkuanem.blogspot.com/2012/07/displacement-current-paradox.html

Non Loop EMF Experiment http://pengkuanem.blogspot.com/2012/06/non-loop-emf-experiment.html

The Lorentz torque experiment http://pengkuanem.blogspot.com/2012/03/lorentz-torque-experiment.html

Documents Links http://pengkuanem.blogspot.com/2012/04/documents-links.html

Please read the following document

Phantom Lorentz force Paradox

Peng Kuan 彭宽                                titang78@gmail.com                           https://twitter.com/pengkuanem

Phantom Lorentz force Paradox

16 July 2012

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

“Displacement Current Paradox” http://pengkuanem.blogspot.com/2012/07/displacement-current-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 I_c, and a wire loop in which circulates a constant I_l. 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

Used documents links

(1)   Synthesis of the inconsistency of the Lorentz force law http://pengkuanem.blogspot.com/2012/04/synthesis.html

(2)   B-cutting paradox http://pengkuanem.blogspot.fr/2012/05/b-cutting.html

(3)   Lorentz' EMF paradox http://pengkuanem.blogspot.fr/2012/05/lorentz-emf.html

(4)   Displacement Current Paradox http://pengkuanem.blogspot.com/2012/07/displacement-current-paradox.html

Displacement Current Paradox

Peng Kuan 彭宽                                titang78@gmail.com                           https://twitter.com/pengkuanem

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
Used documents links

Synthesis of the inconsistency of the Lorentz force law, http://pengkuanem.blogspot.com/2012/04/synthesis.html

B-cutting paradox, http://pengkuanem.blogspot.fr/2012/05/b-cutting.html

Lorentz' EMF paradox, http://pengkuanem.blogspot.fr/2012/05/lorentz-emf.html

http://pengkuanem.blogspot.com/2012/04/documents-links.html

Non Loop EMF Experiment

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
Used documents links
Lorentz' EMF Experiment http://pengkuanem.blogspot.com/2012/06/lorentz-emf-experiment.html
Lorentz’ EMF paradox http://pengkuanem.blogspot.fr/2012/05/lorentz-emf.html

B-Cutting Solution

B-Cutting Solution

Peng Kuan 彭宽titang78@gmail.com

Monday, June 18, 2012

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.

Used documents

B-cutting paradox http://pengkuanem.blogspot.fr/2012/05/b-cutting.html

Lorentz' EMF paradox http://pengkuanem.blogspot.fr/2012/05/lorentz-emf.html

Lorentz' EMF Experiment http://pengkuanem.blogspot.com/2012/06/lorentz-emf-experiment.html

Correct differential magnetic force law http://pengkuanem.blogspot.com/2012/04/correct-law.html

Please read the following document

Lorentz' EMF Experiment

Lorentz' EMF Experiment

Peng Kuan 彭宽titang78@gmail.com

Thursday, June 07, 2012

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

http://pengkuanem.blogspot.fr/2012/05/lorentz-emf.html

https://docs.google.com/open?id=0B3YDEaOyRUwccTlqdS0wclkzTXc

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 Paradox

Lorentz' EMF paradox

Peng Kuan 彭宽titang78@gmail.com

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

http://pengkuanem.blogspot.fr/2012/05/b-cutting.html

https://docs.google.com/open?id=0B3YDEaOyRUwcRzRITFgtdzA5VHc

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

Please read the following document.

B-cutting

B-cutting paradox

Peng Kuan 彭宽titang78@gmail.com

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
http://pengkuanem.blogspot.com/2012/04/synthesis.html
Mathematical cause of the existence of the remaining resultant internal Lorentz force
http://pengkuanem.blogspot.com/2012/04/mathematical-cause-of-existence-of.html
Proof of the remaining resultant Lorentz force internal to a triangular coil

http://pengkuanem.blogspot.com/2012/04/analyze-of-lorentz-forces-internal-to.html

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.

Curve shape

Curve shape of the magnetic torques

Peng Kuan 彭宽, titang78@gmail.com

Friday, May 11, 2012

In the article The Lorentz torque experiment

(http://pengkuanem.blogspot.com/2012/03/lorentz-torque-experiment.html)

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 (http://pengkuanem.blogspot.com/2012/05/torque-calculation.html) .

Comparison

Comparison of the 2 magnetic force laws

 Peng Kuan 彭宽

titang78@gmail.com

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.

Torque Calculation

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

Peng Kuan 彭宽

titang78@gmail.com

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.

Correct law

Correct differential magnetic force law

Peng Kuan 彭宽

titang78@gmail.com

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.

Synthesis

Synthesis of the inconsistency of the Lorentz force law

Links in the document

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

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

Lorentz torque experiment

I need help

Complete study

Paradoxes and solutions about Lorentz force law

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

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.com/open?id=0B3YDEaOyRUwca0lsRlVfSXpYbWM

http://pengkuanem.blogspot.com/2012/04/analyze-of-lorentz-forces-internal-to.html

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). 

Documents Links

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

PengKuan 彭宽, titang78@gmail.com

12 April 2012

The Lorentz force respects the third Newton's law. Is the Lorentz force internal to a coil consistent with the third Newton'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.

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  .

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 or below).

I need help

 I need help

PengKuan, titang78@gmail.com

15 April 2012

No, I do not need money.

The help I need is you, young and enthusiastic physicists. I need your hand, your faith in physics, your belief in the progress of physics. I need some experiments to be done, some ground-breaking ones.

The standard theory of electromagnetism with more than 150 years has proven its great value. However, its merit must not impede the improvement of our understanding of the electromagnetic phenomena.

I have found some new knowledge on electromagnetism. The big problem is that this finding contradicts the standard theory, and the wall I encountered in the physical community is harder than the Great Wall of China. Actually, the mainstream physicists believe in the Maxwell system like a religion, and all questioning of it is rejected without consideration.

This immediate refusal constitutes the greatest obstacle of progress. History has many lessons for us. The refusal of reconsideration of the geocentrism has prevented the heliocentrism to be known. So, never refuse to think that our present knowledge is wrong, no matter how exact it was until now. If we have an alternative theory, why not see if it were right? Do not blind our eyes by believing that the last theory is the ultimate one. Horizon can never be reached, but by trying to approach it, we will find new horizon.

The best way to decide which horse is the fastest is to make them contest. The best way to decide which theory is best is to do experiment. You, our generation's physicists who may complain not to live in a glorious epoch, who dream to make great discovery, do the experiment I propose. It confronts the predictions of the Lorentz force law and that of the differential Ampere's force law. The outcome of experiment is the only judge.

Galileo discovered acceleration by experiment and proved that Aristotle was wrong. Dare to be the Galileo of today by uncovering hidden nature of magnetic force and proving that Lorentz was wrong.

Do not fear failure, failure is an aphrodisiac of sciences that gives birth to beautiful children. Do not fear to appear ridiculous. Nothing is more ridiculous than to assert that train will shorten when moving fast. Ridiculousness to the contemporary, to the standard theory, is a characteristic of all great scientists and great ideas.

Make the true force reveal! It will be "one small step for a man, one giant leap for mankind"!

It will not be my step, but yours. So, let's go.

Equilateral triangle coil case

Analyze of the Lorentz forces internal to an equilateral triangle coil

Take an equilateral triangle coil shown in the Figure 1, which is rigid to obtain the resultant of the forces on all sides; a current I flows in it. Each sides would feel a Lorentz force from the magnetic field of the other sides. Due to the magnetic field of the base side S_b , the force on the left side S_l is F_bl; the force on the right side S_r, is F_br. So, the force that the base exerts on the 2 upper sides is the sum:

R_up= F_bl + F_br

Due to the magnetic field of S_l , the force on S_b is F_lb; due to the magnetic field of S_r , the force on S_b is F_rb. So, the force that the upper ensemble S_l + S_r exerts on the base is the sum:

R_b= F_lb + F_rb

R_b and R_up are the action forces between the 2 parts (S_b and S_l + S_r) that form the triangle. Their sum is the resultant internal force that the 2 parts exert on each other:

R_net= R_b + R_up = F_lb + F_rb + F_bl + F_br

Can we find the value of R_net? Let us examine the right and base sides and their forces. The force F_br is perpendicular to S_r , F_rb is perpendicular to S_b . Because S_r and S_b have the same length, F_br and F_rb have the same magnitude and their resultant R_br will lay on the bisector of the angle. In the same way, we find that the resultant R_bl of the forces F_bl and F_lb has the same magnitude than R_br but with an opposite x component.

R_br =F_rb + F_br ,   R_bl = F_lb + F_bl

So, the sum of R_br and R_bl will be vertical:

R_br + R_bl = R_y e_y≠0

We notice that this sum is equal to R_net:

R_net= (F_rb + F_br ) + (F_lb + F_bl ) = R_br + R_bl = R_y e_y≠0

So, R_net is vertical and non null. The total force internal to the coil, R_net, must be 0 according to the principle of dynamic. But it is not, violating the third Newton's law. R_net is predicted by the Lorentz force Law, thus, this law is in contradiction with the third Newton's law, and is flawed.

 Pengkuan

Polygon coil

Lorentz forces internal to a polygon  coil, analyze and computation

Take a coil of the shape shown in the Figure 1, which is made rigid by a wooden plate (yellow in the Figure 1); a current I flows in it. Each of the 5 sides would feel a Lorentz force from the magnetic field of the other sides. The forces on the left and right low sides, S_ll and S_rl , are F_ll and F_rl , which are horizontal and symmetrical. The forces on the left and right high sides, S_lh and S_rh , are F_lh and F_rh , which are perpendicular to their sides and make an angle between them. The force on the base side, S_b, is F_b, which is vertical.

These forces are internal to the coil. What is the sum of F_ll , F_rl , F_lh , F_rh and F_b? F_ll and F_rl cancel because of symmetry. The x components of F_lh and F_rh cancel because of symmetry but their y components make a vertical resultant force F_top. So, the sum of these forces is:

R=F_ll + F_rl+ F_lh + F_rh + F_b = 0 + F_top + F_b

As R is the sum of all internal forces, it must be 0. However, this requires that F_top and F_b have the same magnitude. Is this condition fulfilled? Let us analyze a coil having long vertical sides S_ll and S_rl. For this coil, the top and base sides are distant from each other. For sufficiently long vertical sides, the intensity of magnetic field being inversely proportional to the square of the distance, the magnetic field from the base becomes negligible at the top and vice versa. In this case, the Lorentz force on the base and the top due to the opposite sides are very weak. In fact, from a certain length of S_ll and S_rl, F_b and F_top become independent to the opposite sides.

F_top depends on the angle of the top. When this angle varies, F_top varies strongly. But F_b will stay unchanged since the distance is large. Because of the variability of F_top and the constancy of F_b, they do not have the same intensity. Hence, the resultant force R is not constantly 0.

R is the sum of all internal forces, but is not 0. This is a violation of the third Newton's law. As R is predicted by the Lorentz force law, the latter is not consistent with the third Newton's law.

Above we have used distance to separate the top and the base in terms of magnetic field. In reality, this trick is not necessary. The resultant of internal Lorentz forces is non null even for ordinary triangle. The Figure 2 gives the result of a computation for the shown triangle coil. The base line is 1 and the height is 10. The values of the forces on all sides are given in the figure, they are dimensionless. The resultant force is:

R=35.21

This is not permitted by the fundamental laws of dynamic. The analyze and the numerical example have shown that the Lorentz force law does not predict correct internal forces. Thus it is flawed. 

Paradoxes and Solutions

Lorentz torque experiment

The Lorentz torque experiment

Peng Kuan 彭宽, titang78@gmail.com

Sunday, April 15, 2012

The paradoxes have shown the deficiency of the Lorentz force law; the differential Ampere's force law has successfully solved all these paradoxes. It is however necessary to confirm by new experiments never carried out before. A success will show the flaw of the Lorentz force law and prove the new law experimentally. Below is the design of the experiment.

Paradoxical Lorentz force internal to a triangle coil

Take a rigid triangle coil (Fixed on a wooden plate, yellow in the Figure 1), a current I flows in it. The 3 sides would feel a Lorentz force from the magnetic field of the other sides. These force are internal to the coil.

Now, put the side s₃ inside a ideal magnetic shield. So, the sides s₁ and s₂ would not feel the magnetic field from the side s₃ and the latter does not feel that from s₁ and s₂. What will be the total internal force on the triangle in this case?

The side s₃ would feel no force. The side s₁ would feel the Lorentz force F₁ from the side s₂ and the side s₂ the Lorentz force F₂ from s₁ respectively. So, the total internal force of the triangle coil is F₃= F₁+F₂. As the forces F₁ and F₂ are Lorentz forces, they are perpendicular to their sides and they make an angle between them. Their resultant force F₃ is non null.

If the total internal force is non null, any movement in the direction of the resultant force would do a work and create a energy. This is impossible because energy cannot be created.

So, the fact that the Lorentz force is perpendicular to the current violates the third Newton's law and the energy conservation law. This is the paradox of the internal Lorentz force.

This paradox is explained and solved in the document behind the link Paradoxes and Solutions.

The Lorentz force law presents some deficiencies. A study is in this document..
Paradoxes and Solutions