Internal Lorentz force paradox

[pengkuan]

You already established that mutual Lorentz forces for non-parallel wire segments do not cancel. Why do you assume that they cancel here?

 

This is the very paradox I point out. I established that mutual Lorentz forces for non-parallel wire segments do not cancel using Lorentz law. I established also that they cancel using Newton 3.

 

So, this is the Lorentz law's inconsistency.

[swansont]

This is the very paradox I point out. I established that mutual Lorentz forces for non-parallel wire segments do not cancel using Lorentz law. I established also that they cancel using Newton 3.

 

So, this is the Lorentz law's inconsistency.

 

But wire segments cannot carry a current, and I suspect would not follow Maxwell's equations. The law "fails" for an unphysical situation, i.e. it "fails" in a situation in which it was never meant to hold. If you want to analyze a wire loop, you have to analyze the whole loop.

[pengkuan]

But wire segments cannot carry a current, and I suspect would not follow Maxwell's equations. The law "fails" for an unphysical situation, i.e. it "fails" in a situation in which it was never meant to hold. If you want to analyze a wire loop, you have to analyze the whole loop.

 

Did you say Lorentz law fail? At least for some cases?

 

Do you use Lorentz law to calculate the deflection of an electron beam? If Lorentz law fail for current that does not closes in loop, it should not be used for electron beam, nor in accelerators. The vacuum TV set would not function neither.

Edited March 13, 2012 by pengkuan

[swansont]

Did you say Lorentz law fail? At least for some cases?

 

Do you use Lorentz law to calculate the deflection of an electron beam? If Lorentz law fail for current that does not closes in loop, it should not be used for electron beam, nor in accelerators. The vacuum TV set would not function neither.

 

All currents form loop, including electron beams in a crt, even if you do not recognize it immediately. However, no physics law can be guaranteed to hold when you violate other physics laws.

[pengkuan]

All currents form loop, including electron beams in a crt, even if you do not recognize it immediately.

 

I know perfectly that any current, even electron beams, form loop. Have I said I do not?

 

In this discussion and by this paradox, my objective is to show that Lorentz law is inconsistent somewhere, even it is valid for most of our use.

 

You said

…. The law "fails" for an unphysical situation, i.e. it "fails" in a situation in which it was never meant to hold. ….

 

So, you recognize that it fails for the situation of the shielded parallelepiped. If I said before the discussion that Lorentz law is inconsistent, would you agree? Now, you know even where it fails, and for a situation pretty common.

 

 

But is it an unphysical situation? One can perfectly make this experiment physically, isn't it? Does it break other physical laws?

[swansont]

I know perfectly that any current, even electron beams, form loop. Have I said I do not?

 

Yes, in your last post.

 

So, you recognize that it fails for the situation of the shielded parallelepiped.

 

No; if you think it does perhaps you misunderstand what happens in magnetic shielding.

 

If I said before the discussion that Lorentz law is inconsistent, would you agree? Now, you know even where it fails, and for a situation pretty common.

 

 

But is it an unphysical situation? One can perfectly make this experiment physically, isn't it? Does it break other physical laws?

 

Really? You can send current down a segment of wire that does not form a loop? Without a continuity problem for the current?

[pengkuan]

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.

 

 

[swansont]

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?

 

Magnetic shields don't work this way; they do not shield two magnets from each other, only a region from a single field. The field from s3 will be inside the shield. s1 and s2 will be attracted to the shield.

 

Also, since we're in this thread, I will point out that the Biot-Savart law, mentioned earlier, uses a path integral for a closed loop, so you cannot apply it (or anything derived from it) to only part of a current loop. You will end up with mistakes.

 

—————

addendum:

 

http://www.mushield.com/faq.shtml#q11

Can I shield one magnet from another?

No. There is no such thing as a magnetic insulating material. High permeability material works to shield from magnetic interference by attracting and diverting the field through itself. The only way in which to halt the attractive or repulsive forces between two magnets is to separate them by the distance proportional to their respective magnetic field strengths

 

(emphasis in orange added)

[pengkuan]

Magnetic shields don't work this way; they do not shield two magnets from each other, only a region from a single field. The field from s3 will be inside the shield. s1 and s2 will be attracted to the shield.

 

Also, since we're in this thread, I will point out that the Biot-Savart law, mentioned earlier, uses a path integral for a closed loop, so you cannot apply it (or anything derived from it) to only part of a current loop. You will end up with mistakes.

 

First, thank you for speaking so kindly and giving valuable information. It's a pleasure.

 

For the magnetic shield, I do not need the shield to screen completely the field, a diminution is enough. Suppose that without the shield, the internal force of the triangle is zero. With the s3 in the shield, the magnetic field on the s1 and s1 will diminish and so does the force on the ensemble s1+s2. As the force F3 does not change, the total internal force will have a resultant toward the left. More complex is when the length of the shield varies, and the field on s1+s2 will increase or diminish. What will compensate this variation of force? No law exists to describe this case.

 

By the way, why s1 and s2 will be attracted to the shield if the field from s3 will be inside the shield?

 

For the Biot-Savart law, no explicit text forbids the use of it for part of a circuit.

[swansont]

With the s3 in the shield, the magnetic field on the s1 and s1 will diminish and so does the force on the ensemble s1+s2.

 

No, that's the point of the link: you do not diminish the force at all.

 

For the Biot-Savart law, no explicit text forbids the use of it for part of a circuit.

 

That's because they expect you understand the underlying math, and what the "C" means on the integral: that it's a line integral around some path.

[pengkuan]

Magnetic shields don't work this way; they do not shield two magnets from each other, only a region from a single field. The field from s3 will be inside the shield. s1 and s2 will be attracted to the shield.

 

Also, since we're in this thread, I will point out that the Biot-Savart law, mentioned earlier, uses a path integral for a closed loop, so you cannot apply it (or anything derived from it) to only part of a current loop. You will end up with mistakes.

 

 

I admit that magnetic shields and Biot-Savart law forpart of a current loop are tricky. Below, there is neither.

 

Lorentzforces internal to a 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 theFigure 1); a current I flows in it. Each of the 5 sides wouldfeel a Lorentz force from the magnetic field of the other sides. The forces onthe left and right low sides, S_ll and S_rl , are F_lland F_rl , which are horizontal and symmetrical. The forces onthe left and right high sides, S_lh and S_rh , are F_lhand F_rh , which are perpendicular to their sides and make anangle between them. The force on the base side, S_b, is F_b,which is vertical.

 

 

 

These forces are internal to the coil. Whatis the sum of F_ll , F_rl , F_lh, F_rh and F_b? F_lland F_rl cancel because of symmetry. The x components of F_lhand F_rh cancel because of symmetry but their y components makea vertical resultant force F_top. So, the sum of these forcesis:

 

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

 

 

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

 

 

 

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

 

 

 

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

 

 

 

Above we have used distance to separate thetop and the base in terms of magnetic field. In reality, this trick is notnecessary. The resultant of internal Lorentz forces is non null even forordinary triangle. The Figure2 gives the result of a computation for the shown trianglecoil. The base line is 1 and the height is 10. The values of the forces on allsides are given in the figure, they are dimensionless. The resultant force is:

 

R=24.77

 

 

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

 

[pengkuan]

That's because they expect you understand the underlying math, and what the "C" means on the integral: that it's a line integral around some path.

 

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_bris perpendicular to S_r , F_rb is perpendicular to S_b. Because S_r and S_b have the same length, F_brand F_rb have the same magnitude and their resultant R_brwill 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_lbhas 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_blwill be vertical:

 

R_br + R_bl= R_ye_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_ye_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_netis predicted by the Lorentz force Law, thus, this law is in contradiction with the third Newton's law, and is flawed.

 

 

 

Pengkuan

 

[swansont]

What part of "line integral" isn't registering? You can only analyze a field from current flow from a complete current loop. To do otherwise violates the assumptions of the equations, and when you do that, you create an unphysical system. It's unsurprising that you get an unphysical result.

 

IOW, if you could magically create and destroy current, you could create a reactionless drive.

[pengkuan]

What part of "line integral" isn't registering? You can only analyze a field from current flow from a complete current loop. To do otherwise violates the assumptions of the equations, and when you do that, you create an unphysical system. It's unsurprising that you get an unphysical result.

 

IOW, if you could magically create and destroy current, you could create a reactionless drive.

 

In this logic, a ring coil do not receive Lorentz force when a current is in it. Or one can not analyse the Lorentz force on a element of the ring, of length dl, because the magnetic field on dl is necessary from the rest of the coil, which is not complete.

[swansont]

In this logic, a ring coil do not receive Lorentz force when a current is in it. Or one can not analyse the Lorentz force on a element of the ring, of length dl, because the magnetic field on dl is necessary from the rest of the coil, which is not complete.

 

You can analyze the effect of/on dl, but only in the context of integrating around the entire loop.

[pengkuan]

You can analyze the effect of/on dl, but only in the context of integrating around the entire loop.

 

This is exactly what I did for my numerical calculations. You would say "do it properly, your math is flawed".

 

If you do it with a commercial software, you would find the same results.

[swansont]

This is exactly what I did for my numerical calculations.

 

Yet you discuss components, and say things like "Each sides would feel a Lorentz force from the magnetic field of the other sides." which means you didn't analyze it in a valid way. There is no way to field the field from a piece of wire that is not a complete loop, since that's the only way the equations are defined. When you break the assumptions, the rest of the application is wrong.

[pengkuan]

You can analyze the effect of/on dl, but only in the context of integrating around the entire loop.

 

This means that if we want to analyze dl , it must be in the magnetic field of the entire loop, isn't it? If we compute the magnetic field by cutting the ring into 1 000 pieces, at each point, we have to add the elementary magnetic filed from the 1 000 pieces using Biot-savart law?

[swansont]

This means that if we want to analyze dl , it must be in the magnetic field of the entire loop, isn't it? If we compute the magnetic field by cutting the ring into 1 000 pieces, at each point, we have to add the elementary magnetic filed from the 1 000 pieces using Biot-savart law?

 

The Biot-Savart law tells you what the field is from a complete loop. Period.

 

 

In your analysis you didn't break the loop up into 1000 pieces; for the triangle you broke it up into 3.

[pengkuan]

The Biot-Savart law tells you what the field is from a complete loop. Period.

 

 

In your analysis you didn't break the loop up into 1000 pieces; for the triangle you broke it up into 3.

 

I have broken this triangle into 200 pieces. And for each piece, I have integrate the other 199 pieces. The number on the figure is the result. If you compute with the software you like, you wil get the same value.

 

http://www.sciencefo...40110_thumb.jpg

[swansont]

You evaluated an equilateral triangle and came up with a net force. If you rotate by 120º, you'd get a force on a different element. By symmetry, that's not possible. Ergo, your methodology is flawed. There is no reason to believe that you have done a valid analysis of any problem when you get and obviously wrong answer on the easy test case.

[pengkuan]

Yes, my mistake.

 

There is no reason to believe that you do not mistake in your mind.

[swansont]

There is no reason to believe that you do not mistake in your mind.

 

Actually, there is. More than 100 years of the physics working, without anyone noticing this "problem" and, of course, no reactionless propulsion systems being built. Most students of physics, when they encounter a quandary such as yours, assume they have made a mistake and go find it. Thought problems, after all, are simply math — calculus algebra and geometry, and these are self-consistent. Errors are in the misapplication of the math. But there are some who decide that physics must be wrong, despite the widespread success of it. The operative word in those cases is hubris.

 

Good luck and goodbye.

[pengkuan]

Actually, there is. More than 100 years of the physics working, without anyone noticing this "problem" and, of course, no reactionless propulsion systems being built. Most students of physics, when they encounter a quandary such as yours, assume they have made a mistake and go find it. Thought problems, after all, are simply math — calculus algebra and geometry, and these are self-consistent. Errors are in the misapplication of the math. But there are some who decide that physics must be wrong, despite the widespread success of it. The operative word in those cases is hubris.

 

Good luck and goodbye.

 

Thanks and goodbye.

[pengkuan]

I need help

PengKuan

2 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.

 

[link removed by moderator]

 

The Lorentz torque experiment

The paradoxes have shown the deficiency of the Lorentz force law; the differential Ampere's force law (an improvement of the Lorentz 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.

 

The suggested experiment makes 2 rectangular coils interact. The coil 1 is horizontal, the coil 2 is tilted at an angle with respect to the coil 1 (See the Figure 1). The magnetic force will create a torque on the 2 coils, which are calculated numerically. For the detail of the calculation, please read « Paradoxes and solutions about Lorentz force law».

 

The parameters for the calculation are as follow:

The dimensions of the horizontal coil: lx=0.4 m, ly=0.8 m

The dimensions of the tilted coil: lx=0.36 m, ly=0.144 m

The current in the 2 coils: I=3000 A·turn

 

The torques in N·m predicted by the Lorentz force law and the differential Ampere's force law are the 2 curves drawn in the Figure 3. The torque varies with respect to the angle between the 2 coils. For angle between 0° and 180°, the torque predicted by the Lorentz force law draws a single-hump-shaped curve, whereas the prediction of the differential Ampere's force law draws a double-hump-shaped curve. The values of the predictions are very different. At 90°, the Lorentz force law predicts 1.2755 N·m, against 0.1877 N·m for the differential Ampere's force law.

 

The shapes of the curves are very distinguishable. If the measured data has a double-hump shape, the magnetic force follows the differential Ampere's force law; if the measured data has a single-hump shape, the magnetic force follows the Lorentz force law.

 

The quantity of wire is calculated here. The lengths of each turn of the 2 coils are:

l1=(0.4+0.8)*2=2.4 m

l2=(0.36+0.144)*2=1.008 m

 

For coils of 3 000 turns in each, the lengths of wire are:

L1 = 7 200 m

L2 = 3 024 m

 

The total length of wire needed is: 10 224 m

 

If we measure the force on the top of the coil 2, at angle 20°, the expected force is:

F₀ = 0.4450 N·m / 0.072 m = 6.18 N

 

We can use currents of different values, coils with different number of turn. The expected forces at angle 20° with the corresponding currents, wire lengths are given in the Table 1.

 

The torque can be measured using diverse methods. In Figure 2 the torque is measured by a balance that has the advantage of amplifying the force and good precision. For each fixed angle, the counterweight will be adjusted so that the balance beam stays horizontal. Then, the position of the counterweight gives the torque directly if appropriately marked.

 

Edited April 2, 2012 by CaptainPanic