Lorentz Force Paradox

[eram]

I don't think you've misunderstood anything.
Although the velocity of the magnet counts in both explanations, the theoretical explanation as to why there is no force on the charged ball is different. And both explanations sorta contradict.

Tach's explanation says that the ball is not "cutting" the field lines as the field lines themselves have a velocity, which is not something usually associated with them.

i have also seen others give przyk's explanation. it says that there is a magnetic force on the ball, since the ball has a relative velocity in a magnetic field. but this balanced by an electric field generated by the moving magnet.

I also referred to the magnetic field generated by a lone, moving charged, where the magnetic flux density generated is based on the charge's relative velocity. But Tach said little on the matter.

Quite a wordy post, but now you know why i'm confused.

 

[Tach]

I don't think you've misunderstood anything.
Although the velocity of the magnet counts in both explanations, the theoretical explanation as to why there is no force on the charged ball is different. And both explanations sorta contradict.
.......

Quite a wordy post, but now you know why i'm confused.

There is no contradiction, just your inability to follow simple physics.

 

[eram]

There is no contradiction, just your inability to follow simple physics.

that is your view, but simply insulting me and not elaborating doesn't help.

both explanations apparently give the same result, but the underlying reasons differ.

 

[Tach]

that is your view, but simply insulting me and not writing anything else doesn't help.

I am simply pointing out that you are unable and unwilling to understand some basic physics. That's all. If you used half of the time you are wasting trolling this forum for studying, you would be far ahead. Others told you the same thing.

 

[eram]

that is your view, but simply insulting me and not elaborating doesn't help.

both explanations apparently give the same result, but the underlying reasons differ.

I am simply pointing out that you are unable and unwilling to understand some basic physics. That's all. If you used half of the time you are wasting trolling this forum for studying, you would be far ahead. Others told you the same thing.

I am not trolling, and I am quite willing but you think otherwise; that's fine but you don't have to keep bringing it up.



A problem can have two different solutions but they must be from the same underlying principles. Though it doesn't seem to be so in this case.



A good example of a problem with two solutions would be the derivation of $$\frac{mv^{2}}{r}$$
We can use Newton's original derivation, or one that comes from simple harmonic motion. They both seem different at first, but they produce the same result.

 

[Tach]

A problem can have two different solutions but they must be from the same underlying principles. Though it doesn't seem to be so in this case.

The solutions you received have the same underlying principle: the theory of relativity. The fact that you still fail to understand them , is your limitation, don't blame it on the people that explained it to you.

 

[eram]

The solutions you received have the same underlying principle: the theory of relativity. The fact that you still fail to understand them , is your limitation, don't blame it on the people that explained it to you.

i didnt blame anyone, though no one has actually shown me how they branch from the same principle. i'm hoping to get the viewpoint of other forum users.

 

[madus]

i didnt blame anyone, though no one has actually shown me how they branch from the same principle. i'm hoping to get the viewpoint of other forum users.

There is this case that seems paradoxical to explain with relativity.

...................................e1 ->

...................................e2 ->


Two parallel electrons. Their relative velocity is zero, and yet experiments clearly show with given enough speed, relative to static reference frame (classical physic), their magnetic attraction will overcome even their electrostatic repulsion at some point and they will actually start to attract. In an electron beam this is called 'electron bunching', and for free electrons or plasma it's called Z-pinch. http://en.wikipedia.org/wiki/Z-pinch

Actually, to consider the problem we only need to look at single electron and formation of its magnetic field due to linear velocity:

http://en.wikipedia.org/wiki/Biot-savart_law

...'v' relative to what? But that's wrong question to ask when looking at classical equation, I guess. What I know is that this works, without relativity, whatever that means. And funny enough this equation called Biot–Savart law, whatever it is relative to it amazingly not only works in electromagnetics but in hydro/aero dynamics too, go figure.

 

[Pete]

Two electrons moving in parallel will experience a repulsive force between them.
The Z-pinch involves charge flowing through a plasma, not electrons moving in isolation.

 

[Pete]

http://en.wikipedia.org/wiki/Biot-savart_law

...'v' relative to what?

Relative to the frame in which you want to know the magnetic field. The magnetic field is frame dependent.
This is why we talk about the electromagnetic field, because the electric and magnetic components look different in different reference frames.

 

[madus]

Two electrons moving in parallel will experience a repulsive force between them.
The Z-pinch involves charge flowing through a plasma, not electrons moving in isolation.

They will experience repulsive electrostatic force, but they will also experience magnetic force proportional to velocity vector. That's exactly what Lorentz force is all about. Main form of Lorenz force and Biot-Savart law is their "point charge" equation, which is meant to be used for exactly such scenario as with two electrons. And when you integrate it over line or circle you get Ampere force law, and all the other equations that have anything to do with this 'magnetic field due to moving charge'. It does not mater whether charge is free or plasma, or confined to conductor. Two parallel electron beams will attract and two parallel current carrying wires will attract just the same as two parallel electrons. That's what equations say, and they have been tested to work.

http://en.wikipedia.org/wiki/Lorentz_force

http://en.wikipedia.org/wiki/Biot–Savart_law

http://en.wikipedia.org/wiki/Ampère's_force_law

 

[madus]

Relative to the frame in which you want to know the magnetic field. The magnetic field is frame dependent.
This is why we talk about the electromagnetic field, because the electric and magnetic components look different in different reference frames.

I'm afraid not, it would not work like that, try it. Try to calculate magnetic force between two parallel electrons travelling at say 500m/s and are 1 meter apart, try to put numbers into equation and you will see.

'r' is just reference to distance to our "virtual probe", the place where we want to measure the field, which will be defined by the position of other electron in our example, but this has nothing to do with the velocity, which is given, and it must be relative to common static reference frame, like centre of Earth or corner of your room, if you want equations to work.

 

[OnlyMe]

Two electrons moving in parallel will experience a repulsive force between them.
The Z-pinch involves charge flowing through a plasma, not electrons moving in isolation.

They will experience repulsive electrostatic force, but they will also experience magnetic force proportional to velocity vector.

Madus, I believe you are misunderstanding Pete's point. It seems that you are confusing how electrons move through and interact with a plasma or even say the air, with how they would interact when moving through vacuum. When electrons move through a plasma, air or any material, they are actually moving from one ion or atom to another. They are not moving freely.

If what you suggest we're true, atoms and matter could not exist.

 

[madus]

Madus, I believe you are misunderstanding Pete's point. It seems that you are confusing how electrons move through and interact with a plasma or even say the air, with how they would interact when moving through vacuum. When electrons move through a plasma, air or any material, they are actually moving from one ion or atom to another. They are not moving freely.

http://en.wikipedia.org/wiki/Z-pinch
- "The Z-pinch is an application of the Lorentz force, in which a current-carrying conductor in a magnetic field experiences a force. One example of the Lorentz force is that, if two parallel wires are carrying current in the same direction, the wires will be pulled toward each other. In a Z-pinch machine the wires are replaced by a plasma, which can be thought of as many current-carrying wires. When a current is run through the plasma, the particles in plasma are pulled toward each other by the Lorentz force, thus the plasma contracts."

http://en.wikipedia.org/wiki/Plasma_(physics)
- "The free electrons in a metal may be considered an electron plasma."

What is there to misunderstand? Plasma or no plasma, electric and magnetic fields still obey the same laws, apparently. I did not perform any of those experiments myself, so don't ask me for proof. And plasma is irrelevant to basic premise of the paradox where we are considering vacuum and only two electrons 1 meter apart.

If what you suggest we're true, atoms and matter could not exist.

I'm just quoting Wikipedia. What are you suggesting, Lorentz and Biot-Savart equations are wrong?

 

[OnlyMe]

http://en.wikipedia.org/wiki/Z-pinch
- "The Z-pinch is an application of the Lorentz force, in which a current-carrying conductor in a magnetic field experiences a force. One example of the Lorentz force is that, if two parallel wires are carrying current in the same direction, the wires will be pulled toward each other. In a Z-pinch machine the wires are replaced by a plasma, which can be thought of as many current-carrying wires. When a current is run through the plasma, the particles in plasma are pulled toward each other by the Lorentz force, thus the plasma contracts."

http://en.wikipedia.org/wiki/Plasma_(physics)
- "The free electrons in a metal may be considered an electron plasma."

What is there to misunderstand? Plasma or no plasma, electric and magnetic fields still obey the same laws, apparently. I did not perform any of those experiments myself, so don't ask me for proof. And plasma is irrelevant to basic premise of the paradox where we are considering vacuum and only two electrons 1 meter apart.





I'm just quoting Wikipedia. What are you suggesting, Lorentz and Biot-Savart equations are wrong?

Read the quote again. The electrons are moving through wires not freely in space.

 

[eram]

Read the quote again. The electrons are moving through wires not freely in space.

So a plasma is kinda like the wire in this case. In two parallel wires, the wires always remain electrically neutral.

In Gonick's book (I've also seen similar online articles but can't find them now), he said that the Lorentz force is an "illusion" caused by Time Dilation. And that the repulsive electric force between the charges always exceeds the attractive magnetic force.

This is contrary to Purcell's explanation.


And sorry OnlyMe, I must've been sleeping cos I've realized my previous explanations were quite muddled.


According to one explanation, Bob has to consider the relative velocity of the magnetic field lines w.r.t. the charge.
But according to pryzk, as long as the charge is in a magnetic field the and has a relative velocity w.r.t. Bob, it experiences a Lorentz force.
Then due to EMI, the moving magnet creates an electric field that balances the Lorentz force. This is part where we have to take the magnet's velocity into account.

Both explanations give the same conclusion, but with different theoretical approaches.

Tach presented me with some complicated relativistic force expressions, then said its all based on relativity but didn't explain why. But whatever, I'm not exactly anticipating his reply.

 

[madus]

Read the quote again. The electrons are moving through wires not freely in space.

- "In a Z-pinch machine the wires are replaced by a plasma, which can be thought of as many current-carrying wires."

I don't understand what is your objection about. They explicitly say its all the same thing, as far as this force is concerned anyway. According to these experiments and those equations it is irrelevant where electrons are and whether the are "free" or not. All it matters to Lorentz force is velocity vector, mass, charge and distance. Classical theory can apparently work it out with its basic equations, the paradox I suggested is how relativity can explain it - the case of two parallel electrons.

 

[eram]

I don't understand what is your objection about. They explicitly say its all the same thing, as far as this force is concerned anyway.

technically,...almost the same.

but how do we reconcile both explanations? the ones i already mentioned.

 

[madus]

So a plasma is kinda like the wire in this case. In two parallel wires, the wires always remain electrically neutral.

It does not matter, electric fields will superimpose and neutralise, but magnetic force still gets created due to electrons motion just the same. And as you know magnetic force is independent of electric force just as they are independent of gravity force - they all can coexist in the same space. It's all the same, free electrons, electron beams, electron plasma, electrons in wires... electrons are still electrons, just as you would expect.

This is underlying principle for the definition of the ampere, the SI unit of current. Biot-Savart law and Lorentz force that is, so every measurement ever made regarding magnetic fields or electric currents directly depends on this principle. It's called Ampère's force law.

http://en.wikipedia.org/wiki/Ampère's_force_law

According to one explanation, Bob has to consider the relative velocity of the magnetic field lines w.r.t. the charge.
But according to pryzk, as long as the charge is in a magnetic field the and has a relative velocity w.r.t. Bob, it experiences a Lorentz force.
Then due to EMI, the moving magnet creates an electric field that balances the Lorentz force. This is part where we have to take the magnet's velocity into account.

Both explanations give the same conclusion, but with different theoretical approaches.

Tach presented me with some complicated relativistic force expressions, then said its all based on relativity but didn't explain why. But whatever, I'm not exactly anticipating his reply.

The essence of the paradox is best expressed with two parallel electrons, or two parallel wires as in Ampère's force law above. Our SI unit for el. current is defined by it, almost everything we know about EM relates to this is specific case. It's well known and tested, so you should stick with it as otherwise people will come up with all sorts of theories out of nowhere and you will never be able to conclude anything for certain.

 

[eram]

It does not matter, electric fields will superimpose and neutralise, but magnetic force still gets created due to electrons motion just the same. And as you know magnetic force is independent of electric force just as they are independent of gravity force - they all can coexist in the same space. It's all the same, free electrons, electron beams, electron plasma, electrons in wires... electrons are still electrons, just as you would expect.

Starting to sound a wee bit crankish...

This is underlying principle for the definition of the ampere, the SI unit of current. Biot-Savart law and Lorentz force that is, so every measurement ever made regarding magnetic fields or electric currents directly depends on this principle. It's called Ampère's force law.

http://en.wikipedia.org/wiki/Ampère's_force_law

You're not wrong there.

The essence of the paradox is best expressed with two parallel electrons, or two parallel wires as in Ampère's force law above. Our SI unit for el. current is defined by it, almost everything we know about EM relates to this is specific case. It's well known and tested, so you should stick with it as otherwise people will come up with all sorts of theories out of nowhere and you will never be able to conclude anything for certain.

A well proven fact, but how does it not reconcile both explanations?