Why do moving charged particles feel a force in a magnetic field?

[nicobzz]

TL;DR Summary

Why moving charged particles feel a force whereas if one change the referential as the particle now don't move it receive no force.

When I read things about magnetism on internet, I don't understand at all about one thing:
If a moving particle receive a force if it's in a magnetic field, so it should accelerate, so what happen if we change the referential so that the particle now don't move?
The particle shouldn't receive any force, and so it shouldn't accelerate at all!

Having the same particle in exactly the same situation but seen from different referential make the particle behave differently?

That's impossible!
Do you understand my thought?

Nothing explain me how to resolve this illogical thing in all documentation I have read.Thanks for your answer!

 

[Ibix]

The electromagnetic field transforms between frames as well. A given field can only be purely magnetic in (at most) one frame - in other frames it will present as a mixture of electric and magnetic fields.

Does that answer your question?

 

[kuruman]

According to special relativity, in the reference frame of the particle, there is a moving magnetic field that has an electric field component. See here for more details.

 

[Nugatory]

Having the same particle in exactly the same situation but seen from different referential make the particle behave differently?

The particle does not behave differently. The electrical and magnetic fields are different in the two frames, and the difference in the electrical field is exactly what is needed to make up for the lack of force from the magnetic field when we're using the frame in which the particle is at rest. This is not a coincidence; there is just a single electromagnetic field and how it is sliced into a magnetic field and an electrical field depends on the frame that we're using.

 

[nicobzz]

thanks very much, it seems that it answers my question! i was becoming crzay :)
by frames, do you mean referential?
( I am french, I don't perfectly speak english)
thank you!

 

[Ibix]

Frame is shorthand for reference frame, which I would guess is what you mean by "referential", yes. An inertial reference frame, for example, is one in which a particle moving inertially has constant velocity.

 

[Baluncore]

Welcome to PF.

It makes no difference if the charged particle moves through a stationary magnetic field, or if the magnetic field sweeps past a stationary charged particle. The force on the particle is the same in each case. It is the relative motion of the magnetic field and the charge that is important. The relative motion is not changed by moving the observer.

 

[kuruman]

thanks very much, it seems that it answers my question! i was becoming crzay :)
by frames, do you mean referential?
( I am french, I don't perfectly speak english)
thank you!

Google translate, which speaks quite a few languages, translates "frame of reference" as "cadre de réference". Does that make sense?

 

[PeroK]

thanks very much, it seems that it answers my question! i was becoming crzay :)
by frames, do you mean referential?
( I am french, I don't perfectly speak english)
thank you!

Einstein addressed your question at the beginning of his famous 1905 paper:

"It is known that Maxwell’s electrodynamics—as usually understood at the
present time—when applied to moving bodies, leads to asymmetries which do
not appear to be inherent in the phenomena. Take, for example, the recipro-
cal electrodynamic action of a magnet and a conductor. The observable phe-
nomenon here depends only on the relative motion of the conductor and the
magnet, whereas the customary view draws a sharp distinction between the two
cases in which either the one or the other of these bodies is in motion. For if the
magnet is in motion and the conductor at rest, there arises in the neighbour-
hood of the magnet an electric field with a certain definite energy, producing
a current at the places where parts of the conductor are situated. But if the
magnet is stationary and the conductor in motion, no electric field arises in the
neighbourhood of the magnet. In the conductor, however, we find an electro-
motive force, to which in itself there is no corresponding energy, but which gives
rise—assuming equality of relative motion in the two cases discussed—to elec-
tric currents of the same path and intensity as those produced by the electric
forces in the former case."

You might even look for a French translation!

 

[nicobzz]

Thanks perok, I appreciate your last comment because it make me feel inteligent

kuruman: google translate doesn't always translate well, in this case I should use wikipedia by clicking on the link to the french page of the english page of Frame of reference, or the opposite, it works well to translate technical terms unknown by google, but this time I forgot.

I still have some questions:

So it means that the moving electric wire, from the frame where the particle is fixed, create an electric field, in order for the particule to move like if the frame was fixed from the point of view of the wire?

So does an elctric field with a current create an electric field?

​

 

[Ibix]

So it means that the moving electric wire, from the frame where the particle is fixed, create an electric field, in order for the particule to move like if the frame was fixed from the point of view of the wire?

Yes.

So does an elctric field with a current create an electric field?

I don't understand what you mean here. A changing electric field does require a magnetic field also, if that's what you are asking.

 

[nicobzz]

Yes.

I don't understand what you mean here. A changing electric field does require a magnetic field also, if that's what you are asking.

So does an electric wire with a current create an electric field, even if the wire is not moving?

 

[Ibix]

So does an electric wire with a current create an electric field, even if the wire is not moving?

Oh I see. Depends on your frame. In the rest frame of the wire, no, its field is purely magnetic. In other frames the wire is slightly charged and there is an electric component to the field as well.

 

[andresB]

So does an electric wire with a current create an electric field, even if the wire is not moving?

Ibix already answered, I just want to emphasis that "moving" is a relative concept. So you always have to have in mind in what reference frame you are asking this kind of questions.

 

[nicobzz]

Yes

But that's not logical because, imagine an infinite wire with current, the frame moving parallel to the wire in the direction and speed of the electrons in the wire... Then you told me it creates an electric field, but if you exchange protons and electrons, then in the wire, with this frame I just described, the protons don't move from this frame and the electrons goes backwards, it's like a not moving wire with electrons going backward. I mean if we exchange the positive charges and negative ones, the rules of electromagnetism should stay the same. But here it's like the wire don't move and it creates an electric field.

Do you understand what I don't understand about that!

Andres:I meant that the frame was somewhere around the wire where the wire is not moving in that frame.

 

[nicobzz]

But that's not logical because, imagine an infinite wire with current, the frame moving parallel to the wire in the direction and speed of the electrons in the wire... Then you told me it creates an electric field, but if you exchange protons and electrons, then in the wire, with this frame I just described, the protons don't move from this frame and the electrons goes backwards, it's like a not moving wire with electrons going backward. I mean if we exchange the positive charges and negative ones, the rules of electromagnetism should stay the same. But here it's like the wire don't move and it creates an electric field.

Do you understand what I don't understand about that!

Andres:I meant that the frame was somewhere around the wire where the wire is not moving in that frame.

What I mean is that the moving particle receive a force, if the frame is fixed to the wire, its because there is a magnetic field, and when the frame correspond to the particle its because there is an electric Field, ok I understand that. But when you choose the moving particle as frame, and you exchange electric charges, when you exchange protons with electrons , then it's like the wire is not moving so the particle shouldn't feel forces, but we saw that it feels forces.
Quite complicated but from what I understand from the theory there is a problem, I should misunderstand the theory.

 

[nicobzz]

What I mean is that the moving particle receive a force, if the frame is fixed to the wire, its because there is a magnetic field, and when the frame correspond to the particle its because there is an electric Field, ok I understand that. But when you choose the moving particle as frame, and you exchange electric charges, when you exchange protons with electrons , then it's like the wire is not moving so the particle shouldn't feel forces, but we saw that it feels forces.
Quite complicated but from what I understand from the theory there is a problem, I should misunderstand the theory.

I learned on french wikipedia that not moving particles doesn't feel forces in a magnetic field, is that true?

 

[PeroK]

I learned on french wikipedia that not moving particles doesn't feel forces in a magnetic field, is that true?

This is true, we have the Lorentz force law:$$\vec F = q(\vec E + \vec v \times \vec B)$$

 

[Ibix]

Do you understand what I don't understand about that!

This is one of those applications where you can't approximate a wire as infinitely long - you need to take care about what happens at the ends. Current flows in a loop or else it flows from a "pool" of charge. Either way, you'll find electrons entering and exiting the wire, or entering and exiting the section of wire that points in one direction. The protons don't. Once you pay attention to that (see for example post #3 in this thread) you'll find apparent paradoxes like this go away.

 

[nicobzz]

This is one of those applications where you can't approximate a wire as infinitely long - you need to take care about what happens at the ends. Current flows in a loop or else it flows from a "pool" of charge. Either way, you'll find electrons entering and exiting the wire, or entering and exiting the section of wire that points in one direction. The protons don't. Once you pay attention to that (see for example post #3 in this thread) you'll find apparent paradoxes like this go away.

Ok thank you very muck perok and Ibix.

Do you know a good documentation for electromagnetism? does knowing details of electromagnetism also requires to know Special relativity?

 

[andresB]

Ok thank you very muck perok and Ibix.

Do you know a good documentation for electromagnetism? does knowing details of electromagnetism also requires to know Special relativity?

Plenty of electrical engineering is done without people caring much about SR. If you are never moving between reference frames then chances are you don't need special relativity for practical calculations.

Electrodynamics is a relativistic theory, though. And a deeper understanding of it do requires knowledge of SR.

===========
There are a lot of text on electromagnetism. To give you a good reference it is better if you tell us your level and intentions.

 

[Nugatory]

Do you know a good documentation for electromagnetism? does knowing details of electromagnetism also requires to know Special relativity?

As a matter of history, electrodynamics was discovered first (Maxwell, 1865) and Special Relativity second (Einstein, 1905). People were able to do a lot of good work between those dates, so it’s certainly possible to do good work in E&M without learning SR.

However, electrodynamics without SR is inconsistent at its core and physicists spent much of the forty-odd years in between trying unsuccessfully to resolve these inconsistencies before Einstein succeeded. Thus, a modern physics curriculum won’t follow the historical sequence: you’ll do SR before E&M.

 

[vanhees71]

Oh I see. Depends on your frame. In the rest frame of the wire, no, its field is purely magnetic. In other frames the wire is slightly charged and there is an electric component to the field as well.

Of course there's an electric and a magnetic field.

To really understand the issue you need of course relativity. The key is to also use the relativistic covariant constitutive equations. In this case you need the relativistic version of Ohm's Law, which takes into account both the electric and magnetic part of the Lorentz force. This leads to a self-consistent inclusion of the Hall effect, leading to both an electric and a magnetic field also in the reference frame, where the wire is at rest (of course you get also an electric field when treating the problem in the usual non-relativistic approximation, which is an utmost good approximation for the wire at rest, because the drift velocity of the electrons in a standard wire with a household current is of the order of millimetres per second :-)).

You find the full relativistic treatment here:

https://itp.uni-frankfurt.de/~hees/pf-faq/relativistic-dc.pdf

 

[cmb]

"Why moving charged particles feel a force..."

Or as Feynman puts it

"How does a person answer 'why' something happens?"



"If a moving particle receive a force if it's in a magnetic field, so it should accelerate, so what happen if we change the referential so that the particle now don't move?
The particle shouldn't receive any force, and so it shouldn't accelerate at all!"

Correct. When a charged particle is stationary in a magnetic field, it experiences no magnetic force that might accelerate it.

But more than that, a magnetic field is a cross product field and cannot perform any work on a charged particle. So it can never 'accelerate' the charge. Only an electric field can do work on a charged particle.

When a charged particle starts moving in a magnetic field, "some of the magnetic field is converted into an electric field" (this is a Feynmann 'how one might answer the question', is this a satisfactory answer?).

The charged particle is accelerated only by electric fields in its own frame. No electric field = no acceleration. These electric fields might not be apparent to you in a different inertial frame.

But there is a conundrum not answered here, and is a Feynmann-deep-dig sort of question; how do you know what 'moving' relative to a magnetic field is?

Do you mean a charged particle moving relative to a physical mass of a permanent magnet? If so, the above and previous answers all cover it.

But consider this;
Imagine two magnet discs facing each other across a small gap, N-to-S, in the vacuum of free space. Imagine they are 200,000km across, infinitely stiff and supported at the edge by some support, and the gap is big enough for you to fit in the middle of the assembly with your little non-magnetic non-conductive space probe that you can't see out of, and watch what happens to a test charge you are watching inside you probe.

First case; everything is stationary relative to everything else, floating in space. No apparent motion.
Second case; you give the charged particle a small nudge and see it follows a circular path where the radius of the path is a function of its speed and mass.

OK, as above. Then...

Third case; You can't see out, so as far as you are concerned nothing is moving. You have some way to determine the magnetic field and find it is constant. Yet the test charge you are observing begins to circle around. Why?

Maybe you are moving through the gap, or maybe the magnets are moving past you while you are stuck in between.

The question is; what is changing in the magnetic field from one moment to the next? It is a uniform and constant field, so is the same field no matter where you are within those discs, so what is in the nature of a 'uniform' magnetic field that has this effect? Why does a field that appears stationary to all reference frames have a different effect on a charged particle depending on how the particle is observed?

How can you tell if the charge is moving, or the space probe is moving (moving relative to the magnet), and what does that even mean in a uniform magnetic field?