Electromagnetism and special relativity

[dRic2]

Hi I just saw this video . Here it's said that that electromagnetic force is just a consequence of special relativity, but I don't get the explanation. According to the video the electromagnetic force is generated by relative motion of charges, so it is essentially an electric force. It doesn't convince me: if this is correct, why can a magnet (which has no electric change) feel this force?

Thanks
Ric

 

[DennisN]

It doesn't convince me: if this is correct, why can a magnet (which has no electric change) feel this force?

What are magnets made up of (i.e. what chemical elements/type of element)?
And after that answer, here is a "spoiling question":

Spoiler

Which particles are the atoms of those elements made up of?

 

[dRic2]

I still don't get it.

What are magnets made up of (i.e. what chemical elements/type of element)?

Fe or something like it with similar properties.

Which particles are the atoms of those elements made up of?

Protons and electrons.

But this can't be the end of the story because otherwise every element would be attracted by magnets/electromagnetic field. After a little research I convinced myself that it has to be because of the spinning of the electrons around the nucleus. Ok so now here's my question: according to the video I linked if charges are moving they contract or expand (depends on the frame of reference) thus the density of charges will change and the force will "appear"; how can this apply to a single electron spinning around a proton? The density of charge is constant right? It's 1 because I only have one charge (one electron and one proton)!

Going on. Let's take it for granted. With further researches I found out that ferromagnetic properties generally applies to atoms which have unpaired electron and "odd" orbitals otherwise the effects of different electron will cancel out. So why do Li, Na, K show no ferromagnetic properties?

Thanks
Ric

 

[Nugatory]

With further researches I found out that ferromagnetic properties generally applies to atoms which have unpaired electron and "odd" orbitals otherwise the effects of different electron will cancel out. So why do Li, Na, K show no ferromagnetic properties?

The magnetic property of atoms with unpaired electrons and odd orbitals is not ferromagnetism, it is paramagnetism. Sodium, lithium, potassium are indeed paramagnetic, as are many other materials.

For a material to be ferromagnetic, it needs more than these unpaired electrons. It also has to have a microscopic crystalline structure that allows the atoms to orient themselves so that their magnetic moments are aligned and then holds them that way. Why one material but not another should be ferromagnetic is therefore a somewhat non-trivial problem in solid state physics if you want more than a handwaving explanation (like the previous sentence).

Another problem here is that the video is using a semi-classical model in which electrons and atomic nuclei are thought of as tiny charged objects, like grains of sand only smaller and with a charge. That model works well enough to explain the magnetic forces around a current-carrying wire, as the video does. You can also get a reasonable hand-waving description of the magnetic effects of a single moving charged object that way (draw the electrical field lines, accept the pretty decent hand-waving picture that the field strength is proportional to the density of the field lines, consider how Lorentz contraction changes that density). But there is no sensible classical description of electrons that are bound into atomic orbitals, nor of the magnetic moment and spin of an electron; these are quantum mechanical phenomena, and the classical model in that video doesn't work for explaining the magnetic behavior.

 

[ZapperZ]

There appears to be a misunderstanding here by both the OP and the responses posted.

The video is about magnetic fields in current-carrying wires, not magnetism in materials (which is a whole can of worms in condensed matter physics by itself). It is trying to demonstrate how SR is applied to Maxwell equations when applied to field generated by current-carrying wire, i.e. why the classical Maxwell equations are not covariant under Galilean transformation.

It requires the "relativistic" form of Maxwell equations to to be logically consistent (covariant) with what we observe. That is why it is arguing that Relativity is the explanation on why ELECTROmagnets (not any magnets) work the way they do and not run into some logical paradox.

Zz.

 

[dRic2]

Okay, I'm starting to understand something. Sorry but I'm pretty dumb when it comes to electromagnetism.

@ZapperZ: Yes, but that only explain why a "the cat" (see video) is repelled by the wire, it doesn't explain why steel or a magnet (neutral overall charge) should behave the same way. Giving the fact that the force coming from a current-carrying wire is an electric force, why things that do not posses electric charges should feel the force?

Summing up:

1) If I want to explain the electromagnetic field generated buy a current-carrying wire then electromagnetism and special relativity should be enough. (So I guess it all comes down to Maxwell's equations and nothing more)

2) If I want to explain the "existence" of magnets then I need Quantum Mechanics to get accurate, right? Ok, now I remember tacking an introductory course about QM and I remember the a chapter called "Spin-Orbit Coupling". In the chapter the electromagnetic field felt by the electron was calculated using Biot-Savart law. The dipole moment was also calculated in a "classical" way. Then two corrections are applied: "Dirac's 2", and Thomas Precession. Now my question is: why did the author use Biot-Savart Law if it should not be possible? Also Biot-Savart Law involves current, how does this concept apply when I'm only considering one electron? I'm a bit confused

 

[ZapperZ]

2) If I want to explain the "existence" of magnets then I need Quantum Mechanics to get accurate, right? Ok, now I remember tacking an introductory course about QM and I remember the a chapter called "Spin-Orbit Coupling". In the chapter the electromagnetic field felt by the electron was calculated using Biot-Savart law. The dipole moment was also calculated in a "classical" way. Then two corrections are applied: "Dirac's 2", and Thomas Precession. Now my question is: why did the author used Biot-Savart Law if it should not be possible? Also Biot-Savart Law involves current, how does this concept apply when I'm only considering one electron? I'm a bit confused

If you want to know why certain material exhibit BULK magnetism, then you need to learn quantum magnetism, which is a many-body physics. For example, why are certain material ferromagnet, paramagnet, antiferromagnet, etc...etc. It requires knowledge of how each magnetic dipole interact with its nearest neighbor, next nearest neighbor, next-next nearest neighbor... etc. It is not as trivia as you think, and whole books are written on just this.

But this does NOT require relativistic effects in all cases. The basic Hamiltonian for something like an Ising magnet does not need to be relativistic. That is why I said that this has more to do with the EM fields as dealt with in Maxwell equations. The video isn't about quantum magnetism!

Zz.

 

[dRic2]

Ok, I get it is far more advanced than I expected. But why a single electron spinning around a nucleus generates a magnetic field? Is it the same effect of a current flowing through a wire?

 

[ZapperZ]

Ok, I get it is far more advanced than I expected. But why a single electron spinning around a nucleus generates a magnetic field? Is it the same effect of a current flowing through a wire?

Solve the hydrogen atom wavefunction!

Look, you are beginning to (i) deviate from your own thread and (ii) mix "spin" and "angular momentum". Electrons have intrinsic spin, even when it is not in an atom. This can already generate a magnetic dipole moment.

But in an atom, there is an ADDITIONAL source of magnetic moment - the angular momentum quantum number. This is the major source of why some atoms have magnetic moment, while others may not.

If you want to know WHY these generate magnetic moment, then that's a different topic. There have been numerous threads on electron spins etc. in this forum.

Zz.

 

[dRic2]

If you want to know WHY these generate magnetic moment, then that's a different topic. There have been numerous threads on electron spins etc. in this forum.

Yep. In my simple mind I though "current = moving electrons, so the principle behind this should be the same". I was wrong.

Thanks
Ric

PS: I apologize for any mistake/complicated sentences, english's not my strongest point ;)