Fundamental - Magnetic fields generated by moving electrons

[MrPidooma]

TL;DR

Magnetic fields generated by moving electrons, electrons spin, magnetic flux density

Trying to understand something fundamental about how magnetic fields are generated by moving electrons in a conductor. I have read many forums, studied Emag and am left with more questions. Looking for some practical insight not Bio-Savart derivations, etc. These still do not explain why the magnetic field around the conductor is concentric and how that is manifested by 'electron spin' and its magnetic properties. I did come across a post that was asking a similar question that only left me with more questions see below. Any insight welcome.

 

[berkeman]

Why are you trying to obfuscate the basic Biot-Savart Law? Electon magnetic moments should not enter into the basic B-field calculations for a current-carrying wire. Please post links to your reading about this. Thanks.

 

[MrPidooma]

Thank you berkeman. Not trying to obfuscate if that answers the question but I'm dubious about that. Where does the B-field come from, I mean really come from? No definitive answers from the below but very interested and wishing to pursue.

https://physics.stackexchange.com/q...ation-of-the-free-electrons-in-a-current-carr

 

[MrPidooma]

Initially an answer to the original question may help me get to the answer of mine.
Q: What is the the orientation of the magnetic moments of the free moving electrons inside the wire?

Cheers!

 

[Vanadium 50]

Where does the B-field come from, I mean really come from?

So you don't want to know where it comes from, but where it really comes from? Why not where it really, really comes from?

: What is the the orientation of the magnetic moments of the free moving electrons inside the wire?

Irrelevant to the situation at hand.

 

[berkeman]

Q: What is the the orientation of the magnetic moments of the free moving electrons inside the wire?

Who cares? Why do you think that affects the external B-field that you calculate from the Biot-Savart Law for a current carrying wire? Please post a link to a credible source for that belief of yours...

 

[berkeman]

https://physics.stackexchange.com/q...ation-of-the-free-electrons-in-a-current-carr

That is not a valid technical reference here at PF. Please review the PF rules (under INFO at the top of the page) to refresh your memory on what constitutes a valid reference here. Thank you.

 

[MrPidooma]

Apologies for that berkeman. I care in that the magnetic field must be coming from somewhere and I was attributing that to the 'spin' of the electron(s). I get the feeling you have a different answer...can you point me to something that might help me further level my understanding or why you don't think that is what is causing the B-field?

 

[MrPidooma]

So you don't want to know where it comes from, but where it really comes from? Why not where it really, really comes from?Irrelevant to the situation at hand.

Why is it irrelevant, please help me understand why there is no correlation?

 

[Ibix]

It's just the electrons' electromagnetic fields. If you are not moving with respect to the electron then you only see electric components. If you are moving with respect to it you see some magnetic components as well. It's the same field, it just looks different (or, better said, you measure it differently).

There are a few subtleties around how that works in a wire (you have to take into account the wire's protons' electromagnetic fields too), but that's the basics of it.

 

[MrPidooma]

Thank you Ibix. Do we know or understand the orientation of the magnetic moments of the free moving electrons inside the wire? Are they what we know to make up the magnetic field around the conductor?

 

[kuruman]

It behooves me to point that the picture of the magnetic field shown in the figure is incorrectly drawn. If the negatively-charged electrons are moving in the direction shown, the direction of the current will be in the opposite direction. This means that B-field will circulate in the opposite direction from the one is shown.

That is not a valid technical reference here at PF. Please review the PF rules (under INFO at the top of the page) to refresh your memory on what constitutes a valid reference here. Thank you.

It's also a non-existent reference. I clicked on the link and I got "Page not found". In all likelihood it was taken down but I will not speculate why.

I am perplexed by the attempt to link electron spin to the direction of circulation of the magnetic field lines. A beam of ions with zero total spin will still produce a circulating magnetic field according to Biot-Savart.

 

[MrPidooma]

kuruman, thank you for your response, yes agreed on the magnetic field direction. Not sure what link you clicked but I've been asked to not link unverified references per PF rules...apologies. It was an interesting question and seemed related to my query. Can you point me to the info on beam of ions with zero spin? Do we know what produces the magnetic field in that case? My understanding is we can utilize the Bio-Savart law to determine the magnetic flux cause by a current in a closed path but it still does not explain what is ultimately causing the magnetic flux. I was thinking it must be because of the spin...what else is there to consider?

 

[Ibix]

Do we know or understand the orientation of the magnetic moments of the free moving electrons inside the wire?

Totally random, I'd expect. You can do my analysis above for an electron beam where there is zero magnetic field in the electron frame and thus obviously no reason for magnetic moments to align. There is still a magnetic field in other frames.

what else is there to consider?

That the electrons are moving.

 

[PeroK]

I care in that the magnetic field must be coming from somewhere ...

Where does the electric field really come from?

 

[vanhees71]

That is not a valid technical reference here at PF. Please review the PF rules (under INFO at the top of the page) to refresh your memory on what constitutes a valid reference here. Thank you.

Yes, but it provides the explanation for what is asked, and it's not as unsensical as many of the answers here suggest. If I understand it right, it's ask about the orienation of the magnetic moment of the electrons making up the current in a current conducting wire.

I'd answer this question, by first calculating the magnetic field inside the wire and then it's clear that the magnetic moment of the electrons should point in the direction in this field. What do you think is so "non-sensical" that you are not even willing to look at the link provided by the OP? I must say, here the discussion on stackexchange is much more straight to point than what we provide here at PF!

 

[Ibix]

Yes, but it provides the explanation for what is asked,

I'm not sure. OP appears to me to be asking if the origin of the magnetic field around a wire is electron spin, while the provided illustration seems to be asking what is the orientation of the spin magnetic moments of electrons in a wire. The answer to the former is that spin has nothing to do with the magnetic field. The answer to the latter is doubtless that the magnetic moments of free charges do align according to the magnetic field.

 

[Nugatory]

Apologies for that berkeman. I care in that the magnetic field must be coming from somewhere and I was attributing that to the 'spin' of the electron(s). I get the feeling you have a different answer...can you point me to something that might help me further level my understanding or why you don't think that is what is causing the B-field?

A good heuristic explanation of the B field around a current-carrying wire comes from Edward Purcell. I first encountered it in his E&M textbook but Googlng for “Purcell magnetism relativity” will find some good online sources.

 

[MrPidooma]

Thank you.

 

[MrPidooma]

So you don't want to know where it comes from, but where it really comes from? Why not where it really, really comes from?Irrelevant to the situation at hand.

Thank you.

 

[vanhees71]

I'm not sure. OP appears to me to be asking if the origin of the magnetic field around a wire is electron spin, while the provided illustration seems to be asking what is the orientation of the spin magnetic moments of electrons in a wire. The answer to the former is that spin has nothing to do with the magnetic field. The answer to the latter is doubtless that the magnetic moments of free charges do align according to the magnetic field.

That's also an interesting question! Of course within classical electrodynamics you just have the macroscopic Maxwell equations with the charge-current density as source of the (static) magnetic field, but taking into account also spin there's an additional contribution to the current due to the magnetic moment associated with spin. Also there's the effect discussed in the link in #3. The solution of the selfconsistent problem to get the manetic field seems not so trivial. For practical purposes these effects are of course completely negligible, and the Biot-Savart law the right approach ;-).

 

[Ibix]

Of course within classical electrodynamics you just have the macroscopic Maxwell equations with the charge-current density as source of the (static) magnetic field, but taking into account also spin there's an additional contribution to the current due to the magnetic moment associated with spin. Also there's the effect discussed in the link in #3. The solution of the selfconsistent problem to get the manetic field seems not so trivial.

So, to paraphrase, the magnetic field would exist whether electrons (or whatever mobile charges) had spin or not. Because they do have spin there's a tiny correction to the current and hence to the magnetic field as a result of an interaction between the field and the electrons. But that correction is minuscule and also hard to calculate.

 

[MrPidooma]

Thank you for your responses. Much appreciated gang.

 

[vanhees71]

So, to paraphrase, the magnetic field would exist whether electrons (or whatever mobile charges) had spin or not. Because they do have spin there's a tiny correction to the current and hence to the magnetic field as a result of an interaction between the field and the electrons. But that correction is minuscule and also hard to calculate.

Of course, the only question is what's the current density. Magnetostatics is determined by the equations
$$\vec{\nabla} \cdot \vec{B}=0, \quad \vec{\nabla} \times \vec{B} = \mu \vec{j},$$
where
$$\vec{j}=\rho \vec{v} + \vec{\nabla} \times \vec{M},$$
where $\rho$ is the charge density, $\vec{v}$ the flow field of the charged medium, and $\vec{M}$ the magnetization.

For sure the magnetization current is negligible for the usual applications in macroscopic electrodynamics, but in the context of the here discussed question, it should be mentioned.