Stupid question relating to electric induction

[ZapperZ]

I'm not sure that I understand what this debate is about, and it's hard to read the entire thread. Since @Charles Link has asked in a PM, let me try to put in another point of view to the debate.

Then I'll make it VERY clear for the final time, and then I'm outta this one.

It has NEVER been about the physics and the validity of the derivation of this "surface current", even though there is no such surface current on a permanent magnet. @Charles Link can't seem to get past that. From the very beginning, and in repeated posts here, I've asked for the USEFULNESS of this model.

I remember waaaay back when I was still in college, we had an exercise where we used the electron magnetic moment and its charge, and then, using the electron's classical radius and assuming that it is a sphere, we estimated, based on the magnetic moment, how fast the sphere is spinning. In other words, we had a model that mimic the result. But is this model useful? Just because I was able to derive, using standard theories and equations, at something that has some resemblance of matching some result, is this useful to be used elsewhere?

THAT, from the very beginning, was my question. And as far as I know, the usefulness of this model has not been shown at all! @Charles Link has as much as admitted on the lack of usage of it. All I've been given are these derivations of surface currents and how it ties in with magnetization, etc.. etc, as IF I haven't had my education in classical E&M.

I can show you numerous usage of photon model. I have not been shown numerous usage of the magnet surface current model. PERIOD!

There is also a risk of introducing this model to the general public. It gives them the impression that this surface current on a magnet is real! People have been shown to misunderstand things on something less significant than this. The OP clearly didn't understand basic, classical E&M. And yet, we're piling on him/her something that most of us know doesn't exist, and it is simply the tail end of the dog. But if you look closely at his/her posts, it appears that the tail is wagging the dog!

Let me also be VERY clear on this: If this were a lesson in undergraduate classical E&M (and it often is), I wouldn't have given it a second thought. Heck, I would even teach it myself! But it isn't! And it is presented to people who don't know any better! What you intended is often NOT what the "audience" understood!

I've stated my opinion of this model in this thread, and in the relevant Insight article. It may be ignored as irrelevant if you wish. I have nothing more to add to this.

Zz.

 

[Charles Link]

Thank you @vanhees71 You helped clarify the quantum mechanical aspects of this problem.

 

[vanhees71]

Then I'll make it VERY clear for the final time, and then I'm outta this one.

It has NEVER been about the physics and the validity of the derivation of this "surface current", even though there is no such surface current on a permanent magnet. @Charles Link can't seem to get past that. From the very beginning, and in repeated posts here, I've asked for the USEFULNESS of this model.

I don't know, why this is a topic to get furious about. As I've shown, it's just one of at least three equivalent ways to calculate macroscopic electromagnetic fields of permanent magnets. Of course, microscopically there's no surface current on a permanent magnet but just a magnetization due to quite interesting collective quantum many-body effects. All this I've tried to explain in my previous posting.

The "surface current model" may be useful or not to calculate the fields, no more no less. As I've also stressed, usually the direct way using the magnetic potential is the most convenient way (usually even not using the "ready-made integrals" but just solving the Poisson equation for the potential directly.

I remember waaaay back when I was still in college, we had an exercise where we used the electron magnetic moment and its charge, and then, using the electron's classical radius and assuming that it is a sphere, we estimated, based on the magnetic moment, how fast the sphere is spinning. In other words, we had a model that mimic the result. But is this model useful? Just because I was able to derive, using standard theories and equations, at something that has some resemblance of matching some result, is this useful to be used elsewhere?

Well, in this case I'd caution my students not to put too much into such "classical-electron models". This was a historically very important issue around 1910-1925, before the now considered correct description of electrons in terms of a quantized Dirac field (or its non-relativistic approximation as a Weyl-Pauli spinor) has been found.

Already the Born-rigid model of a spherical electron of finite extension which, by construction, cannot spin at all, is very complicated, and it's amusing to think about it to learn how much simpler in fact the full perturbative QFT (in this case QED) really is. I'm not aware of any rigorous treatment of a spinning electron which for sure cannot be a Born-rigid body. Maybe one can construct something like this for the pure fun of the academic problem. I don't think that one gets much physical insight about the "nature of the electron" from it.

THAT, from the very beginning, was my question. And as far as I know, the usefulness of this model has not been shown at all! @Charles Link has as much as admitted on the lack of usage of it. All I've been given are these derivations of surface currents and how it ties in with magnetization, etc.. etc, as IF I haven't had my education in classical E&M.

I can show you numerous usage of photon model. I have not been shown numerous usage of the magnet surface current model. PERIOD!

Well, here I am very sceptical. The usage of the "photon model", whatever you mean by this, is causing more trouble than it helps students either. The only "photon model" which doesn't provide conceptual trouble I know of is QED, and you can go a very long way without using photons even in quantum optics. The compromise I've made in my lecture on QM was to use a semi-naive photon picture to introduce the quantum concepts on hand of an example a classical analogon is well-known by the students from the lecture on classical E&M in the previous semester, i.e., the polarization "states" of electromagnetic waves. Then I gave a hand-waving introduction to the notion of "photons" using the "dimmed-classical-laser-light argument" with the caution of course that these are still not the true "single photon states". I'm not sure, whether this is the best concept to introduce beginners with QM, but I found it better than to just use the Stern-Gerlach experiment with spin 1/2 particles, without the possibility to adequately explain spin, which is not possible without the formal structure of QM (and in fact some representation theory of the rotation group).

There is also a risk of introducing this model to the general public. It gives them the impression that this surface current on a magnet is real! People have been shown to misunderstand things on something less significant than this. The OP clearly didn't understand basic, classical E&M. And yet, we're piling on him/her something that most of us know doesn't exist, and it is simply the tail end of the dog. But if you look closely at his/her posts, it appears that the tail is wagging the dog!

Let me also be VERY clear on this: If this were a lesson in undergraduate classical E&M (and it often is), I wouldn't have given it a second thought. Heck, I would even teach it myself! But it isn't! And it is presented to people who don't know any better! What you intended is often NOT what the "audience" understood!

I've stated my opinion of this model in this thread, and in the relevant Insight article. It may be ignored as irrelevant if you wish. I have nothing more to add to this.

Zz.

If it's about popularization of science, there's no use of this surface-current concept at all. I think, in this case, it's much simpler to introduce the idea that magnetic moments are something elementary, i.e., part of the properties of elementary particles. Of course, there's no way to observe the magnetic moment of the only elementary particle we have easily at hand, namely the electron (that's a famous idea by Bohr, who estimated correctly that a Stern-Gerlach experiment with electrons is practically impossible). The next-best example, where it can be directly observed is the neutron. I think there have indeed been Stern-Gerlach experiments with neutrons, but I'd have to look for the papers in google scholar myself.

Then it might also be possible to explain, how a macroscopic permanent magnet comes about due to the spontaneous orientation of these elementary magnets (although it's a collective phenomenon and the electrons making up the macrosopic magnetization are in fact in-medium quasiparticles rather than free electrons, and it's maybe also hard to explain the exchange-force concept which is crucial at least for the Heisenberg model of ferromagnetism).

I think, in fact, the most difficult task in physics education is to explain things on an understandable popularized level "as simple as possible but not simpler than possible" (Einstein). As I said, indeed, for this purpose the surface-currents of the Ampere model are clearly not a good idea to describe a permanent magnet to the general public.

 

[Mister T]

Magnetic fields result from moving electrons. That indicates that a permanent magnet has electrons inside it moving in a circular fashion to produce poles (essentially an electromagnet but the material itself retains that flow).

That model doesn't account for that magnetic field. Atomic electrons are indeed a source of a magnetic field, but that magnetic field cannot be accounted for by the motion of the electron.

Now the thing that I'm wondering about is this: You can put an iron core inside a copper coil- run electricity through the coil and you induce a magnetic field in the iron (by causing the electrons in the iron to get dragged along by the current in the copper coil in that same direction).

The electrons don't get "dragged along".

Those electrons have an orbital magnetic moment and an intrinsic magnetic moment. That is the model used to explain the interaction.

 

[Charles Link]

@ZapperZ and @vanhees71 : One simple use for the mathematics of the magnetic surface current model: By the fact that the magnetic surface currents of a uniformly magnetized cylinder (of finite length) have the same geometry as those of a solenoid, it immediately allows for the use of the magnetic pole model to determine what the magnetic field is from a solenoid of finite length, without needing to do extensive Biot-Savart calculations with the currents of the solenoid. $\\$ In addition, from this pole model analogy, the result emerges very readily, (neglecting the small effects from the far end face), that 1/2 of the $\vec{B}$ flux lines emerge out of the end face of the solenoid, and 1/2 of them emerge before the end face. $\\$ (Many years ago, I saw this last result mentioned without proof in a professor's notes that he handed out to our undergraduate class, and it said the result is proven in advanced E&M classes.) $\\$ As it turns out, with the magnetic pole model analogy, the proof is quite simple.