Stupid question relating to electric induction

[ZapperZ]

Does anyone other than me thinks that this thread is going in a million different directions, that it lacks focus, the original issue has been buried, and that someone is trying to do the sprint in the Olympics before he learned even how to crawl?

Zz.

 

[atommo]

Does anyone other than me thinks that this thread is going in a million different directions, that it lacks focus, the original issue has been buried, and that someone is trying to do the sprint in the Olympics before he learned even how to crawl?

Zz.

Honestly, the OP question has been answered but I don't see a 'mark post as best answer' button anywhere or anything of the sort...

 

[ZapperZ]

Honestly, the OP question has been answered ...

I'm not sure that it has, at least based on your continued misunderstanding in Post #33.

You are attempting to understand the origin of magnetism in matter, without first understanding the origin of magnetic moment in atoms. Magnetism in matter is a many-body phenomenon, and significantly more complex than magnetic moment in an atom. Thus, my comment about attempting the sprint before you learned how to crawl. But not only that, it also appears that you haven't understood classical E&M either.

Please note that "visualization" and "modeling" are meaningless if they are not accompanied by quantitative analysis. If what you visualize does not produce numbers that match experiment, your visual model is incorrect, no matter how beautiful, or how useful it is to you. Just because you are happy with it does not make it correct.

Physics just doesn't say what goes up must come down. It must also say when and where it comes down. This is the component of physics that many non-experts trivialize.

Zz.

 

[atommo]

Post #19 is what I considered to be the answer I was looking for- here's how I interpreted it:

- As a permanent magnet, the material has more up electrons than down so there is potential for an overall magnetic field.

- As per the description in http://farside.ph.utexas.edu/teaching/302l/lectures/node77.html (figure 30), when influenced by an external field the electrons can line up in generally the same way to produce the overall pseudo-current (due to electrons acting the same way) around the perimeter

- This does not make up a complete current circuit, but at the same time there is still current in each atom due to the electrons lining up the same way. Because of this there would (if I'm understanding this right) still be an extremely small current.

- Because there is (albeit an extremely small) current, in theory it would induce a very small current in a coil going round the outside (due to the magnetic field from the magnet)

I think I got the positive and negatives the right way round this time!
So what the image is trying to show is a small magnetic field would be induced in the coil from the big magnetic field... This is what I have been wondering all this time and from what I've seen I thought this was the case (but on such a small scale it would barely be measurable)

...Have I understood that right?

 

[Charles Link]

Post #19 is what I considered to be the answer I was looking for- here's how I interpreted it:

- As a permanent magnet, the material has more up electrons than down so there is potential for an overall magnetic field.

- As per the description in http://farside.ph.utexas.edu/teaching/302l/lectures/node77.html (figure 30), when influenced by an external field the electrons can line up in generally the same way to produce the overall pseudo-current (due to electrons acting the same way) around the perimeter

- This does not make up a complete current circuit, but at the same time there is still current in each atom due to the electrons lining up the same way. Because of this there would (if I'm understanding this right) still be an extremely small current.

- Because there is (albeit an extremely small) current, in theory it would induce a very small current in a coil going round the outside (due to the magnetic field from the magnet)

View attachment 236106
I think I got the positive and negatives the right way round this time!
So what the image is trying to show is a small magnetic field would be induced in the coil from the big magnetic field... This is what I have been wondering all this time and from what I've seen I thought this was the case (but on such a small scale it would barely be measurable)

...Have I understood that right?

The magnetic surface currents are quite large. A solenoidal current of 1 ampere with 500 turns(=wire windings) per meter, results in a solenoidal current per unit length of $K=500$ amperes/meter. The magnetic surface currents (current per unit length $K_m$) in an electromagnet and/or a permanent magnet are much larger and can easily be 1000 x this number. And that is why an electromagnet which consists of a solenoid (wire windings carrying a current), plus an iron core will generate a magnetic field that can be 1000 x as strong as the magnetic field from the solenoid without the iron core. $\\$ The magnetic surface currents are of a similar strength in a permanent magnet. The stronger the magnetic field, the higher the magnetic surface current number for the same geometry. In principle, it is the magnetic surface currents that generate the magnetic field in an electromagnet and/or permanent magnet.

 

[sophiecentaur]

The magnetic surface currents are quite large.

It's fair enough to use a term like that as long as we realize that it's no more 'really like that' than all the other constructs we use in advanced treatments of Physics. There is nowhere we could put an ammeter to measure that current and that's why I have a problem with presenting this to the uninitiated because they will grab at the analogy and treat it as actuality. We have exactly the same for of problem when people grab at photons as if they will help with all the EM wave problems because the corpuscular theory dies very hard! Dear old Feynman has a lot to answer for, here I think - however brilliant he was.

 

[sophiecentaur]

Please note that "visualization" and "modeling" are meaningless if they are not accompanied by quantitative analysis. If what you visualize does not produce numbers that match experiment, your visual model is incorrect, no matter how beautiful, or how useful it is to you. Just because you are happy with it does not make it correct.

@atommo You have 'liked' the post with this quote in it but you do not seem to be taking its message on board. For heaven's sake get yourself familiar with the basic theory of permanent magnetism before you reach for 'fringe' treatments of it. How can you expect to grasp it without learning the basics?

 

[Charles Link]

It's fair enough to use a term like that as long as we realize that it's no more 'really like that' than all the other constructs we use in advanced treatments of Physics. There is nowhere we could put an ammeter to measure that current and that's why I have a problem with presenting this to the uninitiated because they will grab at the analogy and treat it as actuality. We have exactly the same for of problem when people grab at photons as if they will help with all the EM wave problems because the corpuscular theory dies very hard! Dear old Feynman has a lot to answer for, here I think - however brilliant he was.

My generation (college days 1975-1980) was taught the magnetic pole model, with the magnetic surface currents mentioned only very quickly as an alternative theory which really wasn't quantified in detail. From what a University of Illinois physics professor who has taught E&M for 20+ years now has told me, they are now presenting the magnetic surface current approach to the undergraduate students, and only present the pole model as an advanced topic in the graduate classes. I think the magnetic surface current approach is indeed a good one. Yes, I agree, you can't measure the magnetic surface currents with an ammeter. That has its pluses in that the plastic laminations of a transformer don't block the magnetic surface currents. $\\$ Meanwhile, I have used the photon concept when considering the response of photodiodes, where essentially (with an efficiency number of .8 or thereabouts), you get one photoelectron per incident photon. It also comes in handy in deriving the Planck blackbody function, but I don't want to stray too far off the present topic which is the subject of permanent magnets and electromagnets, and trying to find a good way to explain how their magnetic fields arise.$\\$ The magnetic surface current approach is the best way I know of at present to explain the origin of the magnetic fields in magnets. It far surpasses the magnetic pole model for explaining the underlying physics. The pole model is mathematically accurate in the magnetic field vector $\vec{B}$ that it computes, but if it is used to try to understand the underlying physics, it can generate many misconceptions.

 

[ZapperZ]

The magnetic surface current approach is the best way I know of at present to explain the origin of the magnetic fields in magnets. It far surpasses the magnetic pole model for explaining the underlying physics. The pole model is mathematically accurate in the magnetic field vector $\vec{B}$ that it computes, but if it is used to try to understand the underlying physics, it can generate many misconceptions.

You and I have had disagreement on this before, and I have stated my argument in the relevant Insight article that you created.

And as I've stated there, the problem here is that you are giving the impression that this is a valid model to those who don't know any better. As you can already see, it is creating a huge amount of confusion here. Undergraduate physics students will learn about QM, and those who go into condensed matter/solid state physics, will get to see the quantum description of magnetism. But many people on here do not, and will not get to see the accurate picture! It is difficult to justify using this classical picture of magnetism as the end picture that we leave these folks with. That's like leaving the planetary model of an atom as the valid picture of an atom, regardless of how good of an approximation it is for H atom.

I do not have the same problem with the photo picture as sophiecentaur. I've worked with phothocathodes and photomultipliers, and the photon picture has no counterpart in many situations that we dealt with. The idea of multiphoton photoemission and quantum efficiency are very much well-established.

The OP needs to first learn about magnetic moments of individual atoms. Then migrate to how each individual moments then interacts with other neighboring moments. The arrangements of these individual moments can make a huge difference. For the same type of atoms, one arrangement can mean something being ferromagnetic, while another it can be something else! This basic fact cannot be explained by your circular surface current model.

Zz.

 

[Charles Link]

This surface current model isn't expected to explain even a good portion of the subject. It does provide accurate calculations though for magnetic field strengths $\vec{B}$ under the assumption that the magnetization vector $\vec{M}$ is approximately uniform. It doesn't begin to treat the quantum mechanical aspect, and I haven't even introduced the exchange effect in this thread. I'm also not trying to answer questions like why some materials make permanent magnets while others like soft iron have the magnetic field go back to near zero once the external magnetic field is removed. $\\$ I do think my response gave a reasonably satisfactory answer for the OP and the questions of his initial post. If he continues his studies of the magnetism subject, in another week or two he might come back fascinated by the force/torque on a current-carrying loop in a magnetic field and wonder whether it might be possible to make use of this to power machinery. (LOL) $\\$ Back to the magnetic surface current subject: If it wasn't of some importance, I don't think Griffiths would have spent a couple of pages doing a very detailed derivation in his E&M textbook. For me, the surface current model is a tremendous advancement beyond the magnetic pole model, which I saw both as an advanced undergraduate as well as in two graduate courses. In the graduate courses, we used J.D. Jackson's textbook, which was a very good book for its very thorough vector calculus, but his treatment of the magnetism subject is very incomplete. $\\$ IMO, the magnetism subject needs to be presented in the undergraduate curriculum, as it presently is. The case of the transformer problem with its Ampere's law=MMF (magnetomotive force) type solution is also very useful material for both physicists and EE's. $\\$ Although I'm sure it is an extremely interesting subject, but one that also takes an enormous investment of time and effort, an undergraduate does not need to know the details of the solid state and quantum mechanical descriptions of ferromagnetism=there are only a small handful of physics people out there who have that kind of level of understanding, and I will readily admit, I am not one of that small handful. $\\$ Edit: To add a little detail: The interactions of neighboring magnetic moments via the exchange effect makes any near-complete mathematical description of ferromagnetism extremely difficult. It would be nice to say that how a magnetic moment $\vec{\mu}$ in the material behaves depends only on the value of the magnetic field $\vec{B}$ at that location. Unfortunately, this is not the case, so that the problem is extremely complex from a mathematical sense. Weiss' mean field theory is an attempt to work through this difficulty, but that model has its limitations. A more complete treatment of the subject would take an enormous investment of time and effort. Ferromagnetism perhaps is a problem that quantum field theory may provide some insight, but the second-quantized operators of quantum field theory can be very cumbersome for those who are not extremely proficient with them. $\\$ Additional edit: Even though the mathematical mechanics of the magnetic pole method is rather clumsy, I am very glad that we were taught the method, and I am very glad I put the many, many hours into learning it. The magnetic pole method actually only really finally made sense to me after I did some calculations with the magnetic surface current method, and I was able to show how the two were connected. I do think it is a major plus that the magnetic surface current method is now included in the undergraduate E&M courses at many universities.

 

[sophiecentaur]

Meanwhile, I have used the photon concept when considering the response of photodiodes

Naturally; there is no better way of considering quantum phenomena and Photon Efficiency is a very meaningful performance descriptor. But would you discuss light from a distant star in terms of a string of little bullets arriving? That is an analogy too far but its one that's used with gay abandon by people who do not know much Physics.
But, back to these 'currents . . . .

 

[Charles Link]

Some very simple calculations can be done with a cylindrical bar magnet and using either the magnetic pole or magnetic surface current model: $\\$ e.g. If you assume the magnetization $\vec{M}=1.0$ (M.K.S. units with $\vec{B}=\mu_o \vec{H}+\vec{M}$) and is uniform along the z-axis, $\vec{B}$ can be computed everywhere by identifying the magnetic poles, and using $\vec{B}=\mu_o \vec{H}+\vec{M}$ and the inverse square law. $\\$ Alternatively, using the magnetic surface current model, $\vec{B}$ can be computed everywhere using Biot-Savart, once the magnetic surface currents are identified. $\\$ The tremendous level at which we we taught the magnetic pole model in my advanced undergraduate E&M class in 1975 using $\rho_m=-\nabla \cdot \vec{M}$, and $\vec{H}=\int \frac{\rho_m(x')(x-x')}{4 \pi \mu_o |x-x'|^3} \, d^3x'$ + $\vec{H}$ from any currents in conductors using Biot-Savart, and after all that we still couldn't do simple calculations with a cylindrical bar magnet was really carrying the physics and mathematics to the extreme. The very mathematical description is a good one, but the simpler explanations are also necessary. $\\$ Both the magnetic pole method and the magnetic surface current model are highly mathematical. They may be a watered-down version of a many body quantum field theory approach, but they still provide very useful models which offer a reasonably good explanation for many of the phenomena that occur.

 

[ZapperZ]

... but they still provide very useful models which offer a reasonably good explanation for many of the phenomena that occur.

Where exactly do they become useful?

Zz.

 

[Charles Link]

Where exactly do they become useful?

Zz.

IMO, it is a very useful thing to be able to estimate the magnetic field from a cylindrical bar magnet that has $L=4$" and diameter of 1/2". For many commercially available magnets $\vec{M} \approx 1.0$ M.K.S. units within a factor of 2. For a laboratory experiment that a couple of students did using some of these "simpler" theories, and I think it was highly educational for them, see: https://www.physicsforums.com/threa...-function-of-temperature.950326/#post-6020315 $\\$ Quite a lot can be done in studying ferromagnetism without employing advanced quantum field theory.

 

[ZapperZ]

IMO, it is a very useful thing to be able to estimate the magnetic field from a cylindrical bar magnet that has $L=4$" and diameter of 1/2". For many commercially available magnets $\vec{M} \approx 1.0$ M.K.S. units within a factor of 2. For a laboratory experiment that a couple of students did using some of these "simpler" theories, and I think it was highly educational for them, see: https://www.physicsforums.com/threa...-function-of-temperature.950326/#post-6020315 $\\$ Quite a lot can be done in studying ferromagnetism without employing advanced quantum field theory.

How useful and accurate is this? I have several cylindrical bar magnet in my class lab, and they ALL have different strengths even though they all have identical size.

Zz.

 

[Charles Link]

How useful and accurate is this? I have several cylindrical bar magnet in my class lab, and they ALL have different strengths even though they all have identical size.

Zz.

You can measure them, i.e. the $\vec{B}$ from them, with a meter that measures magnetic field strength, if you assume the magnetization $\vec{M}$ is uniform. That's basically what the students did in the "link" of post 49. You can also use a boy scout compass to do some ballpark measurements=see post 21 of the "link" in post 49. $\\$ And how accurate is the assumption that $\vec{M}$ is uniform? I can't readily quantify it, but I think it is quite good. $\\$ Much of my working years were spent doing electro-optic experiments, but had I been doing all kinds of experiments with magnets and devices employing magnets, I think think I would have found it equally exciting.

 

[ZapperZ]

You can measure them, i.e. the $\vec{B}$ from them, with a meter that measures magnetic field strength, if you assume the magnetization $\vec{M}$ is uniform. That's basically what the students did in the "link" of post 49. You can also use a boy scout compass to do some ballpark measurements=see post 21 of the "link" in post 49. $\\$ And how accurate is the assumption that $\vec{M}$ is uniform? I can't readily quantify it, but I think it is quite good.

But you were selling this model as the ability to predict the magnetic field strength of a cylindrical magnet! If you have to measure them, then what's the point of the model?

Again, you have not given me any usefulness of this model.

Zz.

 

[Charles Link]

But you were selling this model as the ability to predict the magnetic field strength of a cylindrical magnet! If you have to measure them, then what's the point of the model?

Again, you have not given me any usefulness of this model.

Zz.

If you would read the "link" of post 49, you measure the $\vec{B}$ to compute the $\vec{M}$. You just need to measure $\vec{B}$ at one location on-axis at some distance, and from there, the model will give you predictions of what $\vec{B}$ is everywhere.

 

[ZapperZ]

If you would read the "link" of post 49, you measure the $\vec{B}$ to compute the $\vec{M}$. You just need to measure $\vec{B}$ at one location on-axis at some distance, and from there, the model will give you predictions of what $\vec{B}$ is everywhere.

I have a better idea. Take out the Hall Probe and measure B where you want it. Done!

Zz.

 

[hutchphd]

But would you discuss light from a distant star in terms of a string of little bullets arriving?

I don't understand your enmity toward the concept. If using a (cooled) high sensitivity cameras for either astrometry (which I haven't done) or fluorimetry (which I have ), the statistics are exactly like shotgun pellets impinging.

 

[Charles Link]

I don't understand your enmity toward the concept. If using a (cooled) high sensitivity cameras for either astrometry (which I haven't done) or fluorimetry (which I have ), the statistics are exactly like shotgun pellets impinging.

I think there is some very good physics in this model, just as there is some very good physics in the magnetic surface current calculations. Neither description is a perfect description, but I think they both have considerable merit.

 

[ZapperZ]

I think there is some very good physics in this model, just as there is some very good physics in the magnetic surface current calculations. Neither description is a perfect description, but I think they both have considerable merit.

Actually, no. There are usefulness in the photon model. You see it in photoemission description, etc. I’m still waiting for you to show the usefulness of the surface current model. Where is it used as extensively as photons?

Zz.

 

[Charles Link]

Actually, no. There are usefulness in the photon model. You see it in photoemission description, etc. I’m still waiting for you to show the usefulness of the surface current model. Where is it used as extensively as photons?

Zz.

Besides using a Hall meter probe, how do you @ZapperZ compute the magnetic field $\vec{B}$ and/or the magnetization $\vec{M}$ from a permanent magnet? $\\$ Do you use the magnetic "pole" model with $\vec{B}=\mu_o \vec{H} +\vec{M}$ ? $\\$ That also works equally well in getting the same results, but it doesn't explain the underlying physics as well as the magnetic surface current model.

 

[ZapperZ]

Besides using a Hall meter probe, how do you @ZapperZ compute the magnetic field $\vec{B}$ and/or the magnetization $\vec{M}$ from a permanent magnet? $\\$ .

I don’t, and neither do you, because you had to use an experimental measurement FIRST to “calibrate” the field before using the model. If I tell you that I’m buying a set of cylindrical magnets with such-and-such a dimension, can you, a priori, tell me the magnetic field strength? Nope!

That is why I said earlier that if I need to know the field, I measure it!

Zz.

 

[Charles Link]

You can measure the magnetic field $\vec{B}$, (externally), but how do you then compute $\vec{M}$ or $\vec{B}$ internally? It's not always possible to put a Hall probe inside the magnet. $\\$ The magnetic "pole" model and the magnetic "surface current" model are the two ways that I know of to get the internal results. I think they are both quite useful.

 

[ZapperZ]

You can measure the magnetic field $\vec{B}$, (externally), but how do you then compute $\vec{M}$ or $\vec{B}$ internally? It's not always possible to put a Hall probe inside the magnet. $\\$ The magnetic "pole" model and the magnetic "surface current" model are the two ways that I know of to get the internal results. I think they are both quite useful.

Again, where is this iseful and how accurate is this when compared to the result from quantum magnetism, so much so that it is used as extensively as the photon model? That is what I’ve been asking. It is one thing to propose a model, it is another to show that it is useful enough that a lot of areas make use of it. I can show plenty of examples for the photon model.

Zz.

 

[Charles Link]

In general, I think E&M has been de-emphasized in the college curriculum over the last 40 years. The magnetostatics is largely a classical description, but I also think that it is getting pushed on the backburner and is largely ignored by many of those in academia. The higher priorities are given to other areas, so that I think presently there are very few who even specialize in E&M.

 

[ZapperZ]

In general, I think E&M has been de-emphasized in the college curriculum over the last 40 years. The magnetostatics is largely a classical description, but I also think that it is getting pushed on the backburner and is largely ignored by many of those in academia. The higher priorities are given to other areas, so that I think presently there are very few who even specialize in E&M.

First of all, you are admitting here that it doesn’t have an extensive usefulness. Let’s get that out of the way first.

Secondly, if you look into the field of Accelerator Physics, the most important topic of that field IS classical E&M! It is the de facto requirement that everyone specializing in this discipline go through and understand it at the level of Jackson. In fact, look up the curriculum at any USPAS program and see how classical E&M permeates in almost every topic in this discipline. So no, it is not ignored in academia.

Yet, we make no use of the surface current model!

Zz.

 

[Charles Link]

And here is a transformer with an air gap https://www.physicsforums.com/threads/absolute-value-of-magnetization.915111/#post-5767374 where MMF equations that arise from Ampere's law in the form $\oint H \cdot dl=I$ is used to solve this problem. $\\$ This form of Ampere's law is most readily understood by using $\nabla \times M=\mu_o J_m$. (Starting with $B=\mu_o H+M$ and taking curl of both sides. Also using $\nabla \times B=\mu_o J_{total}$, where $J_{total}=J_{free}+J_m$).$\\$ This very same equation, $\nabla \times M=\mu_o J_m$, (and using Stokes theorem at the surface boundary), is one way in which the magnetic surface current per unit length $K_m= \frac{M \times \hat{n}}{\mu_o }$ can be derived. $\\$ J.D. Jackson uses the magnetic pole model. The E&M professor at the University of Illinois at Urbana, who I have had some correspondence with,(he has taught E&M there for 20+ years now), tells me he actually had J.D. Jackson as an E&M instructor when he was at Berkeley, but he thinks Griffiths' book, which introduces magnetic surface currents, is a better textbook than J.D. Jackson's. $\\$ He also tells me they most often don't even present the magnetic pole model to the undergraduate physics students. Instead, they now teach them the magnetic surface current model.

 

[ZapperZ]

And here is a transformer with an air gap https://www.physicsforums.com/threads/absolute-value-of-magnetization.915111/#post-5767374 where MMF equations that arise from Ampere's law in the form $\oint H \cdot dl=I$ is used to solve this problem. $\\$ This form of Ampere's law is most readily understood by using $\nabla \times M=\mu_o J_m$. (Starting with $B=\mu_o H+M$ and taking curl of both sides. Also using $\nabla \times B=\mu_o J_{total}$, where $J_{total}=J_{free}+J_m$).$\\$ This very same equation, $\nabla \times M=\mu_o J_m$, (and using Stokes theorem at the surface boundary), is one way in which the magnetic surface current per unit length $K_m= \frac{M \times \hat{n}}{\mu_o }$ can be derived. $\\$ J.D. Jackson uses the magnetic pole model. The E&M professor at the University of Illinois at Urbana, who I have had some correspondence with,(he has taught E&M there for 20+ years now), tells me he actually had J.D. Jackson as an E&M instructor when he was at Berkeley, but he thinks Griffiths' book, which introduces magnetic surface currents, is a better textbook than J.D. Jackson's. $\\$ He also tells me they most often don't even present the magnetic pole model to the undergraduate physics students. Instead, they now teach them the magnetic surface current model.

And this is extensively used and is useful ... where, exactly?

You keep showing me what it can calculate (I’d rather say “estimate”) stuff, without showing me the areas of study where this model has been shown to be indespensibly useful! If you are going to hitch a ride with the photon model, then you must have evidence that this is as equally used as the photon model.

I have come across many models and ideas that have very little usefulness. They too can calculate stuff. It it doesn’t mean that they have any bearing on what we do and use nowadays. This is what I’ve been asking repeatedly, and you have essentially given a defeatist acknowledgment of its lack of use by lumping in the apparent discarding of classical E&M, the latter I’ve shown to be completely false.

Your insistence on pushing this model seems to verge on a solution waiting for a problem.

Zz.

 

[sophiecentaur]

I don't understand your enmity toward the concept. If using a (cooled) high sensitivity cameras for either astrometry (which I haven't done) or fluorimetry (which I have ), the statistics are exactly like shotgun pellets impinging.

I think there is some very good physics in this model,

It's appropriate where it's appropriate. It is pretty nonsensical to discuss a photon 'travelling from a distant star' because there is no 'place' it can be at any time; it has no extent in the meaningful sense of the word. Otoh, Photon Interaction between an EM wave and a material object makes total sense as the Energy and the Momentum are quantised. So the idea that the light can be regarded as little bullets on the way is not only flawed but it is attractive and communicates a misconception to others. It is hard but one should accept it rather than try to over-simplify it. And why not? Have we not progressed since the Corpuscular Theory of Light?
There are many examples where shotgun pellets do not explain what we see. My' enmity' only extends to its mis-use when inappropriate.

 

[Charles Link]

Your insistence on pushing this model seems to verge on a solution waiting for a problem.

Have you not done many E&M calculations using the magnetic pole model? The problem with the magnetic pole model is that you get magnetic fields $H$ from the magnetic poles when there are no electrical charges in motion. The surface current model gets the same answer for the magnetic field $B$ , but instead of doing what seems to be mathematical machinery without any underlying physics, it uses Biot-Savart along with the magnetic surface currents to compute the vector $B$. $\\$ As an undergraduate and graduate student, I got where I could work the pole model calculations (as J.D. Jackson, and Pugh and Pugh present them) quite well, but the mathematical machinery that results in $H$ as being a second type of magnetic field is flawed, and calculations with the surface current model show how $H$ comes about. The equation $B=\mu_o H+M$ suggests that the magnetization $M$ makes a local contribution to $B$. The surface current calculations show this apparent local contribution to $B$ has non-local origins. $\\$ To see this, you would need to work through some magnetic surface current calculations in depth, like the case of a cylindrical magnet of uniform magnetization, and compute the $B$ inside the material. The surface currents for the cylindrical magnet have the same geometry as those of a solenoid. If you were to work through calculations such as this in detail, I think some of your skepticism might start to be reduced.

 

[Charles Link]

And a calculation of much interest is the uniformly magnetized cylinder of arbitrary radius $r=a$ and finite length $L$. $\\$ Without knowing the answer beforehand, you might even think that the surface current calculations might get a different answer for $\vec{B}$ than what the magnetic pole model computes. $\\$ To simplify the problem, you can make it into a cylinder of semi-infinite length with a single pole, (magnetic surface charge density $\sigma_m=\vec{M} \cdot \hat{n}=M$), on the end face (at $z=0$) and compare the magnetic field $\vec{B}$ from both calculations.$\\$ The answers are either going to agree, or one of the models is incorrect. $\\$ In the plane ($z=0$ ) containing the single pole for the cylinder of semi-infinite length, the magnetic pole model gives $B_z=0$ at $z=0$ for $r>a$ by inspection, $\\$ (because $\vec{B}$ must point radially outward, and will simply have a $B_r$ component in cylindrical coordinates). (And note that $B=\mu_o H$ outside of the cylinder, because $M=0$ outside of the cylinder). $\\$ This makes for a simple test case. $\\$ Will the surface current Biot-Savart integral for the semi-infinite cylinder give $B_z=0$ in this entire plane for $r>a$ ? $\\$ I was very surprised at the result when I did the computation of this integral in 2010. $\\$ For this complete calculation see: https://v1.overleaf.com/read/kdhnbkpypxfk $\\$ These calculations with the surface current model make the "pole" model much more complete. $\\$ ........................... $\\$ As a challenge for anyone who wants to attempt it, try writing out the expression for $\vec{B}$ in the plane $z=0$ for this semi-infinite cylinder case using the surface currents, and solving the integrals for $B_z$, $B_r$, and $B_{\phi}$. If you want to see the calculations in detail, instead of trying them yourself, they are done in the "link" given just above.

 

[vanhees71]

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.

First of all, it's of course clear that anything to understand about the "matter part of electromagnetism" from first principles has to do with quantum theory. For everyday matter in many cases you can use non-relativistic many-body theory, which simplifies some things, particularly if it comes to spin, because spin separates from position and momentum observables in the sense that in non-relativistic quantum physics spin is an additional angular momentum commuting with position and momentum observables. Thus you have a pretty simple concept of total angular momentum as the sum of orbital and spin angular momentum (the only technical problem being the understanding of this sum in terms of Clebsch-Gordan coefficients and all that, which is a somewhat more complicated topic of the QM 1 or maybe QM 2 lecture).

The closest intuitive picture of spin in classical physics are twofold: (a) the spin, i.e., intrinsic rotation of a "rigid body" as part of it's total angular momentum and (b) the magnetic moment of current distributions in a compact region of space seen from a far distance, so that the extension of the region can be negelected compared to the length scale where the magnetic field varies significantly. The latter picture is the one I think is most intuitive for introducing spin in the QM 1 lecture (this I've just done before Christmas in my theoretical-physics lecture for high school-teacher students, and I think it has been quite well understood).

Of course, one must emphasize that these are pictures, and the only correct description we have today is quantum mechanics. And all I could do in my QM 1 lecture is to thoroughly discuss the Stern-Gerlach experiment using quantum theory and only quantum theory in an idealized approximation for the interactin of an external static magnetic field with an uncharged "particle" with an magnetic moment (of course the historical example with a silver atom is appropriate, but one can also use neutrons as an example of an even more particle-like object too). This is a very interesting example for a quite simple analytically solvable dynamical (!) problem for a measurement process, which to my surprise seems not to be present in the textbook literature. I'm about to write a paper on it for AJP or EuJP as soon as I find the time after the semester.

To understand a permanent magnet, however, is a paradigmatic example for a collective many-body effect (something I cannot teach in a first lecture on quantum mechanics due to lack of time), i.e., you have a collection of spins interacting via their associated magnetic moments, and the most simple models are the often discussed Heisenberg and Ising models. It's an entire plethora to discuss fundamental many-body physics, including the "exchange forces" due to the indistinguishability of (fermionic) particles (microscopic level) and the concept of effective quantum field theory, using the mean-field approximation and spontaneous symmetry breaking of (global) rotational symmetry, leading to an example for Ginzburg-Landau theory etc. etc.

Of course, one can also treat permanent magnets on a completely classical level. Then of course the treatment of the matter part of electromagnetism completely reduces to the use of phenomenological parameters. In the usual E&M lecture one restricts oneself to the "linear-response approximation", which however goes pretty far towards a realistic description of the electromagnetism of macroscopic matter (see the excellent treatment of the subject in Vol. 8 of Landau&Lifshitz). The reason, of course, is that usually the electromagnetic fields imposed on the matter in everyday life are small compared to the inneratomar fields which hold the matter together, over which one "coarse grains" to the relevant macroscopic degrees of freedom.

For a permanent magnet in the most simple model treatment you simply assume some plausible distributions of magnetization (model of a "hard ferromagnet"). Then the task is to solve Maxwell's equations with the appropriate boundary conditions, in the static case for $\vec{B}$ and $\vec{H}$ with the constituent equation $\vec{B}=\mu_0 (\vec{H}+\vec{M})$ (SI units). Since then there are no free (exernal) currents, the Maxwell equations for the static case reduce to
$$\vec{\nabla} \times \vec{H}=0, \quad \vec{\nabla} \cdot \vec{B}=0\; \Rightarrow \; \vec{\nabla} \cdot \vec{H}=-\vec{\nabla} \cdot \vec{M}.$$
One can in this case thus use a scalar potential for $\vec{H}$, $\vec{H}=-\vec{\nabla} \phi_m$ and then solve for the Poisson equation in the usual way:
$$\phi_m(\vec{x})=\int_{\mathbb{R}^3} \mathrm{d}^3 \vec{x}' \frac{-\vec{\nabla}' \cdot \vec{M}(\vec{x}')}{4 \pi |\vec{x}-\vec{x}'|}.$$
Using Gauss's integral theorem and the fact that at infinity $\vec{M}$ vanishes, one can transform this into the more useful form
$$\phi_m(\vec{x}) = \int_{\mathbb{R}^3} \frac{\vec{M}(\vec{x}') \cdot (\vec{x}-\vec{x}')}{4 \pi |\vec{x}-\vec{x}'|^3} = -\vec{\nabla} \cdot \int_{\mathbb{R}^3} \mathrm{d}^3 \vec{x}' \frac{\vec{M}(\vec{x}')}{|\vec{x}-\vec{x}'|}.$$

Another, equivalent way is to use the vector potential for the magnetic field, $$\vec{B}=\vec{\nabla} \times \vec{A}$$ and
$$\vec{\nabla} \times \vec{H}=\frac{1}{\mu_0} \vec{\nabla} \times \vec{B}-\vec{\nabla} \times \vec{M}=0.$$
Then, imposing the Coulomb-gauge condition $\vec{\nabla} \cdot \vec{A}=0$ one finds
$$\Delta \vec{A}=-\mu_0 \vec{\nabla} \times \vec{M},$$
i.e., the magnetization is equivalent with a current density,
$$\vec{j}_m = \vec{\nabla} \times \vec{M}$$
as far as the magnetic field $\vec{B}$ is concerned.

If you use homogeneous magnetization as a simple model, this effective current reduces to the surface current, corresponding to the jump of the magnetization at the surface of the permanent magnet. Which technique to use to calculate the fields, of course, depends on the problem. Usually the scalar-potential method is more straight forward, because one has not so much problems to struggle with the singulartities of the magnetization and the evaluation of the effective surface current.

You find the example of a homogeneously magnetized sphere, where both methods can be used to evaluate the magnetic field analytically in my lecture notes on E&M for high school-teacher students (in German, but I think with a high enough "equation density" to be understandable also by non-German speakers):

https://th.physik.uni-frankfurt.de/~hees/publ/theo2-l3.pdf (Sect. 3.3.3).

 

[alan123hk]

#1 no movement = no energy, but a permanent magnet DOES contain energy (the electrons in it that are causing it to have a magnetic field in the first place).

The permanent magnet will not release its energy to the copper coil even it does contain internal energy and equivalent circular current, that is why it is called permanent magnet.
If the permanent magnet dose release its energy then its magnetic field strength have to be reduced and thus can not be named as permanent magnet.

Therefore the current is induced in the copper coil only when the permanent magnetic is moving in or out, in this case the energy is come from the external force to move the permanent magnet instead of the permanent magnet itself.