Stupid question relating to electric induction

[sophiecentaur]

; there is an electric current. Its just exclusively on the very outside of the material.

In this case the currents are essentially macroscopic effects (no?) around the outside of the material

I'm referring to bound electron currents=essentially a Bohr atom approach where the electron orbits the atom.

Here, the suggested currents are around the atom. But in a bound state round an atom, where can you say the electron 'is' to be moving in a loop?
The two ideas seem to be totally different and neither seems to be equivalent to electron spin, which is how ferromagnetism is usually explained.
I see no point in trying to bend the accepted theory to fit someones personal intuition. Where could that take @atommo further in understanding the mechanisms of magnetism if you start so far off course?

 

[Charles Link]

In this case the currents are essentially macroscopic effects (no?) around the outside of the material

Here, the suggested currents are around the atom. But in a bound state round an atom, where can you say the electron 'is' to be moving in a loop?
The two ideas seem to be totally different and neither seems to be equivalent to electron spin, which is how ferromagnetism is usually explained.
I see no point in trying to bend the accepted theory to fit someones personal intuition. Where could that take @atommo further in understanding the mechanisms of magnetism if you start so far off course?

The electron spin is different classically from orbital electron current, but in Griffiths derivation in chapter 6 of his book, he treats the case of a magnetic moment $\vec{\mu}$ of either form (spin or orbital angular momentum). (Note: $\vec{\mu}_s=\frac{g_s \mu_B \vec{S}}{\hbar}$, and $\vec{ \mu}_L=\frac{g_L \mu_B \vec{L}}{\hbar }$,(c.g.s. units), where the Bohr magneton $\mu_B=\frac{e \hbar}{2 mc}$, and where $g_s=2.0023...$ and $g_L=1.0$ ).$\\$ He considers an arbitrary distribution of such magnetic moments and derives the equation for the vector potential $\vec{A}$. This vector potential takes the form (c.g.s. units) of $\vec{A}(x)=\int \frac{\vec{J}(x')}{c|x-x'|} \, d^3x'$, where $\vec{J}$ is any arbitrary current density distribution. With a couple of vector identities, he shows that the potential from his arbitrary distribution of magnetic moments has two terms that are of the following: $\vec{A}(x)=\int \frac{\vec{M}(x') \times \hat{n}'}{|x-x'|} \, dA' +\int \frac{\nabla' \times \vec{ M}(x')}{|x-x'| } \, d^3x'$, where $\vec{M}$ is the density of magnetic moments $\vec{\mu}$ per unit volume. By looking at this result, one can conclude that the magnetic surface current density per unit length $\vec{K}_m=\vec{M} \times \hat{n}$, etc. $\\$ The first integral is the magnetic surface currents with magnetic surface current per unit length $\vec{K}_m=\vec{M} \times \hat{n}$, and the second integral involves gradients in the magnetization with bulk magnetic current density $\vec{J}_m=\nabla \times \vec{M}$, where I may have left off $\mu_o$ and/or $c$, (or a $4 \pi$ ), in a couple of places. (Switching between c.g.s. and various SI units requires a little extra work. Griffiths uses a form of SI units). $\\$ (It is left open for discussion whether these currents are real or not. There is no actual charge transport here, but these currents can be used with Biot-Savart to compute the magnetic field $\vec{B}$. Alternatively, the magnetic field is given by $\vec{B}=\nabla \times \vec{A}$ ). $\\$ Many physics students who have studied Griffiths textbook seem to overlook this very important derivation that he does. The magnetic surface currents that arise here can be used to readily explain the magnetic field of a permanent magnet of cylindrical shape that has uniform magnetization $\vec{M}$ along its axis. The magnetic surface currents can be used to compute the magnetic field that exists both inside and outside the permanent magnet.

 

[atommo]

You cannot 'see' any virtual photons and they are a very sophisticated concept - way beyond the level of this thread and yet you feel you can visualise electrons buzzing around in circles?? Physics is not a subject that takes well to the intuitive approach. Many invalid experiments and demonstrations have been used in the past. They convinced great minds at the time but have been proved wrong later. Finding something "hard to imagine" is not a good argument one way or another. At PF we. at least try to follow the protocol that's used to advance the subject.

Well not quite buzzing in circles... More like I can visualise electron clouds (since due to quantum mechanics electrons sort of appear and disappear all over a certain area rather than 'orbit' an atom). I can work out on a rather simple level the exchange of energy between these electrons. I know that electrons do not really 'spin'- its just a term used to identify the energy (virtual photon) type they give out.

I would say so long as a good base understanding is there, you can simulate quite a lot in your head (and if it gets crazy you can start writing stuff down/drawing it).

Of course you can get things wrong- science is about testing theories, getting them wrong and then getting closer to a proper understanding. And sometimes simulations don't work out either such as the case here where I needed input from others to help clear up my misunderstanding.

I'm not a maths or science guru for that matter- I do it on the side as a passion because I enjoy it (but sadly I don't know many of the formulas for that reason). But even so, that doesn't stop me from learning about for example the quanta of the electromagnetic force. I just have to try and convert the information I read into something I can understand (which may mean it is not 100% mathematically accurate, but it is usually still generally on the right lines).

Ultimately I want to make something based on what I've learned but I want to have as thorough understanding of electromagnetism as possible before that. I may be back with more crazy questions later on but for now I've got the answer I was looking for so thanks to all of you! Also in future I'm not too particular on mathematical accuracy in answers so long as it gives me a good idea because of the reason above [unless I've stated otherwise in that question] (obviously if so please say it is not completely accurate)

 

[BvU]

Oh boy ...

 

[sophiecentaur]

I want to have as thorough understanding of electromagnetism as possible before that.

Read a serious book on EM theory. There is no other way to achieve what you need.

 

[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.