# Insights Permanent Magnets Described by Magnetic Surface Currents - Comments

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1. Jan 16, 2017

2. Jan 16, 2017

### Greg Bernhardt

Hard work paid off, nice second Insight Charles!

3. Jan 16, 2017

The explanation given of magnetic surface currents for computing the magnetic fields is also mathematically in complete agreement with the "pole method" that many of the older generation use to compute the magnetic field. This author has done calculations to show the mathematical equivalence of the two methods. The magnetic surface current method provides a much better understanding of the underlying physics while the "pole method", although getting the precisely correct answer for the magnetic field $B$, can easily give incorrect interpretations to what the $H$ from the poles represents, particularly in the material. For a more complete discussion of the pole method, I refer the reader to some calculations that I did connecting the pole method to the magnetic surface current method: https://www.overleaf.com/read/kdhnbkpypxfk This "Overleaf" paper was my very first attempt at Latex, so that some of the typing may appear a little clumsy, but hopefully you find it readable.

4. Jan 16, 2017

### ZapperZ

Staff Emeritus
There is something not quite right with this.

Let's say that I measure some magnetic field geometry. Without knowing the source, and simply looking at the geometry and the boundary conditions, I can come up with a particular geometry of the current source. This is what the article is doing, i.e. deducing the current source based on the fact that there is some configuration of a magnetic field.

But is there really a surface current that is responsible for the magnetic field of a ferromagnet? Or is this simply a model that is made to match the magnetic field geometry?

When I move a magnet into a coil, I get create a magnetic field that opposes the change in the magnetic field experienced by the coil. This opposing magnetic field induces a current in the coil. This is not a "model" current. It is real. If you connect a bulb to the circuit, it'll light up.

So is this surface current real, or is it simply a model that matches the field geometry? If I connect 2 ends a wire to various parts of the surface of the magnet, will I measure a current?

The picture of small, closed current loops to model atomic magnetic moment is highly outdated and not very accurate. Maybe to the first approximation, it might be useful, but that is as far as it can go. There are no current loops, and as far as I know, there are no ferromagnetic surface currents. There are modeled Amperian currents to emulate the magnetic field produced by the magnet, but this isn't real.

The other problem with this scenario is the difference between ferromagnets and paramagnets. If all we care about is this surface currrents, then why, in some material, the magnetization dies off when the external field goes away, while in permanent magnets, they stay aligned. This is one of the topics in quantum magnetism, where, among others, the Heisenberg coupling between nearest neighbor, next-nearest neighbor, next-next-nearest neighbor, etc... magnetic moments comes into play. The determination of the magnetic moment configuration of the lowest energy state is significant to result whether something is a paramagnet, ferromagnet, antiferromagnet, etc. This is the ORIGIN of permanent magnet, not the existence of "surface currents".

Zz.

5. Jan 16, 2017

I urge you to read through the derivation that Griffiths does for the magnetic potential $A$. He begins with the potential for a single magnetic dipole and then computes the potential $A$ for an arbitrary distribution of magnetic dipoles. It is a rather unique and roundabout proof that gets the result that the potential $A$ consists of two terms: Magnetic currents from $\nabla \times M=J_m/c$ and magnetic surface currents $K_m=c M\ \times \hat{n}$. He does it using SI units, and doesn't really emphasize the very important result. $\\$ In addition, the exchange effect plays an important role in the permanent magnet=otherwise the permanent magnet would only exist at very low temperatures=i.e. near the temperature of liquid helium. The exchange effect causes the spins to cluster, thereby making the unit much more thsan a single electron spin, and causing the Curie temperatures to be of the order of T=1000 degrees Centigrade.

6. Jan 16, 2017

### ZapperZ

Staff Emeritus
I have done something similar. This is an exercise the same way I ask my students to compute the centripetal force that is required to keep an electron in "orbit" around a nucleus. But none of this has any bearing on reality.

You could have easily showed me an experiment that actually measured this surface current, and I'll be satisfied with that. But my claim here is that this is nothing more than a model-equivalent, that IF this was modeled by currents, then it will have such-and-such a configuration and value. The magnetic field of permanent magnets is not caused by surface currents.

Zz.

7. Jan 16, 2017

I have already gotten feedback from a well-established E&M professor at the University of Illinois at Urbana-Champaign. (This dates back a year or two already). Please don't be too quick to discard the calculations. Meanwhile, because the surface currents are atomic in nature, they don't experience any ohmic losses. It is impossible to measure them with an ohm meter. There is no actual electrical charge transport in these magnetic surface currents.

8. Jan 16, 2017

### ZapperZ

Staff Emeritus
You don't seem to understand the problem.

There's nothing wrong with the calculation. If you want to model the magnetic field as being generated by a current, then fine! This was never in dispute!

But there is an implicit idea that this surface current is REAL for a permanent magnet. I question this, and I've asked for evidence to support that argument, rather than simply regurgitating the model. An electron has a magnetic moment. It has no "surface current". The requirement for the existence of a current to always produce a magnetic field is not valid.

Zz.

9. Jan 16, 2017

I've given as much rebuttal as I can for the moment. All I can do is ask for others to carefully look over the calculations and provide their opinions.

10. Jan 16, 2017

### ZapperZ

Staff Emeritus
And I want others to think "Wait, if there's a surface current, then there should be a surface resistance (permanent magnets are not superconductors), and since there's no net potential to maintain this current, this current will decay and die off very quickly. And that means that if the origin of this magnetic field is this surface current, then the magnetic field of a permanent magnet should die off in seconds!

Zz.

11. Jan 16, 2017

The origin of these magnetic surface currents is the magnetic moment at the atomic level. These states will persist without experiencing any ohmic losses. This is even the case with the plastic lamination that is used to block the Faraday currents in the ac transformer. The plastic laminations do not block the magnetic surface currents, because there is no actual electrical charge transport. The magnetic field occurs in the transformer from the surface currents, and meanwhile the "eddy" currents are successfully blocked. $\\$ Is there actually an electrical current at the surface? You may be correct in that there perhaps really isn't because there is no electrical charge transport, but assuming the existence of the surface current gives precisely accurate results for all magnetic field computations.

12. Jan 16, 2017

### ZapperZ

Staff Emeritus
And this is what I meant as it being simply a MODELED current. Haven't I said that there really isn't an actual, real surface current?

I can solve an electrostatic problem of a charge above a conductor plane by using an image charge. Everything about it is accurate. But is there really an image charge? No, there isn't! It is there simply to MODEL the charge distribution on the surface of the conductor. This charge distribution is real. The image charge isn't.

Your surface current can be used to model the magnetic field produced by the magnet. This is NOT is dispute. However, this surface current isn't real, similar to the image charge. It doesn't explain the origin of ferromagnetism. That is my point of contention in your article.

Zz.

13. Jan 16, 2017

I didn't include the exchange effect, because that is an additional topic that is very necessary to explain the high Curie temperatures, but isn't needed to explain the magnetic fields that are produced by permanent magnets. To first order, the exchange effect causes a coupling of adjacent spins to create clusters of spins (perhaps 100 or more) that all respond as a unit. Thereby, the $\frac{ \mu_s B}{kT_C}=1$ that gives an estimate of the Curie temperature will have a $\mu_s$ that is much more than a single electron spin. Although there may be some additional "local" effects, the magnetic field $B$ used in this calculation of the Curie temperature is basically that that is computed from the magnetic surface currents.

Last edited: Jan 16, 2017
14. Jan 16, 2017

@jtbell Might we have your inputs on the topic? In some previous discussions of magnetic surface currents (about a year ago), you were very much a proponent of the concept, where you described in detail the form of the derivation that Griffiths uses in his text.

15. Jan 16, 2017

### Staff: Mentor

In general the goal of science is to provide models that work, and asking "is there really ..." is just a philosophical exercise. If your phisophocal preference is to treat it as just a model and not real then that is fine, it is your choice. You are free to think of it merely as a computational aid and others are free to consider it to be real.

The J in Ohm's law is the free current. The bound current idea doesn't predict a surface resistance, so its absence isn't contradictory evidence.

16. Jan 17, 2017

### vanhees71

I like the mathematics displayed in this Insights article very much. However one should indeed emphasize that the surface currents are mathematical equivalents to mimic the influence of magnetization of the material in terms of the usual local Maxwell equations, as stressed by @ZapperZ.

17. Jan 17, 2017

### fluidistic

Last edited by a moderator: Jan 17, 2017
18. Jan 17, 2017

The magnetic surface currents are what results from Maxwell's equations, and the result is that the magnetic field that occurs in most magnetic solids is basically from non-local causes. (i.e. from surface currents). If you look at the equation $B=H+4 \pi M$ as presented by the pole method where $H$ includes contributions from the poles (the long cylinder geometry essentially has no poles), you could easily conclude that the magnetic field $B$ is caused by a local magnetization $M$. Calculations with the magnetic surface currents shows that the magnetic field is instead caused by the non-local surface currents. $\\$ For a thin disc shape, the surface currents are minimal and the magnetic field from such a shape is predicted to be rather weak. At least in one set of flat "refrigerator sticker" type magnets that I have, I found by experiment that they actually contain thin rows, spaced about 1/8" apart of alternating + and - magnetization. $\\$ My generation was actually taught the magnetic pole method (1975-1980), and the equivalent magnetic surface current was presented almost qualitatively as an alternative explanation. It wasn't until I did some rather detailed calculations to show/prove that both methods give the exact same result for the magnetic field $B$, that I realized that the surface current theory is a far better approach. In the magnetic pole method that I was taught=(basically from the textbook by J.D. Jackson), there are two different kinds of magnetic fields= $B$ and $H$. In a spherical shaped permanent magnet, the $H$ from the poles points opposite the $M$ in the material. The detailed magnetic surface current theory calculations show that this $H$ in the material is not a magnetic field, but simply a (negative) correction term to the $B$ in the material. (The $H$ of the pole theory is basically a mathematical construction, and not a second type of magnetic field). For the uniformly magnetized sphere $H=-(1/3) 4 \pi M$ and $B=H+4 \pi M=+(2/3) 4 \pi M$ with the $B$ pointing in the direction of the magnetization $M$ in order to maintain it. It was very handwaving arguments that came from the pole method that said the $H$ (in the opposite direction to $M$ was maintaining the magnetization $M$. (They would use the $M$ vs. $H$ hysteresis curve as a reason for how this was possible.) The pole method actually gets the precisely correct answer for the magnetic field $B$, and is a very useful computational tool, but it can easily be misinterpreted. The $H$ contribution from the poles, particularly in the material, is not a second type of magnetic field. From what I learned from a E&M physics professor at the U of Illinois, the "pole" method has now become replaced by the magnetic surface current theory in the curriculum. A computation just using the magnetic surface currents gets the very same result that $B=+(2/3)4 \pi M$ for the magnetic field inside the uniformly magnetized sphere. $\\$ For those who may have studied the "pole" method, I'd be interested in your feedback on what you might think of the surface current method. In the "pole" method, magnetic poles with magnetic pole density $\rho_m$ where $-\nabla \cdot M=\rho_m$ are considered to be sources of $H$, analogous to the polarization charge density $\rho_p$ that arises from $-\nabla \cdot P=\rho_p$ as sources for the electric field $E$. The problem that arises here is the magnetic "poles" are rather fictitious and there is no moving electrical charges/currents to generate the magnetic field in this model. The method does get the correct result for the magnetic field $B$ by employing the equation $B=H+4 \pi M$. It also can be a very good computational tool, where Legendre polynomial type solutions can be employed. (The calculations mentioned above, for the case of a uniformly magnetized sphere, are very difficult to do without Legendre methods, except for the point at the center of the sphere.) Anyway, I welcome your feedback.

Last edited: Jan 17, 2017
19. Jan 18, 2017

It might be worth mentioning that there are basically two ways to compute the magnetic fields of magnetic materials: The "pole method" and the magnetic surface current method. $\\$ One advantage of the "pole " method is that the mathematics are a little simpler, and for a simple uniformly magnetized bar magnet, all that is needed to compute the magnetic field is to assign a "+" pole to one endface, and a "-" pole to the other, and the magnetic field $H$ from each outside the magnetic obeys the inverse square law. The poles have magnetic surface charge density equal to $\sigma_m=M \cdot \hat{n}$. Inside the magnet, the $H$ points opposite from the $M$, and the magnetic field $B=H+4 \pi M$ will be found to point in the same direction as the magnetization $M$. A second advantage of the "pole" method is that the Legendre polynomial method can be employed for what would otherwise be very difficult calculations.
$\\$ The magnetic surface current method doesn't recognize the existence of any magnetic poles, but instead has a magnetic surface current per unit length $K_m=c M \times \hat{n}$ on the outer surface of the cylindrical magnet, and the magnetic field $B$ is computed everywhere by using Biot-Savart's law. The Biot-Savart integrals used to compute the magnetic field $B$ are much more complex, and it is rather remarkable that these integrals get the exact same answer for the magnetic field $B$ as the simpler "pole" method in all cases. Meanwhile, the magnetic fields are explained in this method as arising from currents=in this case "bound" currents. The agreement between the two methods in the computed magnetic field $B$ is quite remarkable, and the surface current method offers the advantage of explaining the underlying physics=i.e. magnetic fields arise from electrical currents. It is for these reasons that this author finds the magnetic surface current method of calculating magnetic fields in the materials as one that would be quite useful to be emphasized in the physics undergraduate curriculum. $\\$@Dale and @vanhees71 I would enjoy any feedback you might have.

Last edited: Jan 18, 2017
20. Jan 18, 2017