Talk:Magnetic field/Archive 6

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A mess

This Wikipedia article is a rambling, confusing, badly written hodgepodge that can only be understood (and that only maybe) by someone who already has a PhD in physics. It is worthless to the uninitiated, yet the uninitiated are those who you want to use Wikipedia as an information source. — Preceding unsigned comment added by 108.36.71.119 (talk) 22:44, 19 March 2020 (UTC)

Thank you for the feedback. I pretty much agree, although I am not criticizing the editors who wrote this article; this is just a difficult concept to explain to nontechnically educated readers, more difficult than Electric field. But as you say I think the majority of people coming to this page will be general readers who just want a simple explanation of magnetic fields in ordinary language, and this article could use some improvement on that score. --Chetvorno^TALK 18:18, 20 March 2020 (UTC)

B and H are never the same!

Even in a vacuum, B and H are NOT the same. These are two different entities! Why do you think they have different names? — Preceding unsigned comment added by Koitus~nlwiki (talk • contribs) 12:24, 17 February 2020 (UTC)

It doesn't say they are the same. The sentence in the introduction says: "In a vacuum, $\mathbf {B}$ and $\mathbf {H}$ are the same aside from units..." In a vacuum the relation between them is $\mathbf {B} =\mu _{0}\mathbf {H}$, where $\mu _{0}=4\pi \cdot 10^{-7}\approx 0.000001257$ is a unit conversion factor. $\mathbf {B}$ and $\mathbf {H}$ are vector fields, so this sentence is saying that at any point in a vacuum, the $\mathbf {B}$ and $\mathbf {H}$ vectors have the same direction and their magnitudes are proportional, with the magnitude of B equal to 0.000001257 times the magnitude of H. --Chetvorno^TALK 01:15, 20 March 2020 (UTC)

You state that "$\mathbf {B} =\mu _{0}\mathbf {H}$", so you've proved that they are not "the same aside from units", their magnitudes are proportional, not the same. How can you state that any two vector fields are the "same" without them both sharing the same magnitudes and directions for each of their constituent vectors? --Benjamin J. Crawford (talk) 14:43, 20 May 2020 (UTC)

Just to note that I have now edited the article accordingly. --Benjamin J. Crawford (talk) 16:11, 20 May 2020 (UTC)

An American and a Canadian are standing side by side. For the American the temperature is 68°F, while for the Canadian it's 20°C. Are they experiencing the same temperature? Suppose that temperature was labelled τ in Fahrenheit and T in Celsius? Would they now be different entities? Or are they the same aside from units? RockMagnetist(talk) 17:06, 20 May 2020 (UTC)

It is possible to have a unit system where the permeability of free space is unity. Constant314 (talk) 17:43, 20 May 2020 (UTC)

@RockMagnetist "Would they now be different entities?" - Yes. It would be correct to say that they both describe the same temperature, but it would be a stretch to make the statement that they are the same, aside from units. It's important for this to be unambiguous. In its original form, it was easy to read it as $\mathbf {B} =\mathbf {H}$ (except for units), which is simply false. In the same way that in your example τ=T would be inaccurate. Fundamentally they have different magnitudes, and a scaling algorithm which needs to be applied. Benjamin J. Crawford (talk) 17:51, 20 May 2020 (UTC)

As @Constant314 rightly pointed out, you can always define natural units that do away with these distinctions. This is the same argument as mass energy equivalence, whether or not it is semantically correct, this is common usage in academia. They describe the same thing (insofar as the permeability nicely accounts for the behavior of the field in materials), therefore they are equivalent models (not necessarily the same, but definitely equivalent). Footlessmouse (talk) 04:53, 23 August 2020 (UTC)

Intro

Hi all, I don't think the first two references are needed in the first sentence and I think they may be improper: unless I'm mistaken, Feynman was including magnetized materials when he referred to charges in motion, so including them on only the first half of the statement seems dubious. Can we try for another rewrite? How about:

A magnetic field refers to one of two closely related force fields used to describe the influence of moving electric charges (electric currents) and magnetic dipoles on other nearby moving charges and magnetic dipoles. Charges moving within these fields experience a magnetic force that is perpendicular to both the field and the direction of their movement within the field...

First sentence adapted from proposition by @Chetvorno in discussion in archives here. I am repoposing with modifications I believe circumvent the original objections. For 2nd paragraph:

In electromagnetism, the term "magnetic field" is used for two distinct but closely related vector fields: the magnetic field strength, B, and the magnetic flux density, H. The two fields differ in how they account for magnetization and are measured in different units: in SI units B is measured in tesla while H is measured in amperes per meter. In a vacuum, the two fields are related through the vacuum permeability, $\mathbf {B} /\mu _{0}-\mathbf {H} =0$, while in a magnetized material, the difference is given by material's magnetization.

Also, half-jokingly, I prefer the term "psudovector valued function of space" to "field of psudovectors" and think that neither is particularly informative to normal readers, even if they follow the link. Can this entire statement go in the body of the article? I noticed that is the only time pseudovectors are mentioned and the lead is supposed to summarize the article. Any feedback is appreciated, thanks! Footlessmouse (talk) 08:39, 23 August 2020 (UTC)

Note: I realize the term "force fields" is somewhat questionable, but I believe it is slightly more appropriate than vector field currently being used, which is also technically incorrect. It has the benefit of pointing to an article discussing at least a very similar topic from a physics perspective. Another alternative could be to use field (physics), which even discusses magnetostatics. Footlessmouse (talk) 09:16, 23 August 2020 (UTC)

Hi @Footlessmouse:, thanks for your work... it's being noticed (in my watchlist feed). Honestly, I think this whole article is a mess, and the idea of two different fields is a mess. There is only one 'fundamental' magnetic field, the three components of the Maxwell field tensor (Penrose, The road to reality). Feynman (Lectures vol II) treats it as such, Greiner (Classical Electrodynamics), Griffiths (Intro to electrodynamics), Purcell (Purcell - Electricity And Magnetism), Serway and Jewett (Phys for scientists and engineers), Holbrow (Modern Introductory Physics), and many more. Griffiths calls H the "Auxiliary Field", which it really is - it could be called B_{from free currents}. H+B_{from molecular currents}=B_total. So H is just what the field would be without the material in it.

I am against the new proposal for the lead, not only because of the "two fields". How familiar with magnetic dipoles is someone reading, for the first time, about the magnetic field? Everyone knows magnets, but dipoles? Nearby - is that 1 m, 10 km? I am not sure if the name "force field" is the most appropriate, modern physics somehow likes to stay away from forces (=Newton). Let's make sure we're not defining Force=Charge*Field, and Field=Force/Charge. When you follow the Force_field_(physics) link, it again says "a force field is a vector field". Do dipoles need to be moving?

The first two citations were left there because I needed to check whether the sources talk about magnetized materials. I just didn't have time to do that.

I put the "field of pseudovectors" because some others were trying to have it in the first sentence over and over again, as "pseudovector field" (no wikilink). Later I found that some (on the Internet) do use this name, I have in my 20+ years in the field never heard of it. I was going to work on the article in my user space, and the plan was to mention pseudovectors further below. I was going to follow the approach of Griffiths (and Greiner). The topic should be no harder than Electric field, and definitely not this confusing - there's absolutely no need for the two mysterious fields that are sometimes the same, and sometimes not.

Griffiths says: Many authors call H, not B, the "magnetic field." Then they have to invent a new word for B: the "flux density," or magnetic "induction" (an absurd choice, since that term already has at least two other meanings in electrodynamics). Anyway, B is indisputably the fundamental quantity, so I shall continue to call it the "magnetic field," as everyone does in the spoken language. H has no sensible name: just call it "H". /For those who disagree, I quote A. Sommerfeld's Electrodynamics (New York: Academic Press, 1952), p. 45: "The unhappy term 'magnetic field' for H should be avoided as far as possible. It seems to us that this term has led into error none less than Maxwell himself.."/

Look how ridiculous the name "flux density" for B is: You take a surface element dA, multiply it by B to get the flux Φ, then you divide this by dA... to get the B back?! Or is it H?

Ponor (talk) 12:24, 23 August 2020 (UTC)

Hi @Ponor, thanks for the response. I agree with all your points, honestly, I am sorry I didn't have a better draft. I fundamentally agree on the nature of the fields, and your reasons for given (flux density is a pretty terrible name and induction is worse). I also use Griffiths' convention on naming (though it's almost always just B and H); to me, the magnetic field unambiguously refers to B, I was just using what the article had. This was meant to be a rough draft, though, to see what could be done and if others had ideas. I agree that Griffiths would be a great approach to go with here (honestly, its probably the best approach to go with in any of the fields he has books on, he makes things very simple). Also I get your point on the lax use of nearby. Notice my use of the words "used to describe", though, I meant for it to be a statement of practicality. The term pseudovector field is worse than field of pseudovectors, IMO, and I also have never heard the term used IRL. I tend to just call it a vector field with a transformation deficiency. Anyways, I think your plan sounds good and I'm glad to know you are working on it. Thanks! Footlessmouse (talk) 13:15, 23 August 2020 (UTC)

My humble opinion on these subjects: I agree with Ponor that the mention of two fields in the proposed lead sentence is misleading and unsupported by sources. The two fields B and H have to be in the introduction to make it an adequate summary of the article, and also to explain the two sets of units used for the magnetic field, but they are two alternate mathematical descriptions of a single field. I think the 2nd para is a good explanation of them and should stay. It seems to me that "vector field" is the best descriptive term for what the magnetic field is in the introduction, rather than "force field", "tensor field" or "field of pseudovectors". It is the term most textbooks use; although it is mathematical it is easy to explain to general readers that it just means the field has a magnitude and direction at each point. "Force field" would be good, but it has kind of been co-opted by science fiction. I don't think "pseudovector" should be in the intro; that can be explained in the body. I also agree that "magnetic materials" is a better term than "magnetic dipoles" in the lead sentence. --Chetvorno^TALK 14:17, 23 August 2020 (UTC)

In the paragraph on B and H above, you use the name "magnetic flux density" for H where it is usually used for B. Intentional? Regardless of how irrational it is, the article must use accepted terminology.

The current introduction, particularly the first paragraph, was the result of an extensive discussion on this Talk page a few years ago. I'm not saying it can't be improved, but there has been a good deal already written on these topics, which can be seen at Talk:Magnetic_field/Archive_5.--Chetvorno^TALK 14:17, 23 August 2020 (UTC)

Hi Chetvorno . These old discussions is what always discourages me from changing anything: should I waste hours of my (covid19) time on improving articles if that's going to be reverted in a second because of the lack of consensus. Just few days ago this was the first sentence (by consensus?) here: "A magnetic field is a vector field (more precisely a pseudovector field) that describes the magnetic influence of electric charges in relative motion and magnetized materials." What does this mean? Who influences what? I've listed a number of highly respected sources above (that'd be the accepted modern terminology), of which Griffiths I like the best. I agree with Footlessmouse, Griffiths is a great writer, and he's bold about things. If you have a chance, please read his chapter on Magnetism, you'll see what I mean. Some people like to use H because that's the field they can measure before putting their samples in, and then they think of B as that field plus the response. This could have all been Bs with different subscripts; but ok, I like to think, H is just B with something missing (two horizontal bars, or the full description of the situation). This reminds me of the E vs D dichotomy (where E kind of wins as the fundamental field), or the "rest mass" vs "relativistic mass" debate (modern view, which is probably 70+ years old, is that there is only one, invariant mass because gamma*m works only in formulas for some special cases). It's time to go bold and get rid of these historical misconceptions. The H-field can be discussed at the bottom of the article, alongside the discussion on a material's response to a given B_{from free currents}, just the way D is discussed at the bottom of Electric field. I'd say this is how physics is now taught, and how it should be taught. One field, (small) response, additional field, their superposition.

I've read Griffiths; I have the 4th Ed. in front of me now. It's great. I learned EM from Purcell. Zangwill's Modern Electrodynamics is good too, and more up to date than both. But all electromagnetics texts include both B and H, that's not going to change soon. I think our article should define them together as it does now. Most texts rightly emphasize B. As you say, that is the fundamental field, which includes the molecular dipole sources ("bound currents") and is accurate at a microscopic level. Our article should make this clear. But as you also said, H is widely used wherever magnetic materials are used, a lot of applications equations are simpler when written in terms of H because its only source is free currents. The properties of magnetic materials are always given by their B-H curve. A lot of readers are confused by B and H, that's why our article should describe them together as it does now, comparing their definitions, names, units, and uses. I certainly agree with rewriting the section to emphasize the fundamental nature of B. --Chetvorno^TALK 19:43, 23 August 2020 (UTC)

I am not saying that H is meaningless, it's the magnetic field (in diff units) due to known currents - all fine. It's unnecessary (we could work with superposition of B's and M's, when we're actually interested in magnetic materials), but if people like to use it, so be it. But to understand what B and H are... I don't think this article does a good job at all. Many things are clear only when you know what they are. Second paragraph: look at all these names - magnetic field strength, magnetic flux density, all those units. The fields, they say, differ in a material - but what good does H even serve there? Which field do we use around the material? In a little hole inside the material? I am a condensed matter physicist with a PhD and I'm confused. What should a high school kid (me 20 years ago) think about this? Ponor (talk) 01:42, 24 August 2020 (UTC)

On the lead sentence: I think the current lead is a little better, but for accuracy "magnetic influence on an electric charge" should be replaced by "magnetic influence on an electric charge or magnetic material". The other sentences in the first paragraph explain in more detail what a "magnetic influence" is. I think a common mistake in technical articles is to try to cram too much abstract definition into the lead sentence. Any lead that is comprehensible to general readers is going to look like a crude mess to scientists and engineers. I personally would like to see the word "force" in the lead sentence, since that is the main effect of magnetic fields on matter. --Chetvorno^TALK 21:19, 23 August 2020 (UTC)

I agree, but don't find it too necessary, because magnetism in magnetic materials is due to electrons (charges)... and-OK-their spin. Ponor (talk) 01:47, 24 August 2020 (UTC)

Everybody makes good points. I find myself in most agreement with Chetvorno. H and B must both be mentioned in the lede section. Reliable sources use both. It should be pointed out that although both H and B are casually referred to as the magnetic field, physicists and engineers almost always mean the B field, because it is the B field that produces the forces. However, H shows up in the Poynting vector as P = E X H and it shows up when discussing propagating EM fields in vacuum. Of course, if magnetic monopoles are ever discovered, H will come into its own prominence. We are stuck with what is out there in the sources.Constant314 (talk) 22:03, 23 August 2020 (UTC)

Well, H=B in vacuum. All my definitions used P=ExB. H-field is, as Griffiths put is, just an auxiliary field. Something we'd normally call B', and add to it some B due to whatever to find the total B. And it's OK to have them both. B in general discussion, H when we come to materials' response to the field. Just like it's done for E and D. Ponor (talk) 01:42, 24 August 2020 (UTC)

Hi all, thanks for the responses. @Chetvorno no, that was not intentional, it was a mistake. It's funny to note, though, the root of the mistake it the obscurity of the names of these fields. No one in physics, that I know, calls it the "magnetic field strength" or "flux density". I think both of you have great points, is there room for a compromise? Such as, for example, relegating the H-field to a section of the article, but also mentioning this in the lead? Something along the lines of "The magnetic field typically refers to the B-field, but is sometimes used to refer to the H-field." along with "the H-field" simplifies Maxwell's equations". (very rough-draft ideas) I think the article could mention both fields and explain their differences while still maintaining the B-field is the "real" magnetic field. Side note: I've never used the term force-field IRL, I thought it was only a sci-fi thing, it wasn't until editing Wikipedia that I noticed there is an article for it. Also, I apologize if I didn't read deeply enough into the previous conversation before starting a new one. It was my intention to begin a collaborative conversation where we could discuss improvements that could be made. Also, I think my proposal, while bad overall, did have a couple of improvements, such as the second sentence and second paragraph that I believe may be easier to understand for nontechnical readers (after fixing the mislabeled fields). Footlessmouse (talk) 22:10, 23 August 2020 (UTC)

I would stay away from designating B as the real field. Here is Feynman’s definition of a real field: A “real” field is then a set of numbers we specify in such a way that what happens at a point depends only on the numbers at that point. You can compute the forces from both E&B or E&H so both have equal claim to being real. When you get down to it, most physicists consider the A field to be the real field and B is just another name for curl {A}. So, I advise against saying B is real and H is not.Constant314 (talk) 22:35, 23 August 2020 (UTC)

Sorry, I didn't mean to imply we should say it's the "real" one in the article, I just meant that as a short hand for "the magnetic field generally (almost always) refers to the B-field, though there is some ambiguity as it can also refer to the H-field, depending on the context". Footlessmouse (talk) 22:47, 23 August 2020 (UTC)

@Constant314 but with H alone there's some information missing, right? H is due to free currents that we can measure, so it's just one part of the resultant field. Am I missing something here? (sorry, never liked, never needed the H-field, thanks to Feynman, Purcell and Griffiths) Ponor (talk) 01:42, 24 August 2020 (UTC)

@Ponor and Constant314: Yeah that's the way I see it. B is the only field that includes all the sources, potentially including the molecular dipoles. If you want to get an accurate picture of the magnetic fields at an atomic level in a magnetic material, there is just B. The H model accounts for microscopic dipole sources with a "magnetic dipole moment density" M which is just an "average" of the dipoles over an area large with respect to the molecules. Of course you can also use M with B by replacing $\mathbf {H} =\mathbf {B} /\mu _{0}-\mathbf {M} .$

I was thinking... why should there be any mention of B and H in the intro? A lot can be said with just words that is valid for all descriptions of the field. How the field is produced, how it affects charges and spins, where it's used, what is its relation to the electric field, etc. Second para is punch in the eye: all those silly names, all those units, magnetization this, permeability that... I don't see any Es and Ds in the intro of Electric field. Ponor (talk) 02:54, 24 August 2020 (UTC)

What if we create a new page for the magnetic auxiliary field and leave a notice at the top? (This article is about the magnetic flux density, commonly known as the magnetic field. For other uses of the term magnetic field, see auxiliary magnetic field). And include a statement in the lead about the ambiguity between the two fields, but only include units and symbols for one field on each page. Electric field and electric displacement field are appropriately split into two articles. Footlessmouse (talk) 05:00, 24 August 2020 (UTC)

@Ponor, I believe the main argument to introduce both symbols in the lead is to disambiguate their units. Footlessmouse (talk) 05:06, 24 August 2020 (UTC)

@Footlessmouse Could be, but it not only does a bad job at disambiguating them, it introduces bad naming of things (tradition is not always good) and makes everything sound so complicated. Why would people need to know about units if they know nothing about the object of measurement, the field? The field is independent of our units after all. Ponor (talk) 10:10, 24 August 2020 (UTC)

@Ponor, I think I am in agreement with all of your statements. That was my first thought too, but after surfing around, all the other articles give units in the lead. (though I agree tradition is definitely not always good) Footlessmouse (talk) 10:21, 24 August 2020 (UTC)

@Footlessmouse When I ask my colleagues how strong their magnet is, they say 18 tesla, or 45 tesla, or 63 tesla, or 90 tesla. They bend particle trajectories with teslas CERN. Their Nobel prize experiments use B in teslas (Klitzing, Geim), they publish in B/Tesla [1], [2]... Modern textbooks (from Feynman in 1960s to Purcell, Greiner and Griffiths) don't explain magnetism in terms of B and H in parallel. The H field is missing information about the atomic and molecular currents. So I think the choice is clear. If all other articles give units in the lead, this article should say that the SI unit of the magnetic field is tesla, full stop. The lead is not the place to discuss magnetization-agnostic fields, do unit conversions, confuse. Those who know about H and B already know too much, and I doubt they'll be reading the article (lead). The worst choice we can make is not to make any choice and continue discussing all historic fields, all historic units, all historic ideas—from start to end. Ponor (talk) 15:58, 24 August 2020 (UTC)

I think two articles is a really bad idea. The two fields are introduced together in texts, and are used together in much electromagnetics literature. B and H are much more closely interrelated than E and D; it is probably impossible to avoid all mention of H in this article. Are you going to just not include the B-H curve? This is exactly opposite to what our readers need. Do we want to force them to switch back and forth between two articles to understand the difference between B and H? Artificially separating these two topics is getting into WP:POVFORK territory. Fragmenting this topic into two articles will require a lot of redundant explanation. Whatever we want to say about B and H can be better explained in a single article. --Chetvorno^TALK 06:03, 24 August 2020 (UTC)

Wow, my bad. You should know that what I had in mind was just keeping a slightly altered version of the Relationship between B and H section, similar to electric field, and add a statement about possible ambiguities in the leads of each. I get your point, though, and that's fine, it was just an idea I thought might be helpful. Footlessmouse (talk) 07:51, 24 August 2020 (UTC)

I am sorry, @Chetvorno, but there is really nothing special about these extra fields. And no, H is no more special than D. They both add to the confusion. I've cited many books in introductory and advanced physics above that clearly avoid mentioning the H-field until when materials' response is discussed. Griffiths and Sommerfeld have a strong opinion about it. Can it stay in this article? - sure! But it's a bad idea to discuss both fields in parallel. Then mix them up wherever possible, like when calculating the field of a wire. Then make B a less important field because it's only relevant in materials, and give H some magic powers as it "helps factor out this bound current". H is just for Hiding things. In physics at least, you know all sources of B, and you know of superposition of B's. Need nothing more. Ponor (talk) 10:10, 24 August 2020 (UTC)

@Ponor: I don't think I suggested that B is a "less important field", or that it is only relevant in materials, or that H should be used when calculating the field of a wire. I said repeatedly above that B is the fundamental field, that it includes all the sources, and the article should state that. But H is the standard machinery used for dealing with magnetic fields in materials, particularly ferromagnetism, and magnetic materials is a huge part of both pure and applied electromagnetics. Readers are going to come across it, so I think it needs to be covered in this article.

Griffith, p.281: "As it turns out, H is a more useful quantity than D. In the laboratory, you will often hear people talking of H (more often even than B) but you will never hear anyone speak of D (only E)." --Chetvorno^TALK 15:30, 24 August 2020 (UTC)

@Chetvorno:All good, I never said B_{free currents} aka H should be ignored. And I never said that you called B a "less important field". I'm saying that this wiki article is, sort of, saying that B is (only) relevant when it comes to the field in materials. What I said about H and D is at the end of the paragraph you cited from Griffiths ("theoretically, they're all on equal footing": just a way of bringing material's currents, spins and charges into Maxwell's eqs with free sources , which is in some way hiding the real physics of the material's responses to the outside fields). Also note that chapter 6 (about H and M) in Griffiths only comes after chapter 5 (about B), and that's essentially all I want from this article here: not to start with B and H in parallel, and to say that H is there because we like to separate cause (of magnetization) and consequence. This separation, as Griffiths warns in the next section, can be deceptive. Most papers that I read nowadays use either B (tesla) or, less often, mu0*H (tesla) for the field of their magnets, and call it simply the magnetic field. Ponor (talk) 16:40, 24 August 2020 (UTC)

I think we're together on this. I understand your and Footlessmouse's points and basically I agree. I don't want to see H treated on an equal basis with B or readers to get the idea there are two magnetic fields. Okay, I guess it is misleading to introduce B and H in parallel. I support introducing H in a separate section at the bottom on magnetic materials, and even developing the equations on materials using B and M and then introducing $\mathbf {H} =\mathbf {B} /\mu _{0}-\mathbf {M} .$ as a convenient simplification. --Chetvorno^TALK 17:48, 24 August 2020 (UTC)

I somewhat disagree with that. Consider the person who comes to the article after reading a text that features H. Don’t make him wade through the article for the first mention of H. Mention it in the lede. A single sentence will be adequate.Constant314 (talk) 17:53, 24 August 2020 (UTC)

Agree, it should be mentioned in the lead, and the section that covers it should have H in the title so readers can find it. --Chetvorno^TALK 18:47, 24 August 2020 (UTC)

@Ponor, if you are still willing to work on the article in the style of Grifith's, I think we would all be interested to see the result. I think you could do this and include a statement in the lead about the H-field, without going into unnecessary detail. I think we all agree on the main points, it's just fine details that need to be worked out. Footlessmouse (talk) 19:49, 24 August 2020 (UTC)

@Footlessmouse, Chetvorno, and Constant314: Alright guys, this motivates me to give it a try. I'll start in my sandbox, and at some point ping you for your thoughts. Thanks for the discussions! Ponor (talk) 21:43, 24 August 2020 (UTC)

I only just noticed this discussion, and I'm sorry to chime in just when you seem to have reached a consensus, but I have strong objections to this consensus:

1. More than one editor is claiming that B is "primary" and there is supposedly some information missing in H. Before writing such a view into this article, please read the following source: Roche, John J. (10 April 2000). "B and H, the intensity vectors of magnetism: A new approach to resolving a century-old controversy". American Journal of Physics. 68 (5): 438–449. doi:10.1119/1.19459. In case you can't access it, I am going to provide a few quotes:

The problem of interpretation of B and H is, perhaps, the most complex of all and has attracted a considerable literature. The caption to a Physics World article relating to this subject in 1994 described it as a ‘‘magnetic Tower of Babel.’’ It is a frustrating problem because, although the physics involved is quite well understood, an agreed interpretation has never been found.

Three major traditions of interpretation of B and H have now been identified, that of William Thomson which gives H and B equal status as field intensities acting on different ‘‘free-body’’ elements of the medium, that of Faraday and Maxwell which makes H the cause of B 􏰚and, for some authors, independent of the medium, and that of Lorentz which interprets B as the average of the microfields and H an artifact.

This suggests that the information content about the field provided by H in a vacuum is always exactly the same as that provided by B and that they are simply different measures of exactly the same field property. H measures it by its cause, B by its effect. It is also surely significant that almost 150 years after Faraday no such pair of distinguishable vacuum field intensities has been revealed experimentally, nor is there any theoretical basis for such a distinction.

The interpretation of H as an artifact has meant that, in Lorentz electromagnetism, its considerable physical importance has often been overlooked. For example, solutions to the wave equation naturally contain H rather than B because H—like E—is defined along a wave front. For a similar reason, H is the vector that appears in Poynting’s energy and momentum flux theory. Again, H appears with equal status with B in the field energy expression and, of course, in Maxwell’s equations. The component of H along its length is the field intensity experienced along its length by a needle element or filament of any orientation in the medium. Similarly, the component of B perpendicular to its area is the axial component of the magnetic intensity experienced by a disc element or lamella of any orientation in the medium. In this interpretation both H and B are necessary for a complete description of the field in the medium; they are qualitatively identical and appear to be equally significant.

Thus, to promote a single view on the relationship between B and H would be to promote a very biased view of a deep and unresolved dispute over their interpretation. The fact that some textbooks ignore H is neither here nor there, because other important textbooks ignore B, including Ashcroft and Mermin, "Solid State Physics". Also, since B and H are only different inside materials, it is important to note that books on magnetic materials emphasize H over B. I provided four such sources at the bottom of this earlier discussion.

2. Of the books that emphasize B, Griffiths is a particularly poor choice for talking about fields in materials. He sets up a straw man, the "Gilbert model", that seems to be his own invention (see this discussion). And he uses this straw man to argue that calculations involving magnetic poles "cannot be relied on for quantitative results" (which would come as a big surprise to everyone who uses micromagnetics; and see also demagnetizing field). Worse, he claims that "Magnetism is not due to magnetic monopoles, but rather to moving electric charges; magnetic dipoles are tiny current loops." Has he never heard of electron spin? Please do not use Griffiths as the main source for discussing B vs. H.

RockMagnetist(talk) 18:36, 25 August 2020 (UTC)

Secondary and tertiary sources, such as Griffith's, are better for Wikipedia than primary sources, such as the journal article you linked to. These are textbooks in electromagnetism. I learned CM from Ashcroft and Mermin, but why would we use it for an overview of the electric field? It seems much more appropriate to use electromagnetism sources, as it is not our job to teach readers every caveat, but to provide an overview. Do you have any proper secondary or tertiary sources that can verify your claim of Griffiths abuse? If not supported by other secondary and tertiary sources, it is just your view and original research is not allowed. No one said that we were going to make Griffith's the primary source for the article, but that he wanted to try to rewrite it in that style. Whatever modern journals may be coming up with and whatever may change in the future, for now, the magnetic field "is" the primary field. Ponor was right when he said, ask a physicists how strong their magnetic field is - the answer is ALWAYS in tesla, why? Wikipedia uses the jargon as used by mainstream science. I don't think anything good is gained from holding up progress, we will all have a chance to comment on the new page after he makes it. That would be the appropriate place to provide additional reliable and verifiable sources that shed a different light on the topic. Footlessmouse (talk) 21:15, 25 August 2020 (UTC)

@RockMagnetist: Sorry, I was a participant in that discussion 6 years ago, but I couldn't remember where it was. Thanks for the thoughtful input and the sources. Am reading the Roche paper now. --Chetvorno^TALK 21:32, 25 August 2020 (UTC)

@Footlessmouse: My source for the Griffiths quotes is Griffiths, David J. (2017). Introduction to Electrodynamics. Cambridge University Press. p. 269. ISBN 978-1-108-35714-2.. Do you really need me to provide a source to say that an electron spin is not a current loop? As for the "Gilbert" model, feel free to look for an independent source for it. I am a professor who has spent decades modeling the magnetic field using fictional monopoles, and I have never heard it referred to as the Gilbert model, nor could I find a single source aside from Griffiths (indeed, it's not even clear which Gilbert he's referring to). But it is the standard approach in the magnetics industry, as several textbooks that are cited in micromagnetics will affirm. Frankly, Gilbert's discussion on page 269 looks like an opinion piece. RockMagnetist(talk) 22:39, 25 August 2020 (UTC)

As for your dismissal of the primary source I cited, that just seems like a convenient excuse not to think about it. This is the talk page, not the article. If you make the effort to at least skim the article, you'll find it makes a pretty convincing case for a long-standing dispute about the relation between B and H. Textbooks also have their limitations. A textbook is not likely to discuss a controversy like this; a review article is probably the best we can hope for. RockMagnetist(talk) 22:46, 25 August 2020 (UTC)

@RockMagnetist, What exactly is your proposal? You don't want the article to change at all? Or you just want the article to include a section on micromagnetics? All you are doing is saying there are more advanced (graduate level) texts that treat the topic in a different manner. I was not meaning to dismiss you, but to point out that secondary and teritary sources is what Wikipedia says is best. Primary sources can only be used to say something about modern research: "In 2020, a group of researchers...". It has to be qualified like that and can't be used to make general statements. No one said anything about the Gilbert model except for you, it doesn't need to be included, and if that's your only problem with Griffiths, I don't see any problem. Griffiths simplifies things, that's basically what he's famous for. Griffiths' is still used in university, most recent edition was published in 2013 and 2017 and is considered a standard undergraduate textbook on the topic. Wikipedia is not a textbook and does not purport to replacing classical education in a topic but merely to provide an overview. Griffiths is a standard textbook and does provide a classical education on the topic. I don't see the need to go into very much detail beyond the standard undergraduate textbooks, except possibly in a separate section to clarify any misconceptions. Footlessmouse (talk) 23:15, 25 August 2020 (UTC)

Also, for clarification, I think you know what Griffiths meant when he said dipoles are like current loops. It may be technically incorrect, but the spirit is not. It is pretty accepted that magnetic monopoles have yet to be discovered. None of this needs to be included either, I therefore do not find it a good argument for dismissing Griffiths entirely. Footlessmouse (talk) 23:25, 25 August 2020 (UTC)

To describe my proposal, I need to first state what I think is the change that is being proposed by the rest of you: delaying the introduction of H until materials are discussed, and treating it as an "auxiliary" field. To a large extent, I'm fine with the former but not with the latter. Most of the time, you only need one of B or H, but there is not one field that has "all the information".

I am fine with using Griffiths as a source for much of the content on electromagnetism, but not for statements about the relation between B and H, because at best his discussion of that is really sloppy. Because his book is so popular, descriptions of the Gilbert model were all over the magnetism pages in Wikipedia when I first arrived. (I'm glad to hear that you don't support re-introducing that.) I don't think even the spirit of his statement about dipoles is correct because it is used to buttress the false claim that all magnetic fields are due to current loops. RockMagnetist(talk) 00:50, 26 August 2020 (UTC)

@RockMagnetist, that is reasonable. More than one source should be used for topics that are not fully universally established, anyways, to maintain NPOV. I am reading the article now, there is a lot of great historical content on here that could help give a little history of the B-H problem, though it would have to be condensed.Footlessmouse (talk) 01:24, 26 August 2020 (UTC)

@RockMagnetist, I never though I'd see so much discussion about two symbols, and now that I've read some archived discussions and this one, it's becoming clearer why the article looks like everyone was protecting their turf. Roche is an interesting read, thank you. He himself kind of leans towards eliminating the symbol H, even though... It seems to me that all ideas about H and B he's discussing appeared before the discovery of the electron, while aether was still there, and no quantum machanic, quantum ED, condensed matter physics etc. Nowadays, I only see the H in measurements where people put their Hall probes to measure the field, then put the samples there to measure their response. Many plot their data against μH (Tesla), and this could be called B_H just as well. The H itself is introduced when materials are discussed, where curlM is taken inside curlB from the sources side of the Maxwell's curlB eq. So instead of introducing H, we could have stayed with B and M, and that would make more sense to me: B and M, in these pre-quantum models carry the same information as B and H. In Roche's paper we don't see what, for example, Feynman thought (vol 2 is all in B's, there are no H's in his EM wave equations; quantum mechanics, he says, cares mostly about A), and what many other quantum mechanics thought about the averages of the magnetic fields inside materials. Now I am curious, why does it seem like things are unsettled (more heated discussions then there are about high T superconductivity) when to me it all looks much simpler:

1) Can we say that there is a magnetic field Ψ that affects a moving charge q by F=qv×Ψ? 2) Do we have a list all possible sources of the magnetic field: currents, atoms, spins... 3) True or false: All matter is predominantly vacuum. To describe matter, we add particles to that vacuum. 4) Can we say we know the expression for the field in vacuum for each of these sources, at least if we stay far from them? 5) True or false: If there are two independent sources, their fields add: Ψ=Ψ1+Ψ2. 6) Field produced by one source can affect the other source, this need not be linear. Is this where problems start? 7) If in a steady field Ψ1 a material responds by creating Ψ1(M), can we say the total field, by superposition, is Ψ1+Ψ2(M) everywhere, inside and outside? 8) Do we use mezoscopic averages of who-knows-what to calculate M and Ψ2(M)? Isn't this inherently wrong now that we know quantum mechanics? 9) If H=B-M, can we forget about H and express everything in terms of B and M? At least we won't have two magnetic fields to worry about. A) Would any of this be a problem if we stayed with Maxwell's empty space eqs and accounted for all the sources, through M, properly? Would anyone miss the H-semifield then. C) did Griffiths know of spins? I'm sure he did. But since we don't know where spins come from, we like to imagine them as something of the current-loop kind, because we can define their ${\vec {\mu }}$'s and work with those as if they were from a current loop. I've seen many, many books where Ψ (or let's call it B again) is the only magnetic field. I would't say they're biased. I'd say they're consistent... in recognizing that our universe has space for only one magnetic field, and that many, many different sources contribute their little fields to it, as in superposition. What is your opinion of the current Magnetic field? Is it a good read for 13-yr-olds? High school kids? Undergrads? Engineers? Historians? Psychologists? Ponor (talk) 07:16, 26 August 2020 (UTC)

@Ponor: Some of that lengthy discussion seems unnecessary to me, so I'll stick to the highlights. Yes, as long as we're talking about a vacuum, we only need one field, and I'm fine with using B for that. Also, if we could stick to a pure quantum mechanical picture, we'd never need two fields. However, it is simply not feasible to make quantum mechanical calculations for more than a very small number of atoms, so we're stuck with those "mesoscopic averages of who-knows-what", and therefore with M and H. I do think that it's better to introduce M and then write H = B-M because that allows a more straightforward discussion of sources of magnetism.

Yes, some textbooks on electromagnetism manage to do without H altogether, but they tend to do a bad job of discussing magnetic materials. (Meanwhile, some books on magnetic materials manage to do without B.) If we want to write a set of Maxwell's equations that are always valid in both vacuum and media, it is simplest to write them in terms of the full set of B, H, E and D. Otherwise, we have to start including assumptions about the properties of the material. Similar concerns apply to expressions for the energy of the field, etc.

This article is not very readable for anyone, but there are plenty of reasons for that. The history section should be moved to the end of the article. Similarly, a lengthy discussion of field lines doesn't belong near the top, and neither does any discussion of the inside of permanent magnets. Start with magnetostatics, and talk about the magnetic field of simple sources like a point dipole, current loop, straight wire. Move to dynamics, still in a vacuum. Then discuss materials. I used a similar approach in Momentum: start simple and build it up. And, while we're at it, let's add a few citations. RockMagnetist(talk) 17:21, 26 August 2020 (UTC)

I agree with most of RockMagnetist's recommendations. I think there should be a separate section on magnetic field lines, since they are so universally used (I'm writing one for the Magnetism article).--Chetvorno^TALK 18:16, 26 August 2020 (UTC)

Sure, I just think that section should come later. RockMagnetist(talk) 18:30, 26 August 2020 (UTC)

@RockMagnetist, Footlessmouse, and Chetvorno:Sorry for the delay, I was busy with some other articles. Currently, Footlessmouse seems to be more interested in working on this article than I (there's been some activity in its/her/his sandbox). I'll be happy with any version that does not introduce B and H in parallel. Few questions and notes: (1) can we all agree that H is due to macroscopic/drift currents alone - I think this is the clearest definition I've seen, because (to me) it's unclear why anyone would define H as B-M, I mean - for what reason, what's the point?! (2) please check what's said of H and D in Maxwell's equations, to keep things consistent across diff. articles (inconsistency is the most confusing thing of all) (3) Would you mind saying that the magnetic field is a property of space (property assigned to space, for those who think physics is more about us). This could help avoid "influence of charged perticles and magnetized materials on other charged particles and magnetized materials", and is closer to the idea that the field, once generated, is detched from its sources (no action at a distance). Check britannica. So the first sentence in all these field articles can be "...property of space caused/generated/... by SOURCES that affects OBJECTS in such and such way" of "...property of space that affects OBJECTS in such and such way. It is generated/caused by...". In our case, for example, B can also influence non-magnetized (non-ferromagnetic) objects---it can make frogs fly. Regards, Ponor (talk) 13:04, 31 August 2020 (UTC)

@@Ponor:, sorry about that, I didn't mean to take your project. I just didn't want progress to stall because of relatively minor disagreements. I was planning on sending it to you in a few days or so as a (potentially) slightly better starting point than the current article. I have mostly just added a bunch of Griffiths' references and a few by Jackson, rearranged the sections to consolidate the H-field material, and cleaned up a bit, rewriting some parts. You can all see what I've done here, though I was not done yet, so please don't judge it too harshly. For Ponor's questions. (1) yes, (2) good point, (3) I like this idea, it is more clear than saying, generically, it is a "field" or "vector field". Footlessmouse (talk) 20:56, 31 August 2020 (UTC)

@Footlessmouse:Oh please, no need to apologize. I'm glad you're working on it! (I am going to miss that horseshoe magnet picture, though. :) It would be good to have it somewhere, IMO, or some other similar photograph, to remind us these things are real and not a computer simulation). Please ping us when/if you need comments, I won't be stalking any more. Best, Ponor (talk) 21:10, 31 August 2020 (UTC)

@Ponor:I accidentally deleted the whole of the magnetic field lines section at some point yesterday (I think I meant to move it and got distracted). I have restored it, I moved the horseshoe picture to the magnetic field lines section where I thought it was appropriate. I like those pictures there as well. I didn't like it as much at the very top, though I think that's a personal preference and related to the fact that it is black and white. Footlessmouse (talk) 21:29, 31 August 2020 (UTC)

@Ponor: Hi, I appreciate all the work you and Footlessmouse are putting into fixing this article. I don't mean to be a buzzkill, but I do have some reservations about the points you mention above:

(1) I am not sure what you mean by: "...can we all agree that H is due to macroscopic/drift currents alone... it's unclear why anyone would define H as B-M". If by "drift currents" you mean free electric currents, Griffiths Sec. 6.3.2 makes clear that H is not determined by free currents, only $\nabla \times H$ is. Consider a permanent magnet with no electric currents nearby. If H was due to currents alone it would be zero. But $\nabla \cdot H=-\nabla \cdot M\neq 0$ at the pole surface of the magnet so it acts as a source of the field... anyway it's all in Griffiths. B and the "auxiliary field" H are alternate models for the field, so the mathematical connection between them $H=B/\mu _{0}-M$ has to be in the article.

(3) I agree the article should explain that the magnetic field is a "property of space" detached from sources. I'm okay with using the term in the lead sentence; something like: "The magnetic field is a property of space surrounding electric currents and magnetic materials, which can exert forces on other electric currents and magnetic materials." This is probably an improvement over the stuffy mathematical term "vector field". But the lead paragraph should explain that it is described mathematically as a vector field.

--Chetvorno^TALK 21:09, 31 August 2020 (UTC)

@Chetvorno: You're absolutely right about (1). Not my field (in all meanings of the word) so I keep forgetting things. As for (3), not sure it should say "surrounding", unless we mean the whole universe (waves!) (HB "originating", "that originates", "caused by"...) OK, I should stop. Best, Ponor (talk) 21:24, 31 August 2020 (UTC)

@Chetvorno and Ponor:, how about this? "The magnetic field is a property of space, generated from electric currents and magnetized materials, which can exert forces on other electric currents and magnetic materials. Similar to a vector field, the magnetic field assigns a direction and a magnitude to each point in space..." I was trying to work on the pseudovector field part, but so far all I have, with this newest rewrite, is: "According to the Lorentz force law, the force experienced by a particle in a magnetic field is directly proportional to the vector cross product of its instantaneous velocity with the magnetic field at its location. However, as both force and velocity are vectors, it follows from the properties of the cross product that the magnetic field at each point is called a pseudovector." Where I use Griffiths for a reference. Maybe this information isn't needed in the lead? I think saying it is similar to a vector field may be enough. Footlessmouse (talk) 22:10, 31 August 2020 (UTC)

My feeling is that pseudovector doesn't need to be in the intro, it should be called vector. The intro is going to be long enough, and there is other info that has a better claim to inclusion than this mathematical detail. Explaining the difference: "Similar to a vector field, the magnetic field assigns a direction and a magnitude..." etc, is too confusing. If it has to be in there, I suggest a simple statement "Technically, the field is a pseudovector, not a vector." tacked onto the definition of vector field. --Chetvorno^TALK 04:52, 1 September 2020 (UTC)

@Chetvorno: I don't really mind either way, but a couple of points. Neither a pseudovector nor a vector valued function are vectors. A vector always transforms like a vector, by definition. While a vector is an element of vector space, a vector-valued function has a vector space as a codomain. A vector field is a vector valued function with a domain of 3D Euclidean space (in the simplest case). Thus, a magnetic field is a pseudovector field or a pseudovector valued function. Maybe not in the lead, but I think it is best to say that the magnetic field assigns a pseudovector to each point in space, due to its relationship with force and the transformation properties of the cross product. Just calling it a pseudovector with no explanation is more confusing, IMO. If everyone else thinks we should just call it a vector, though, we can use a note to spell out the technicalities, or defer the info to a later section. Footlessmouse (talk) 07:17, 1 September 2020 (UTC)

There is a large swath of mathematics that treat anything as a vector that adds like a vector and has a scalar multiplication. The only people that would get something out of being told that the B field was a pseudovector would be people who already knew what a pseudovector was. Keep it out of the lede. By the way, if magnetic monopoles ever show up, D will have to be a pseudovector, too. Constant314 (talk) 07:38, 1 September 2020 (UTC)

@Constant314: I am fine keeping the unnecessary detail out of the lede, but do you think we should call it a vector/vector-field, say it is like/similar to a vector, or just avoid the terminology all together? Footlessmouse (talk) 08:26, 1 September 2020 (UTC)

I would leave out "vector field" and just say that the field is a vector at each point.Constant314 (talk) 17:27, 1 September 2020 (UTC)

This such a Wikipedia thing, spending so much time discussing a few sentences in the lead while neglecting the body. Sooner or later, there will be yet another attempt to change the wording and another long discussion. I'm going to stay out of this and boldly implement some of the changes I suggested earlier. Starting with moving the history to the bottom. RockMagnetist(talk) 17:06, 1 September 2020 (UTC)

I wrote this before looking at Footlessmouse's sandbox. I really like where that is going, so I'm going to stay out of it for now. RockMagnetist(talk) 17:15, 1 September 2020 (UTC)

Lol, gotta agree with RockMagnetist. The amount of time I've spent discussing lead sentences in the last 14 years, only to have them changed.... I could have had a second career. You're a wise man. --Chetvorno^TALK 18:33, 1 September 2020 (UTC)

@Footlessmouse: I definitely prefer "vector field" (I meant to use that in my post above). The word field in "magnetic field", which is used as a shorthand, comes from this mathematical structure, so using it will help general readers understand the origin. Besides it is the common usage in textbooks. --Chetvorno^TALK 18:09, 1 September 2020 (UTC)

I think the general reader has no idea as to what a vector field is and barely has the concept of vector. Constant314 (talk) 18:25, 1 September 2020 (UTC)

Agree. The huge majority of readers will have no idea what either a "vector" or a "vector field" is, so we might as well use the correct term. --Chetvorno^TALK 18:31, 1 September 2020 (UTC)

Improvements

Hi all, the last section is incredibly long and is a little difficult to wade through. Here is a new topic to focus on improvements. It still seems to me that we are all in agreement about a lot of things that could help make the article better. I have a question, though: what should we do with dubious claims of records that will not necessarily age well? The references are primary sources for the initial discoveries. For instance:

The largest magnetic field produced over a macroscopic volume is 2.8 kT (VNIIEF in Sarov, Russia, 1998).

The largest magnetic fields produced in a laboratory occur in particle accelerators, such as RHIC, inside the collisions of heavy ions, where fields reach 10¹⁴ T.

The finest precision for a magnetic field measurement was attained by Gravity Probe B at 5 aT (5×10⁻¹⁸ T).

Thanks! Footlessmouse (talk) 08:49, 29 August 2020 (UTC)

Secondary sources should be found for claims like those. RockMagnetist(talk) 19:15, 29 August 2020 (UTC)

You do need a reliable source to say something is the biggest and something is the smallest and besides, it is a moving target. However, I think just a table of interesting values, sorted by from least to most, could use primary sources.Constant314 (talk) 17:30, 1 September 2020 (UTC)

@Ponor, Chetvorno, Constant314, and RockMagnetist:, at the risk of being overly pedantic, should we use British or American English? I only ask because the article is a bit inconsistent in that department and if we are going to put in the effort to rewrite most of the article, we should also try to bring it up to the standards of a good, or even featured, article (IMO, this is not off the table, the Redshift article is featured). Also, while my draft is not ready for detailed comments, if anyone has big ideas or if you believe I am heading in the wrong direction with anything, please use the talk page to let me know. There is still a lot of work to do, especially in expanding some sections, but I would appreciate any feedback.Footlessmouse (talk) 06:32, 11 September 2020 (UTC)

I prefer American, but can live with British if a majority prefer it. RockMagnetist(talk) 17:37, 11 September 2020 (UTC)

I'm fine with either one, it doesn't matter to me. --Chetvorno^TALK 17:52, 11 September 2020 (UTC)

If no one objects, I will use American English, as @RockMagnetist is the only one to express a view. It will also be easier for me to use the American spellings. though it is not a big deal. Footlessmouse (talk) 06:47, 12 September 2020 (UTC)

References

Definitions rewrite

I've heavily modified definitions section to try to be more clear. Given the massive dicussions above about what to call/describe as B and H, I've stuck closely to the mathematical definitions, and grouped all the naming/interpretation controversy together. Hopefully this is the right approach. I've added some additional references to Griffiths for explicit equations, and the paper brought up by @RockMagnetist: helps give more context to the naming issues, but the section could still use additional references reliable sources.$\langle$ Forbes₇₂ | Talk $\rangle$ 03:44, 23 September 2020 (UTC)

Cool. I started a rewrite on my sandbox but it eventually became overwhelming. I did put a considerable amount of work into it and so I will probably go back and to find many of the things I corrected and transfer them over. (Much of the work I put it was on fixing dozens of small details, and adding many inline references which should be transferred as well.) It was not smart of me to try to rewrite the article by myself. I am sorry if I stalled progress on the page in my ultimately failed attempt.Footlessmouse (talk) 02:51, 3 October 2020 (UTC)

Edit: After going back over it, I think it is best if I keep working on my sandbox, as I greatly prefer its layout to the one currently used. In the meanwhile, if anyone else has spare time, feel free to steal my sandbox material (or just edit my sandbox page) if you also like its layout and think it is a better starting point for the article. As Ponor points out, there are still many issues with it, but I still believe those same issues are even worse in the current version of the article (though Forbes72 did fix many problems). As a side note, I found many mistakes and made hundreds of edits, so it would be easier to incorporate Forbes72's edits into my sandbox than vice-versa. Footlessmouse (talk) 03:04, 3 October 2020 (UTC)

Total H - calculating

The H-field, therefore, can be separated into two independent parts:

$\mathbf {H} =\mathbf {H} _{0}+\mathbf {H} _{\mathrm {d} }\,$ = Applied H-field + demagnetizing field.

$\mathbf {H} _{\mathrm {d} }$ depends on M so we have B = μo(H + M) = μo($\mathbf {H} _{0}+\mathbf {H} _{\mathrm {d} }\,$ + M) = μo($\mathbf {H} _{0}+\mathbf {H} _{\mathrm {d} }(M)\,$ + M)

So to calculate B we take the applied field $\ \mathbf {H} _{\mathrm {0} }\,$ and calculate M (how?) and then take M and calculate the demagnetizing field $\mathbf {H} _{\mathrm {d} }\,$ (how?) and add all three together and multiply by the permeability to get B? In particular how does it all get rolled up into $\mathbf {B} =\mu \mathbf {H}$?

Assuming this is the right procedure, how do we do that for materials that are linear, isotropic, homogeneous and for materials that aren't? How to we do it for infinitely long materials in infinitely long solenoids and finitely long materials in and out of finitely long solenoids? (I appreciate that for non-linear materials history matters.)

I am trying to understand the scope of the the equations. Burraron (talk) 21:18, 18 October 2020 (UTC)

Feynman references lose information

In the recent updating, the distinction between vol. 1 and vol. 2 of Feynman's lectures was obliterated, and errors were introduced.

Similarly, page numbers were removed to the advantage of entire chapters, which seems unfortunate.

Concrete problems (named in square brackets):

1. The first reference to Feynman (in the lead sentence] should refer to Vol. 1 [not Vol. 2] and to page 2-4 [not ch. 1]
2. The first reference to Feynman (in the first sentence in the Description section) should refer to page 13-1 [not ch. 1].
3. The second sentence in the Description section should also refer to page 13-1. [More precision seems courteous, given the chapter has 12 pages.]

Sdc870 (talk)

Hi @Sdc870: there is a discussion on my talk page related to this topic available here. I do not think that exact page numbers are always needed and it helps to save references, but it depends on what is being discussed. I will reserve opinion for now as I look into the matter further. Footlessmouse (talk) 07:04, 18 October 2020 (UTC)

Hi @Sdc870:Let me fist tell you why I though referencing chapters (or sections, if needed) is better than referencing page numbers. I'm in posession of two editions of the Lectures. One is the standard hardcover, the other is a yellow Indian paperback. Chapter II-13 in the latter starts at p856, ends at p871. Obviously, page 13-1 means nothing to the reader of the Indian edition. Free online sources, IMO, are way much better for wikipedia, and for this one, again, page number means nothing. Moreover, if the stuff we're citing is a formula, those are pretty easy to find. If it is a statement, yes, one can be more specific, but only if there is something so controversial about it. There's nothing controversial in our lead sentence. And it is well supported by chapter II-1. The magnetic field on p2-4 of vol 1 only gets a mention in passing, vol 2 is a much better reference. In the Description section, both ch 1 and ch 13 are cited (sentences 1&2), I don't see a problem there. In II-1 he does talk about the two fields. I'd say nothing is lost, we only gained. Ponor (talk) 11:31, 18 October 2020 (UTC)

Why "trust" the Wikipedia author? That is the point of sourcing. Vague referencing is inconvenient and frustrating. A page number is meaningful in an accurate reference, and often useful in relation to another source edition. Sdc870 (talk) 13:09, 18 October 2020 (UTC)

Well, I trusted someone who pointed to volume one, page two-four, where the magnetic field is only mentioned in passing. The best, most available source we now have is the online edition (can we agree on that at least?), which has no page numbers. One click, and you are there, and you can search for whichever term you want (it took me a few minutes to do that yesterday). Can you tell what's on page 413 of my yellow English-Indian edition? Should I, as a wikipedia editor use my red or my yellow book (US is 300M people, India is 1B+ people)? Chapter references are by no means vague references; page references are... unless you own a library of all editions of all books. Ponor (talk) 13:48, 18 October 2020 (UTC)

The way I see it, there are two primary facts relevant to this discussion:

1. The primary version of the book is online with no page numbers, as pointed out by @Ponor, the vast-majority of lay readers hoping to read more about a specific topic will turn to the online version of this book.
2. WP:SCICITE guidelines do not require citations for these statements. They are therefore freebie citations given for the practical use of laypersons interested in learning more. It would be perfectly acceptable, though, for an editor to just remove them all.

Given this, I believe the recent changes are helpful and were appropriate. Footlessmouse (talk) 20:54, 18 October 2020 (UTC)

Thanks, @Footlessmouse. I'd also add that whoever has these books on their bookshelf is unlikely to read the wikipedia article to begin with. The best thing we can do as editors here is to point to the finest and most widely available literature on the subject there is, and to keep that list short. When it comes to trust, the seen by many policy should, ideally, work—probably better than page citations that very few can check. Ponor (talk) 22:28, 18 October 2020 (UTC)

Magnetic pole model

Hi all, so I am going to chalk my sandbox up to a learning experience. I will try to see what I can do to improve the article over time, though. I added in the history section from my sandbox which had minimal changes outside of the record magnetic fields part, which I attempted to clean up some. I have added a citations needed section template to the magnetic pole model section. The section will be removed in a week's time if no reliable references are furnished supporting verifiability and the notability of the topic for this page. I do not think it belongs here, in either case (and I know I am not the only one). However, this will give those who may disagree a chance to fix the problem first. Otherwise, I will be renaming the Ampere loop model section to cut out all the talk of models and we can radically simplify those sections. The information about modern interest in magnetic poles can be kept, as it is referenced, but can be moved to another section. Comments are always welcome, thanks! Footlessmouse (talk) 19:42, 17 October 2020 (UTC)

I'm good with removing it and cutting out the talk of "models". That elevates them above what they really are - ways of calculating the magnetic field for various cases. In the case of the magnetic pole model, it is just a formal solution for zero electric and displacement current, and it's convenient to use the label "magnetic charge density" for a couple of terms inside the integral. Nobody thinks the charges actually exist. Anyway, the details of this solution are somewhat technical and are covered in Demagnetizing field. RockMagnetist(talk) 05:23, 20 October 2020 (UTC)

I agree with both. Models don't belong here. A sentence can be added somewhere saying where to find these models and what good they can do. Ponor (talk) 05:54, 20 October 2020 (UTC)

Efficacy of H and B in the continuity of magnetic fields

Hello. This is actually a continuation of the H versus B discussion. My position is evolving towards:

The $\mathbf {H}$ field should not be depreciated but it can be discussed after the $\mathbf {B}$ field.

I'd like to highlight a couple of bits of information. First, from Griffiths, who is somewhat disdainful toward the $\mathbf {H}$ field, "Many authors call $\mathbf {H}$ and not $\mathbf {B}$ the magnetic field." So, right there you have Griffiths, who is a reliable source, admitting that many authors call H and not B the magnetic field. He doesn't say that most authors prefer one or the other or that modern writers gravitate toward one or the other. Just that many authors say H and he thinks that is not a good idea. And then there is Jackson whose says unequivocally that $\mathbf {H}$ is called the magnetic field. (page 13 in the third edition).

Finally, I would like to direct your attention to the continuity equations of the magnetic field as given by Jackson an page 18.

$(\mathbf {B_{2}} -\mathbf {B_{1}} )\cdot \mathbf {n} =0$ where $\mathbf {n}$ is the vector normal to the interface surface. Roughly this means that the normal component of the $\mathbf {B}$ field is continuous across a boundary.

and

$\mathbf {n} \times (\mathbf {H_{2}} -\mathbf {H_{1}} )={\frac {4\pi }{c}}\mathbf {K}$ where $\mathbf {K}$ is surface current. This reduces to $\mathbf {n} \times (\mathbf {H_{2}} -\mathbf {H_{1}} )=0$ if there is no surface current. Roughly this means that the tangent component of the $\mathbf {H}$ field is continuous across a boundary. Even Griffiths writes it in this form (Eq. 7.62 on page 332 in the 3rd edition). Seems like there is something lost in writing this as $\mathbf {n} \times ({\frac {\mathbf {B_{2}} }{\mu _{2}}}-{\frac {\mathbf {B_{1}} }{\mu _{1}}})=0$

This shows up when you consider a solenoidal winding on a cylindrical core. The H field from the coils is roughly tangent to the walls of the cylinder so H is continuous across the cylindrical wall. H in the core is the same as H in the coils. B is continuous across the face of the cylinder. The ease of switching between H and B as needed to analyze the situation suggests to me that we need to keep both symbols. Constant314 (talk) 19:52, 24 November 2020 (UTC)

I haven't participated in this discussion for a while, but I was in at the beginning (as you were). Yes I definitely agree we have to keep H, as prominently as B. Not because it is called the "magnetic field", which is more an accident of history, but because it is used throughout electromagnetics and it is not going away. The graph universally used to give the magnetic characteristic of a material, the B-H curve, has H as one of the axes. It is really not a question of either-or, both fields are used in typical analyses of magnetic devices. One could be used, but it is usually more convenient to use both. I also respect RockMagnetist's opinion, as one of the most knowledgeable editors on this subject, and he says in this post physicists have not come to a consensus on whether one field is the most "fundamental". Even if they do, on the engineering level H is useful and is here to stay. I don't mind if it is presented in a separate section, if I remember we sort of decided to do it that way at one point in the previous discussion. --Chetvorno^TALK 20:34, 24 November 2020 (UTC)

I've all but given up on working this page. I had just started editing when I joined all those conversations and was in a little over my head. I don't believe we ever wanted to get rid of the H field, though, just relegate it to a section so the concept can be emphasized in a minimally confusing manner. It is obviously important and not going anywhere and must have a place on the page, it is more a matter of how the information is presented and if it can be done so in a way that isn't confusing to high school students. Footlessmouse (talk) 21:08, 24 November 2020 (UTC)

Footlessmouse I agree with everything you said. By the way, I've come across your work on a number of other pages. I respect your expertise, and all the time you've invested; you've made a great deal of improvement to the physics articles. Kudos! --Chetvorno^TALK 21:54, 24 November 2020 (UTC)