Talk:Magnetic field/Archive 4

Archive 1

Archive 2

Archive 3

Archive 4

Archive 5

Archive 6

invisible forces

In my understanding, a field is not a force. It has to be multiplied by a charge, a mass or some property of the object that decides how strongly the object interacts with the field. Thus, the lead: "A magnetic field is the term used in physics to describe the invisible forces" is a half-truth at best. Another objection is the suggestion that physics uses this "term" to describe the "invisible forces". First, physics uses much more than a "term" and second, it is conjectural whether a force is invisible when it is defined in terms of its effect upon an object, which is very visible. It is the field that is invisible. Brews ohare (talk) 20:31, 11 July 2009 (UTC)

The change was made to describe magnetic field in laymen's terms. If you can't figure out how to update it so that it is easy to understand yet not objectionable, I suggest you delete it rather than put a tag on it. Daniel.Cardenas (talk) 00:17, 12 July 2009 (UTC)

There seems to be some problem nowadays with using the term 'lines of force' for the magnetic field. This argument cropped up a couple of years back. It's a bit like centrifugal force. It is a term which is rapidly declining in the modern literature. You will still see the term used in the occasional encyclopaedia, but you will find that it has been purged from most of the modern textbooks. It was good enough in the days of Maxwell and Faraday. In fact, if I recall, Faraday even talked about 'tubes of force'. I personally see nothing wrong with the term. After all, those lines of force connect between a north pole and a south pole and pull the two magnets together. The repulsion situation is slightly more complicated because the lines of force spread outwards and sideways between two like magnetic poles, implying that the force in this case is acting laterally in relation to the lines of force.

You'll notice that the difficulty which arises when trying to write a coherent introduction to this topic lies in the fact that the magnet effect is quite complex. There is the ferromagnetic and electromagnetic pull, and there is the ferromagnetic and electromagnetic push, which both require slightly different explanations. There is the alignment effect and there is also the v×B force that acts on charged particles that move at right angles to the lines of force. The issue is further complicated by the fact that there is that least understood of all aspects of magnetism, which is the attraction and repulsion of paramagnetic and diamagnetic materials.

Hence any attempts to write the introduction without using the politically incorrect term 'lines of force' will always run into difficulties regarding trying to fit in all these effects in a coherent manner with a satisfactory flow. That is why you see so many re-writes to the introduction of this topic. David Tombe (talk) 22:07, 15 July 2009 (UTC)

Photon?

How about the role of photons in magnetic fields? It is surprising photon is not mentioned once.128.180.4.137 (talk) 10:15, 3 August 2009 (UTC)

Very true. The quantum description of the magnetic field is totally absent in this article. Here's my attempt: [1]. I think I said everything correctly, but a second opinion would be nice, I'll try to solicit one. --Steve (talk) 15:34, 3 August 2009 (UTC)

Can we simplify the lead and make another section for QED with a main link to QED. I would like to see 2 or three sentences at most in the lead if possible. TStein (talk) 20:06, 6 August 2009 (UTC)

In principle, that's a good idea. However, what I wrote is the sum total of everything I know, and that would make a pretty small section. Go ahead if you want. --Steve (talk) 20:21, 6 August 2009 (UTC)

Is that ok? I am beginning to think that I need to remove the stuff about fundamental interactions and elementary particles in the lede, though. TStein (talk) 05:40, 9 August 2009 (UTC)

Seems that the photon and standard theory stuff is only mentioned in the introduction now. It shouldn't be mentioned in the intro if it's not in the rest of the article. 194.106.220.83 (talk) 15:21, 24 August 2009 (UTC)

The photon field and standard model description is in the main article under magnetic field#Quantum electrodynamics. The title needs to be fixed to make it easier to find though. TStein (talk) 19:11, 24 August 2009 (UTC)

Major edit to H-field section

I just made a major edit to the H-field section to try and deal with what I thought were the flaws in that section. (See post just previous to this one.) Overall I like the result, although it comes at a large cost of complexity. I have some ideas of what I can remove but I want to brood think about it some more. Comments would be appreciated especially from Brews since I may have undid some of the changes he made. I am hoping that I have kept to the spirit of those changes, though. Please let me know what I can do to make this better. TStein (talk) 22:35, 10 August 2009 (UTC)

Spam/graffity in "Alternate names for H" box

Could anyone restore the original contents of this box? —Preceding unsigned comment added by 87.195.14.60 (talk) 09:08, 25 August 2009 (UTC)

147.197.248.68(talk) took care of the graffiti. Thanks for letting us know. You can undo any graffiti yourself as well by clicking on the history tab then clicking on the undo link beside the offending change. Usually it is the last (and topmost) revision.TStein (talk) 13:15, 25 August 2009 (UTC)

Gravity and the Standard Model

In the section on quantum electrodynamics, an implication is made that the standard model includes a description of the gravitational interaction. This is not true. The standard model is only a description of the electromagnetic, weak, and strong interactions. —Preceding unsigned comment added by 142.103.234.56 (talk) 00:24, 2 December 2009 (UTC)

Well, it includes a perturbative theory of weak gravity...but whatever, it's not important here. I took out all mention of gravity, and some other irrelevant stuff too. :-) --Steve (talk) 08:17, 2 December 2009 (UTC)

Pseudovectors text is frustrating

I feel like the following text almost, but not quite, says something useful:

"Technically, B is a pseudovector (also called an axial vector). (This is a technical statement about how the magnetic field behaves when you reflect the world in a mirror; this is known as parity) This fact is apparent from the above definition of B."

I was going to copy-edit the awkward wording (repeated vague "this", etc.), but I'm having trouble figuring out what the passage means. The footnote is also confusing, claiming that "inverting" (?) the coordinates leaves pseudovectors (e.g. torque) unchanged. If "inverting" means "mirror image", then that is plainly wrong: in general, a mirror image of a torque or angular velocity produces a vector that points in a different direction. The pseudovector article seems to indicate the meaning of toggling the sign of one of the coordinate axes, e.g. replacing x with −x, which would be a mirror image. Secondly, saying that something "is apparent from the above definition" is either superfluous or unhelpful, depending on how much the reader already knows. It would be much better to specify what is meant by "the above definition" and to explain why B being a pseudovector logically follows. Can anyone help clear this up? Otherwise, my opinion is that the article would be improved by removing this entire section of text. CosineKitty (talk) 16:23, 15 December 2009 (UTC)

Thanks to this edit by Sbyrnes321, we now have a diagram that helped me understand what was meant by a pseudovector. I reworked the text that I complained about above to paraphrase the diagram and refer to it. CosineKitty (talk) 16:13, 8 January 2010 (UTC)

Suggestion

I do not know or understand a whole lot about magnets, and all of the scientific and mathematical jargon is great and all. But it does not help me for what I need, I feel like the article could use a section or two in english. This is about magnetic fields, so what is a magnetic field? —Preceding unsigned comment added by 174.106.11.149 (talk) 03:09, 11 December 2009 (UTC)

A magnetic field is a mathematical entity that can be 'visualized' in certain circumstances and is used mathematically to calculate the forces and torques on charges and magnets. The correct article that you are probably looking for is magnet or maybe magnetism. Perhaps we need to be more explicit about that such as "A magnetic field is a mathematical description of the influence of magnets on their environment. For a more qualitative description see magnetism and magnets." TStein (talk) 16:44, 2 February 2010 (UTC)

Force carrier

Someone could write something about what is the Force carrier of a magnetic field?

I'm obsessed with this issue, and I can not find an explanation. Are photons the Force carrier in a magnetic field?

When a permanent magnet attracts a iron coin, what Force carriers are operating? Photons? Gravitons? —Preceding unsigned comment added by Ruakataka (talk • contribs) 00:59, 14 February 2010 (UTC)

Photons. See the end of the introduction, and also the section Magnetic field#Quantum electrodynamics. --Steve (talk) 02:43, 14 February 2010 (UTC)

Copyedit to lead

I've copyedited the lead of the article, however, my understanding of the subject is pretty basic so it needs to be checked to see if I've altered the meaning anywhere. I've added a definition at the beginning, as that should be the starting point of any article. It's is based on one I found here, but altered to be consistent with the definition of an electric field from that article. I still have a couple of problems with what's there - for instance "The interaction of magnetic fields in electrical devices such as transformers is studied in the discipline of magnetic circuits". Is this correct? - there isn't a discipline called "magnetic circuits" as far as I know. I also didn't like the phrase "The Earth itself harbors a giant magnet in its interior". It makes it sound as if some mysterious entity buried a giant bar magnet at the centre of the Earth. I changed it to "The Earth produces its own magnetic field" which sounds more scientific to me - but you may not agree. I would also say that the lead is somewhat overlong, as evidenced by the fact that the contents section is way down the page. The lead should be a summary of the article, so some of the stuff in there should be moved elsewhere - for instance the picture of the iron filings experiment and it's accompanying text. it's not good practice to squeeze text between the infobox and a picture anyway. I think the article could generally be better arranged, with the first section after the lead being the history and the more complex stuff like the B and H fields moved further down. The article should start off with the more simple stuff and generally get more complex as it goes on. I hope the lead is now more accessible anyway. Richerman (talk) 01:59, 29 May 2010 (UTC)

In general, I like the changes. In spite of the fact that this is a very technical subject, the term "magnetic field" is used enough in everyday life that this article needed an introduction understandable by nontechnical readers. However I think a little more of the scientific info needs to be restored, and as you mentioned the entire intro needs to be slimmed down, IMHO. --Chetvorno^TALK 03:55, 29 May 2010 (UTC)

I fixed the first sentence, sorry but it was too long. I think I will add "the magnetic field occupies the space around the magnet or conductor...", to kind of express what you seemed to be trying to say. A lot of the other stuff you edited in the introduction are pretty good edits. Anway User:TStein is doing a great job with this page. He has a PhD. in Physics and teaches Physics, so he definitely has the expertise for this page.

I do have one question for Richerman. What is this about a magnetic field being destroyed, stored, and restored? Can you explain this better? ----Steve Quinn (formerly Ti-30X) (talk) 04:57, 29 May 2010 (UTC)

I presume you mean the sentence "The energy needed to create a magnetic field can be reclaimed when the field is destroyed and this energy can, therefore, be considered as "stored" in the magnetic field." This was just my rewording of the previous text that read "Energy is needed to create a magnetic field, energy which can be reclaimed when the field is destroyed. This energy can be understood as being stored in the magnetic field." The reason why I looked at the article in the first place was because I saw the discusssion here where User:TStein asked how to get a lay person to review the article for understandability, so I'm sure he won't mind some input from a lay person. I may not know too much about magnetic fields but I know a bit about how to write good English and how wikipedia articles should be structured :) I still think the article should begin with "a magnetic field is" rather than "magnetic fields are" - so I've replaced the first bit with the OED definition - why reinvent the wheel? The definition should be referenced anyway. If you don't like that one I'm sure there are a number of good definitions in physics text books. The sentence you restored "The magnetic field interacts with the material so that it produces an additional magnetic field which interacts with itself, etc." really is clumsy - "etc" sounds awful and is far too wishy-washy for a scientific article. Richerman (talk) 12:01, 29 May 2010 (UTC)

Thanks for explaing that. Regarding the introduction, I really like this opening sentence much better than either of the two recent edits. Good job. I hope my earlier comments did not sound too critical. It's always good to remember that "other editor" is a person, not just a group of words on a page.----Steve Quinn (formerly Ti-30X) (talk) 22:15, 29 May 2010 (UTC)

No problem - I didn't expect to get it all right first time. Richerman (talk) 23:18, 29 May 2010 (UTC)

Magnetic field lines, etc.

I have removed the following paragraph, as it seems to be too much of a digression to place in the introduction of the article.

Magnetic lines are obsolete labeling for such lines; pathways are a more descriptive label. It is such circular virtual pathways that the force components follow cyclically from the South magnetic pole and back into the North magnetic pole. This is applicable for both ferromagnetic fields and for electromagnetic fields. The force components are mass energy in the electromagnetic state. Discrete quanta’s of Electromagnetic state mass energy (photons) are a consequence of where thermonuclear fusion reactions occur in stars such as our sun. Where proton mass energies of two Hydrogen atoms become entangled they fuse and a Helium atom is created. Since there is more mass energy in two Hydrogen nuclei than one Helium nucleus the residual binding energy is transmuted into the electromagnetic state as photons. In the iron filing graphic depicted in the forgoing each length of iron is itself a dipole magnet; this is why the iron particles emulate the shape of that field. One dipole magnetic field will always induce another dipole magnetic field regardless of its size.

Since this edit has been reverted once before (citing WP:OR), I thought I'd place it here for discussion. It seems to me that some of this info would be better integrated into the section of the article devoted to field lines, although personally, I feel like that section already has a good discussion on the conceptual nature of field lines and the behavior of iron filings. Any thoughts? Rundquist (talk) 23:35, 12 July 2010 (UTC)

I agree - the lead is far too long and complicated anyway. According to Wikipedia:Manual of Style (lead section) "The lead should contain no more than four paragraphs, should be carefully sourced as appropriate, and should be written in a clear, accessible style to invite a reading of the full article". Richerman (talk) 00:18, 13 July 2010 (UTC)

Direction of field lines

The section Visualizing the magnetic field using field lines discusses the direction of the field lines. In the sub-section B-field lines never end it says “Magnetic field exits a magnet near its north pole and enters near its south pole but inside the magnet B-field lines return from the south pole back to the north.” Then later in the sub-section titled H-field lines begin and end near magnetic poles, it says “Outside a magnet H-field lines are identical to B-field lines, but inside they point in opposite directions. Whether inside or out of a magnet, H-field lines start near the S pole and end near the N.”

$\mathbf {B} =\mu \mathbf {H}$

The second reference (H-field lines begin and end near magnetic poles) contradicts the first reference and is not consistent with other descriptions of the fields. First of all, why would H-field lines point in the opposite direction of the B-field lines? Relative permeabilities are positive numbers and according to the basic relationship shown above, H and B point in the same direction and they do not flip at the material interface. The normal component of H is the same on both sides of the surface interface (only the tangential component changes when there is a surface current).

Descriptions of the magnetic field lines are confusing because there are no “start” and “end”. The field lines do not “point” in opposite directions. Indeed, a statement about going from “north to south” or “south to north” changes when describing the different regions, but this just describes a field that continues to point in the same direction across the material interface.

In all of the books and reference I could find, there was not good description of both magnetic fields (B and/or H) from well inside a material, through the interface into the other medium. The sources I could find only deduce certain properties about the fields right at the interface, but fail to discuss the complete description of the field throughout the bulk into the external medium and back. If I am mistaken and the description in the article is correct, this section needs more detail and references to justify the description. It needs figures of different configurations of the fields showing exactly what is being described. --Mousetrails (talk) 03:45, 27 March 2010 (UTC)

• The equation $\mathbf {B} =\mu \mathbf {H}$ is almost useless for bar magnets or other ferromagnets, which is presumably what the text is discussing. The equation only applies to "linear materials", like paramagnetic or diamagnetic. The H field in these cases is actually a bit complicated to calculate, but you can find examples in any standard electromagnetism textbook. For a uniformly-magnetized sphere, I remember for sure that B and H point in opposite directions inside. For a uniformly-magnetized infinite cylinder, magnetized along its axis, H is exactly zero inside, while B is large, as I recall. :-) --Steve (talk) 04:09, 27 March 2010 (UTC)

• In the B and H section of the page, H is defined properly with

$\mathbf {H} \ \equiv \ {\frac {\mathbf {B} }{\mu _{0}}}-\mathbf {M} .$

The difference between B and H inside a material is due to the magnetization M of the material. The nature of the magnetization is going to vary greatly with materials (e.g., paramagnetic materials, ferromagnetic materials, etc.), and so the mismatch in B and H fields is non-trivial. I notice that the book Fundamentals of geophysics by Wiliam Lowrie is available (for limited preview) on Google Books and has a decent discussion of the difference between B, H, and M on page 236 (geophysicists care a lot about these topics because they deal with fields above and below the surface of the earth). To help you understand the B versus H complication, consider the example which is referenced in the Force on a magnet due to non-uniform B section of a bar magnet trapped inside another magnet. Outside of the magnet, the bar magnet should align itself with the B field; however, inside the magnet, the bar magnet will align itself opposite to the B field. In particular, the bar magnet's south pole will be closest to the outer magnet's north pole. The H field represents the actual "between pole" effects inside the material. Hence, like electric field lines (and unlike B field lines), H field lines start on north poles and end on south poles. H fields allow you to port your intuition from electric field studies to magnetic fields. (at least that's my uneducated "spin" on these things) —TedPavlic (talk/contrib/@) 17:25, 28 March 2010 (UTC)

Continuing that idea, there are no magnetic poles. Inside a real magnetic material, there are (effectively) loops of current that align each other along the lines of the B field that links them all. Hence, if it is a magnetic material, we can define "poles" at the boundary of the material, and those poles will be the endpoints of the H field. The magnetization of the material will relate those H lines with the actual B lines that the atoms of the material feel. Definitely see the History section for more details. —TedPavlic (talk/contrib@) 19:04, 29 March 2010 (UTC)

(unindent)The problem that Mousetrails is referring to is complicated by the fact that some textbooks (particularly engineering books) interpret H completely different. They seem to ignore the part of the H-field due to the magnetic material; this is the part that switches directions. (I am afraid that even after reading them I don't fully understand what they are trying to say or do.) This leads them to have to introduce demagnetization and other strange and confusing things. For engineers that are working with magnetic circuits this isn't a problem. What is important is not H itself but the line integral of H around the circuit. The discontinuous part due to the magnet itself integrates to zero and may be safely ignored.

In response to Mousetrails, I tried to deal with this by noting first of all the equation that TedPavlic mentioned H=B/μ_o - M. I also mentioned that B=μH and that this is only valid in some materials. This is obviously not working. Any ideas how I can make this thought more prominent without causing troubles in other ways will be greatly appreciated. TStein (talk) 23:31, 21 May 2010 (UTC)

I think Mousetrails actually has a point, though: there is a contradiction in this section. The portion discussing B-fields states "Magnetic field lines exit a magnet near its north pole and enter near its south pole, but inside the magnet B-field lines continue through the magnet from the south pole back to the north." I believe this is true; see [2]. However, the portion discussing H-fields states "Whether inside or out of a magnet, H-field lines start near the S pole and end near the N." This is not consistent with the idea that outside a magnet, H-fields are parallel to B-fields. Outside a magnet, both should point from N to S. Furthermore, I don't think it's true that H is always opposite B inside a magnet. Since $\mathbf {H} \equiv {\frac {\mathbf {B} }{\mu _{0}}}-\mathbf {M}$, wouldn't that depend on the value (and direction) of M, not to mention the presence of an external field? As Steve mentioned earlier, it's true for a uniformly magnetized sphere (that's the example Jackson gives), but I'm not sure it's true in general. Finally, I think the title "Magnetic field lines (an important visualization and conceptual tool)" is a bit long, it should probably just be shortened to "Magnetic field lines"; the section itself should explain why it's an important visualization and conceptual tool. I think I'll go ahead and make some of these changes, but I wanted to post here first in case anyone wants to discuss it. Rundquist (talk) 03:23, 13 July 2010 (UTC)

Oops! I messed up. I got my north and south confused. Thanks for fixing it and the other fixes as well. My only problem is introducing the relationship between B and H so early. (The magnetization field isn't properly explained nor can it be explained without interrupting the flow, in my opinion. TStein (talk) 18:48, 16 July 2010 (UTC)

Field lines as an imaginary graphical aid; no more than that!

Due to the "picture" of field lines around a magnet that can be generated by iron filings, it is an extremely common misconception that the lines are somehow "real." They are no more real than the isoclinic lines in a topographic map. The placement of each line is arbitrary-- with a different graph you could have twice as many or half as many. Only their direction has meaning, and (if you keep the same graphical scale) their density as it changes.

The same is true of the lines in the iron filings! They don't form around magnetic field lines (as it appears) for there ARE NO MAGNETIC FIELD LINES in reality. Varying the coarseness of filings or other properties will give twice as many or half as many lines with the same magnet, because what is being "shown" is not magnetic lines at all. I've added some stuff to the images and text to make this point, so hopefully more generations of students won't look at it and make a bad assumption. SBHarris 19:38, 17 April 2010 (UTC)

Yes, the iron filing caption in particular has gone through numerous revisions to help the occasional reader who thinks that there is a magnetic field where the field lines are drawn and there is no magnetic field between the lines. I like most of your edits, good job.

But, in a few cases I think you're being a bit too extreme: I would say a magnetic field line is not arbitrary or imaginary: Given a point, there is a unique field line passing through the point. A full magnetic field depiction using field lines, on the other hand, is arbitrary, in that different choices of field lines are equally valid. I guess you're thinking of only the latter, not the former. I would say an individual field line is just as "real" as a magnetic field vector, whereas a field line depiction of a whole field is definitely an arbitrary ("not real") thing. :-) --Steve (talk) 23:58, 17 April 2010 (UTC)

No, field lines really are no more real than the lines you draw on graph paper, or the lines in a coordinate system. At a given point there's a field line that passes through it IF YOU WANT IT TO. But for the same point, you can draw two lines that miss the point entirely if you like, and that's just as good. The strength of your field determines the spacing of the lines you draw, but exactly where your coordinate axis is, is up to you. Of course, once you fix it at a single point, that and the strength of your field fixes the distance of the lines on either side (once you've determined what the scale is). But you can even change THAT, by changing the scale you picked. The only thing that isn't changable in (locally uniform) field is that once you pin a line, the ones on either side have to be (more or less) equidistant (to the limit of how uniform the field is over that space). But what that distance is, is again up to you.

The analogy with icocline lines on a topo map is good. Topo lines have an absolute magnitude (height) whereas field lines have the same strength (there is a 1 gauss line, a 2 gauss line, etc). The individual lines then are lines of iso [magnetic field]. But to put them any place you want, you just have to decide what strength of field "merits" a line. And it's entirely up to you. SBHarris 01:53, 18 April 2010 (UTC)

I cut a bunch of the additions here, because, quite frankly, I think you were beating a dead horse. Plus some of the comments about the lines representing equal magnetic field is just plain wrong. There is no 1 Gauss line, etc. Just like E field lines the B field can vary along the length of the line. (They are constant for some geometries but not for most.) For that reason much of the comparisons with Isoclines is misleading.

Further, this is a misconception that I rarely run across. By dealing with it so much we take a huge risk about confusing people in other directions. Those who haven't over thought field lines may think that they are missing something because we spend so much time on it. In turn they will over think it in a completely different and unpredictable way.

Finally, understanding the concept of field lines enables an analogy with fluid mechanics that makes understanding of gradient, divergence, and curl almost trivial. Field lines are to E&M what Feynman lines are to theoretical nuclear and particle physics. Neither exist in reality but both enable, describe, and explain a lot of the complex math behind the reality in a very compact way. To spend so much time saying that field lines don't exist is akin to saying the same thing about Feynman lines. Of course they don't exist but what is the point of saying they don't?

Finally, for real this time, something akin to field lines ARE real. Plasma environments like the surface of the Sun is one example. Flux lines in superconductors is another. That probably supports your case because there is a difference between the conceptual field line and the real flux lines. Nevertheless, these are hardly cases that the ordinary reader will run into. (I think that both of these topics while important for their fields are too esoteric for this article.)

Most of my changes are in two of my edits today talking about dead horses. Please look at them. If you have any additional question about why I changed them in this way please ask. I tried to keep the main thought behind what I think you were trying to say. I even added a similar thought in the short paragraph in the lead about the magnetic field lines. TStein (talk) 23:05, 21 May 2010 (UTC)

I agree. A wordy treatise on what field lines do or don't represent does not belong in the caption of the introductory picture; it's beating a dead horse. Nontechnical readers should be shown how useful the field line representation is first. They can always go to Magnetic field line if they have questions. --Chetvorno^TALK 23:50, 21 May 2010 (UTC)

The relative lengths and density of the real (or imaginary) magnetic field lines are an aid in illustrating the relative intensity of the magnetic force field existing in the vicinity of the magnet. The intensity increases as a function of the number of lines per perpendicular area.WFPM (talk) 14:01, 5 August 2010 (UTC)

I need some guidance about whether we need a 'formal' definition at the start of the article

I want to delete the following from the article because it has too much detail at the start of the article for little gain, in my opinion. All of it is repeated later on in the article where it makes sense. I know from experience that some people want to start off with a formal definition. On the other hand, we want to push the mathematical stuff to the end.

Here is what I want to remove:

"The B-field can be defined in many equivalent ways based on the effects it has on its environment. For instance, a particle having an electric charge, q, and moving in a B-field with a velocity, v, experiences a force, F, called the Lorentz force (see below). In SI units, the Lorentz force equation is

$\mathbf {F} =q\left(\mathbf {v} \times \mathbf {B} \right)$

where × is the vector cross product. An alternate working definition of the B-field can be given in terms of the torque on a magnetic dipole placed in a B-field:

${\boldsymbol {\tau }}=\mathbf {m_{m}} \times \mathbf {B}$

for a magnetic dipole moment m (in ampere-square meters). The B-field is measured in teslas in SI units and in gauss in cgs units. (1 tesla = 10,000 gauss). The SI unit of tesla is equivalent to (newton × second)/(coulomb × metre) as can be seen from the magnetic part of the Lorentz force law F_mag = (qv × B).

H is defined as a modification of B due to magnetic fields produced by material media, such that (in SI):

$\mathbf {H} \ \equiv \ {\frac {\mathbf {B} }{\mu _{0}}}-\mathbf {M} ,$

where M is the magnetization of the material and μ₀ is the permeability of free space (or magnetic constant). The H-field is measured in amperes per meter (A/m) in SI units, and in oersteds (Oe) in cgs units.

In materials for which M is proportional to B, the relationship between B and H can be cast into the simpler form: H = B/μ, where μ is a material dependent parameter called the permeability. In free space, there is no magnetization, M, so that H = B/μ₀. For many materials, though, there is no simple relationship between B and M. For example, ferromagnetic materials and superconductors have a magnetization that is a multiple-valued function of B due to hysteresis.

I pulled the trigger on this and removed it. I think it works better this way. TStein (talk) 19:42, 16 July 2010 (UTC)

Charged particle drifts diagram wrong

I believe... In line B of the diagram, the positive particle should drift down (in the direction of the electric field), and the negative particle should drift up. In line C, both particles should drift down. Lines A and D look correct, although I'm confused about the distinction between B and H fields and wonder if perhaps line D should say grad B instead of grad H.

Also, the last part of this sentence next to the diagram doesn't make much sense: "It can and does, however, change the particle's direction, even to the extent that a force applied in one direction can cause the particle to drift in a perpendicular direction." JKtemp (talk) 20:47, 12 July 2010 (UTC)

Actually, I believe both the diagram and the description are correct. For more information, see the guiding center article, where it states: "Generally speaking, when there is a force on the particles perpendicular to the magnetic field, then they drift in a direction perpendicular to both the force and the field." As far as B and H fields go, in this case, they are interchangeable, since we are talking about the motion of individual charged particles in a (presumably) non-magnetic medium, so B = μ H. I suppose the diagram could be changed to "grad B" simply for consistency with the style of the article, but from a technical standpoint, I don't think it matters. Rundquist (talk) 23:50, 12 July 2010 (UTC)

It would take me about eight sentences to explain this properly. For example:

The diagram to the right demonstrates this. For a magnetic field pointing out of the screen a positive charge will circle clockwise. (A positive charge moving to the left at the bottom of the loop for instance feels an upward force.) A second non-magnetic downward force (third row) though will accelerate the charge downward increasing the velocity. As the velocity increases the magnetic force will eventually dominate causing the charge to form a clockwise loop moving left and up. As the charge moves up due to the magnetic field it slows down (the second force is pushing it down). The non-magnetic force begins to dominate until the particle comes to a stop at the peak and the cycle begins again. The end result is that a downward force causes the particle to drift to the left due to the magnetic field.

Would it be worth it? TStein (talk) 17:03, 15 July 2010 (UTC)

The Lead again

As Richerman (talk) points out, in the section just above, the lead is too long and rambling. I think that 4 paragraphs is too small for an article of this size. Nevertheless, I think that the second and the seventh paragraphs (covering magnets and qed, respectively) can be safely eliminated. Further, by moving the history section up to the top I can get rid of the last paragraph as well. That will cut the lead down to a more manageable 6 paragraphs. So what do you think? TStein (talk) 21:11, 14 July 2010 (UTC)

That would certainly be an improvement. I think that moving the history section up is a good idea as it is usually the first section in any article of this type. Also the B and H section is somewhat complicated and should be further down so the reader is led into the subject it a bit more gently. Obviously the B and H fields will have to be mentioned in it but the reader can be referred to the later section for a fuller explanation. I also think it would look better if the image in the lead was on the right as it looks clumsy with the text sandwiched between that and the infobox. Richerman (talk) 21:30, 14 July 2010 (UTC)

I agree; the important point of the second paragraph is already covered by the disambiguation header, and the seventh paragraph could probably be incorporated into the sixth with a quick note about how a more complete description of the magnetic field requires QED (with a link). As far as section order goes, I think the article is quite jumbled up right now. For me, a more logical order would be something like:

• History
• B and H
• Magnetic field lines
• The magnetic field and permanent magnets
• The magnetic field and electrical currents
• H and B inside and outside of magnetic materials
• Energy stored in magnetic fields
• Measuring the B-field
• Important uses and examples of magnetic field
• Electromagnetism: the relationship between magnetic and electric fields

Of course, this would require something of a re-write in order to make everything flow smoothly. Does anyone else have any suggestions? Rundquist (talk) 22:04, 14 July 2010 (UTC)

I am not quite sure that I agree with the order of everything in your proposal, but I see some advantages. I don't like separating the Electromagnetism section too much from the sections on magnetic field and electrical currents because it builds quite a bit on that section. I also don't like sticking the "important uses and examples..." section in the middle since it is independent of everything else and therefore interrupts the flow of the article.

How about this?

• History
• B and H

• Measuring the B-field

• Magnetic field lines
• The magnetic field and permanent magnets
• The magnetic field and electrical currents
• H and B inside and outside of magnetic materials
• Energy stored in magnetic fields
• Electromagnetism: the relationship between magnetic and electric fields
• Important uses and examples of magnetic field

In addition I want to really pare down the "B and H" section. All of the technical details are covered better later in the article. There is no reason to have to introduce the full blown relationship between B and H this early, for instance. A simple "See H and B inside and outside of magnetic materials for the relationship between the two." will do. TStein (talk) 14:54, 15 July 2010 (UTC)

Hopefully, I haven't been too WP:bold in implementing many of the changes I proposed too quickly. Please check the article to make certain that I didn't cause more harm than good. Thanks. The magnetic field line section still needs to be moved up in my opinion, but I didn't want to change too many things at once. TStein (talk) 16:46, 15 July 2010 (UTC)

The structure certainly looks better now. Another problem with this article is the massive overkill on links. There are "see also" links under section headings to articles that are linked elsewhere in the text, there are piped links to other sections of the article (which are totally unnecessary), and then some of these links are duplicated again in the "See also" section at the bottom. I've removed some of them but there are still lots more than are needed. It just gets very confusing and, to be honest, somewhat patronising to the reader. Generally, only the first occurence of a term should be linked, although the second occurence may sometimes be linked if it's a long way from the first. The "See also" section should only have a few links in it and these should be to relevant articles that haven't already been linked. Richerman (talk) 02:12, 16 July 2010 (UTC)

I think I see your problem with the links. It doesn't bother me as much, though. I certainly agree with the duplicate links. Most of them crop up accidentally. Personally, I like having a main link for each section for which it applies in order to relate it better to other articles. The main links are there not only for people to click but to show how articles are related. TStein (talk) 18:59, 16 July 2010 (UTC)

I fixed all the {[main}} links to my satisfaction. Fixing link duplication should generally wait until the article is stable; although it is probably stable enough now. I will probably replace the first use of a link that is the same as the main link with a bold of that term. Does that sound good? TStein (talk) 19:49, 16 July 2010 (UTC)

Yep, that sounds good. I don't have a problem with the main article links - its was the "see alsos" at the top of some of the sections and the duplications in the "See also" at the end that were the real problem. I removed a chunk of those yesterday. And piped links to other sections of the article are a definite no-no. Richerman (talk) 23:05, 16 July 2010 (UTC)

Earth's magnetic field

As the legend on the diagram in this section was very long I've shortened it and moved some of the explanation into the main body of the section. I've also expanded the explanation of dynamo theory and rewritten some of the section to make it clear that dynamo theory and geomagnetic reversal are theories rather than proven facts. Could someone check that I got the explanations right? Richerman (talk) 01:14, 17 July 2010 (UTC)

To Do lists for B class

I would like to push this article to A class and maybe better, but first I would like to at least push it to B-class by making the article complete with no obvious flaws. I am fairly satisfied with the article with one major exception. What do we need to move it up? My list:

• The H-field/magnetization/dipole section needs to be improved.
  • It confuses magnetization and magnetism
  • It repeats the definition of H without really helping to explain it I think I fixed this TS 19:29, 24 May 2010 (UTC)
  • dipole section needs to be worked in better Note: avoided it in this section and moved
  • A common interest from readers (determining the magnetic field of a permanent magnet) is not covered 21:15, 3 August 2010 (UTC) TS
  • It uses the term magnetization before it is defined Note: fixed as best as I think I can.
• determine what we need to do to remove technical tag and do it
  • determine how we should deal with grad, div, curl, line integrals and surface integrals done sort of I am not 100% certain this is the best solution. TS 23:14, 24 May 2010 (UTC)
    • I want to try not to lose non-technical readers, but this is a technical subject-TS
    • I included non-technical description of grad, div, and curl, but they are often after they are used. Do these non-technical descriptions belong and if so where?
      • I am thinking about converting all differential form into integral forms until electromagnetism is reached. There is will start section with short intro to div and curl (moving this up slightly from Maxwell's equations). TS 23:14, 24 May 2010 (UTC) Comments?
• Factor out history section into its own article (History of magnetic field?) keeping only a short summary. 19:41, 16 July 2010 (UTC) not done, but I think that it is good and short enough the way it is TS.
  • Then move to near top? (along with measuring the B-field). A short summary in lede TS 19:29, 24 May 2010 (UTC)
• QED section? done
• vector potential A section?: Need someone to check to make sure not too technical
• Determine what all needs to be in lead and simplify it.03:07, 23 May 2010 (UTC)
• Better diagrams
  • more consistent style
  • better Earth's magnetic field diagram. (I would love to superimpose a picture of Earth.)
  • I would like a diagram of H of permanent bar magnet vs B of permanent bar magnet
  • Diagram of M-field and B-field for simple permanent magnet(s)
• Clean up references
  • Split up references to which text book calls what which and move to side box about different names did that a while back TS

Anything else?

TStein (talk) 20:27, 6 August 2009 (UTC)

Good work - I feel mean to say this, but... 'electrical'? Almost every use of this word should be 'electric' - 'electric field', 'electric charge' etc. You wouldn't say 'magnetical field'! Keep up the good work. AndyI 16:24, 7 October 2010 (UTC) —Preceding unsigned comment added by Aci20 (talk • contribs)

Thanks. The electrical -> electric thing is one of those things that I keep forgetting about and have to correct. I fixed it. This article is almost where I want it to be. The diagrams are really hurting it in my opinion and the references need to be fixed as well. TStein (talk) 18:12, 8 October 2010 (UTC)

If you have any specific ideas in mind regarding the diagrams, then perhaps you would like to contact the Graphic Lab for modifications or even new creations? Just suggesting. —Quibik (talk) 15:48, 9 October 2010 (UTC)

NB 9 says "To see that this must be true imagine placing a compass inside a magnet." I don't think "to see that this must be true" sounds right, and also the reader shouldn't be addressed directly, as in "imagine placing". How about "This can be visualised by imagining a compass placed inside a magnet."? Richerman (talk) 00:45, 10 October 2010 (UTC)

North/South?

Is the following a minor error or something very confusing that needs explanation?

"The Earth produces its own magnetic field, which is important in navigation since the north pole of a compass will point toward the south pole of Earth's magnetic field, located near the Earth's geographical north." Dynasteria (talk) —Preceding undated comment added 09:15, 11 June 2010 (UTC).

That one threw me at first but after some thought I realised that unlike poles attract so, as the north pole of the magnet in a compass points approximately towards the geographical north pole of the earth, that must be the location of the south pole of the Earth's magnetic field. Does that make sense? I suppose if the geographical north pole had been called the "south pole" in the first place it would have been more consistent. Richerman (talk) 12:30, 11 June 2010 (UTC)

Richerman, you are correct. I think the term north and south pole of earth was used before magnets were understood. The north pole of a magnet was then defined as the one that pointed toward the north pole of earth.TStein (talk) 19:37, 11 June 2010 (UTC)

I put the above statement in as a compromise between two halves of my brain. On one hand, it isn't necessary and it IS confusing and any lengthy explanation would be unwarranted in my opinion. On the other hand it is an interesting factoid, that makes people use their brain a little. It adds a little spice to the article. I suppose the best thing to do to make the article more 'encylopedic' is to remove that line. My guess is that is will eventually be removed. I won't put it back if it is, but it will be a sad day for me. The article IS too long and too rambling. In order for this article to make it to A status or higher things that I care about will have to be cut. TStein (talk) 19:37, 11 June 2010 (UTC)

I think it would be reasonable to explain that, as you've just done, in a footnote. Having done a google search on this I was directed back to the wikipedia article North Magnetic Pole where it says "based on the early use of magnets in compasses they were named the "north pole" (or more explicitly "north-seeking pole"), "N", and the "south pole" (or "south-seeking pole"), "S", with the north pole being the pole that pointed north." Richerman (talk) 23:56, 11 June 2010 (UTC)

Confusions like this commonly exist in other parts of our understanding of electromagnetism.

It was at first believed that electricity flows from positive to negative (conventional current), though we now know that to be wrong.

Although we know the current actually flows from negative to positive, circuit symbols such as for the diode point the wrong way from positive to negative. And so we have these ridiculous ideas used in electronics classes describing "holes" flowing in the opposite direction as electrons to try to make some sense of having the diagram symbols reversed.

The truth about north and south poles is much the same. It is much easier to stop talking about poles and just draw an arrow on the magnet and the planet, showing how they tend to form a loop pointing around generally circular field lines. DMahalko (talk) 22:23, 22 October 2010 (UTC)

The Introduction

The introduction is too long. What about starting by getting rid of this paragraph here,

The complex mathematics underlying the magnetic field of an object is usually illustrated using magnetic field lines. These lines are strictly a mathematical concept and do not exist physically. Nonetheless, certain physical phenomena, such as the alignment of iron filings in a magnetic field, produces lines in a similar pattern to the imaginary magnetic field lines of the object.

This seems to be a very amateurish way of saying that the first full mathematical treatment of magnetic lines of force was given by James Clerk-Maxwell in 1861 and that iron filings illustrate the magnetic field by aligning along the lines of force. These two phrases can be re-positioned elsewhere in the introduction accordingly. David Tombe (talk) 20:27, 25 October 2010 (UTC)

FyzixFighter, I appreciate that magnetism is a very complicated topic. And I have never been sure myself exactly how to best word the introduction. The problem is trying to get the right balance between simplicity and not turning the readers off totally. And I fully agree that it does not help to make a complicated topic too simple. In your latest attempt however, I think that you have erred on the side of making the introduction too cumbersome.

I'll make a suggestion. First of all, think about what the magnetic field is. It is a force field. So state that fact. Then state how it appears. The iron filings diagram is usually the best for that purpose. Point out that it is caused by electric currents, moving charges, and ferromagnetic materials. Then point out how it is manifested. It is manifested by the forces which it produces in a variety of contexts. List the main examples that cover the basics of EM theory. That should be the basic framework. There is no harm in having a number of attempts. David Tombe (talk) 10:28, 8 November 2010 (UTC)

Spin and Relativity

FyzixFighter, I think that you're going to need to elaborate on your recent revert. The idea of the introduction is to illustrate to the average readership what a magnetic field is. By introducing concepts such as relativistic spin so early on in the article can only serve to confuse the readers. You are attempting to explain one non-understood concept in terms of an even less understood concept. Now I admit that quantum mechanics is not my strong point and I would certainly never claim to remotely understand quantum mechanics, and so I wouldn't normally have ever considered introducing quantum spin into the introduction. But since you did, and since you claimed it to be a relativistic effect, I thought that I had at least better change it to a 'quantum effect' as I believe that the literature introduces it as a quantum effect. This web link here [3] doesn't give any indication that 'spin' is a relativistic concept as you claim. I know that in 1928, Dirac made the whole thing relativistic, but the concept was introduced before it was relativized. It's maybe best to simple state in the introduction that a magnetic field is found in the vicinity of ferromagnetic materials, and to totally side-step all these issues about both quantum mechanics and relativity. David Tombe (talk) 09:47, 6 December 2010 (UTC)

Pauli (I think it was 1922) first proposed something like spin as an ad hoc degree of freedom for electrons, and there followed several attempts to come up with some kind of physical explanation of what it was. It lost all of its adhocness when Dirac did relativistic quantum mechanics. A lot of quantum texts don't mention why "spin" exists, but a few, usually only briefly, do. For example, from A.F.J. Levi's "Applied Quantum Mechanics" (2nd ed, pg 89): "Electron spin angular momentum, sh-bar, is an intrinsic property of the electron that arises due to the influence of special relativity on the behavior of the electron. In 1928, Dirac showed that electron spin emerges as a natural consequence of a relativistic treatment of the Schrodinger equation." When I was reworking the intro, my intent with that sentence is to describe the most basic sources for magnetic fields, which are currents, time-vary electric fields, and the intrinsic dipole moment of subatomic particle related to its spin. Ferromagnetism is just one macroscopic magnetic effect that arises from the spin of the electrons in atoms, but there are others, which is why I think spin should be mentioned first before ferromagnetism. I really don't think "relativity" in the intro will confuse readers - relativity is a fairly well-known and widely accepted concept. We could help the reader by providing a wikilink either to special relativity or quantum field theory (personally, I favor the former). --FyzixFighter (talk) 18:20, 6 December 2010 (UTC)

Just because "spin" arises in Dirac's treatment of the relativistic electron doesn't mean that spin is a result of relativity (relativistic phenomena) per se. The "spin" terms (splitting of energies) that come out of Dirac's equation, basically come out of the same place they arise in the Pauli equation (which is of course nonrelativistic), which is from adding an extra degree of freedom to psi by hand, by adding an extra term that couples the energy-state of an electron to an external magnetic field, and also writing at least two equations in two different psi variables, so that there is "room" for spin-up and spin-down psi-solutions (of course all this doubles to 4 psi's in the relativistic treatment, since each of the spin-up and spin-down solutions now has an electron plus virtual positronic component as well). Which is why the 4-psi spinor Dirac solution reduces to the 2-psi spinor Pauli solution for non-relativistic energies. Spin solutions proceed from the >2-state, >2-psi formulation, PLUS EM coupling. This adds an extra spin energy term, thus presumes spin itelf, simply by being there. All this happens whether the equation(s) is/are relativistic or not, as the Pauli equation shows. Pauli added the oddly large g-factor by hand, to be sure, but it doesn't NEED to be added by hand, and its origin is not relativistic: the origin is the fact that charged spin-1/2 particles have to have g-factors of 2 (in the non-QED limit) in order to maintain guage invariance of minimal EM coupling for spin-1/2. Levy-LeBlonde showed in the 1950's that a simple system of two linear (linear in space AND time) equations, coupled to each other, but non-relativistic wave equations in two variables (Psi+ and Psi-) with an added minimal EM field interaction potential term, gives the same result as the Pauli equation (which is nonlinear in spacial variables, like Schroedinger). Levy-LeBlonde's nonrelativistic work gives correct g-factor of 2, that does not need addition by hand. Thus, since this is not a relativistic treatment and makes NO assumptions about g-factor, spin itself, and its extra-large g-factor for elections (their angular momentum seems to count double in the making of their magnetic field), is not a relativistic phenomenon.

By contrast, the Thomas precession IS a relativistic phenomenon which arises naturally out of the Dirac equation, but it has nothing to do with spin. All this has caused endless confusion over the years. SBHarris 18:47, 6 December 2010 (UTC)

I would still argue that it was originally an ad hoc addition by Pauli to reconcile theory with experiment, while with Dirac it finally ventures out of ad hocism. I was in favor of keeping "relativity effect" based on the sources I have at hand (like Levi), but if there are mainstream sources (as opposed to a fringe anti-relativists) out there that dispute this then (1) certainly this article is not the place to address the dispute, and (2) it's easy enough to come up with a compromise wording that glosses over the dispute (which I'll try here in a second). I still stand by the opinion though that intrinsic dipole moment due to spin trumps ferromagnetism in importance when talking about sources of magnetic fields. --FyzixFighter (talk) 19:19, 6 December 2010 (UTC)

Well, yes, but "ferromagnetism" relies on electron spin, so it's not one thing trumping another. Electron spins aligned within iron atoms are why iron atoms have their large magnetic moment, and in ferromagnetism, these moments of these atoms simply line up. Grossly, this is shown in the Einstein-de Haas effect, which I still find amazing. Einstein and de Haas basically found that twice as much magnetism was generated per unit of angular momentum change as bulk property in a magnet, as you'd expect from simple charges moving in a circle, ala standard EM, or even the Bohr magneton. That all goes back to the funny g-factor of 2 for electrons (relationship of their magnetic field and angular momentum), a factor which is effectively just 1 with all other types of currents. SBHarris 20:06, 6 December 2010 (UTC)

Sorry if I was unclear. What I meant by trumping in importance is that the intrinsic dipole moment described by spin is more fundamental than ferromagnetism, or as you pointed out ferromagnetism relies on electron spin. This is in response to David's suggestion that we replace the mention of it in the lead about sources of magnetic fields with a statement on ferromagnetism. I think it's better to present the fundamental sources first, then work up to macroscopic fields (which is done a couple sentences later in the lead). --FyzixFighter (talk) 20:53, 6 December 2010 (UTC)

Trimming introduction

FyzixFighter, That is much better thank you. But the introduction still needs to be drastically reduced in size. After introducing the sources of the magnetic field and the manners in which the magnetic field manifests itself, it would be sufficient to simply state that magnetic field and its inter-relationship with electric field is given full mathematical formulation in Maxwell's equations. David Tombe (talk) 19:27, 6 December 2010 (UTC)

For an article of this size, the typical length of the lead is 3-4 paragraphs; the lead currently is 4 paragraphs. When I rewrote it, I tried to follow the guidelines in WP:LEAD. Which guidelines from the MoS do you feel the intro could do better at satisfying? Are there any other editors that feel the intro is too long and might suggest how to pare it down? --FyzixFighter (talk) 20:53, 6 December 2010 (UTC)

FyzixFighter, Have a look at this part of the introduction,

The magnetic fields due to and within magnetic materials is described using two separate fields which can be both called a magnetic field: a magnetic B field and a magnetic H field.

The magnetic field at any given point is specified by both a direction and a magnitude (or strength); as such it is a vector field.[nb 1] This is usually illustrated using magnetic field lines. These lines are strictly a mathematical concept and do not exist physically. Certain physical phenomena, such as the alignment of iron filings and, more generally, of magnetic dipoles in a magnetic field, produce lines in a similar pattern to the imaginary magnetic field lines of the object.

The first bit about B and H could be dropped. It's not needed in the introduction. The second bit could be simplified to a single sentence such as 'the solenoidal pattern of the magnetic field around a bar magnet can be traced out by iron filings which align in sympathy'.

That would be a start. David Tombe (talk) 21:04, 6 December 2010 (UTC)

David, you want to get rid of the most important parts. Ok that is somewhat of an exaggeration. There is some fluff that can be cut from the article including some in the section you mentioned. I will defend some of it though. First, the part about B and H is critical for the reason that some people will come in expecting B (with H in a separate article) while others will come in expecting the reverse. It is important that we deal with this as soon as possible, in my opinion.

Further I would argue that the first two sentences of the next paragraph are the most important since it sets the tone of the article as being a technical one (that is still accessible). The fact that iron filing (approximately) trace out the magnetic field is essentially useless in explaining what the magnetic field is. The part about field lines being 'imaginary' doesn't belong in the lead, IMO, but there is at least one person with a strong belief to the contrary. TStein (talk) 21:28, 6 December 2010 (UTC)

Tstein, You mean there are people who would come to this article to read about 'magnetic field' but who would have a problem if the distinction between B and H were not mentioned in the introduction? At the end of the day, a magnetic field is a magnetic field, and the reader first needs to know the basics, at least as far as anybody knows the basics. Those basics are that it is a solenoidal force field which is induced by an electric current. Ferromagnetism causes a bit of a puzzle, but there is a general consensus that it is rooted in some kind of circulation/spin/angular momentum at atomic level. A magnetic field is manifested by virtue of attraction, repulsion, deflection, or by a mutually aligning torque. There is also the force which is induced when a magnetic field changes, as in time varying EM induction. Beyond that not much more is officially known about the root causes. It is largely an experimentally observed phenomenon which is given full mathematical formulation in Maxwell's equations. I'm sure a shorter and more coherent introduction could be achieved. David Tombe (talk) 00:47, 7 December 2010 (UTC)

I hope that I am not just repeating myself, but I still strongly support keeping the statement about there being two fields (B and H) that can be called a magnetic field it is a very important disambig. (In my opinion they need to be separate articles, but this will have to do.) Further, it is short and easy to understand and there is plenty of much worse stuff in the lead. As a side note, I disagree with the use of the term solenoidal in the lead. First of all the H-field need not be solenoidal. (It isn't solenoidal for the common case of a permanent magnet and in almost all physical (non-infinite) cases.) Second, you could easily understand the vast majority of information about the fields without knowing what the term solenoidal means.

I agree that we should be able to make the lead leaner (at least for the next month or so before it gets bloated again.) The third paragraph is in my opinion the worst. We may be able to simplify it to two sentences. I have tried a few things but none of them felt right so I didn't save them. I am going to try some ideas here in a little bit. TStein (talk) 14:36, 8 December 2010 (UTC)

I think it would be possible to trim the second and third paragraphs a bit (more the third) and merge them together such that the general layout is the definition of magnetic field in the first paragraph (sources and what it does), how the magnetic field is represented in classical & nonclassical physics in the next paragraph, and summary of historical importance and uses in the last. I might try some cutting and rearrangement along those lines.

Two additional thoughts: 1) I agree with TStein that we keep a statement about the two fields. I'm curious what the rationale is for not having two separate articles. Was this discussed previously, and is the single article a result of consensus? I could see some of the awkwardness in the article and the lead being simplified if there were two separate pages. 2) Would it be appropriate to mention magnetic monopoles (and experimental lack thereof) in the lead in the discussion about sources of magnetic fields? --FyzixFighter (talk) 18:07, 8 December 2010 (UTC)

I can see your point about merging the first two paragraphs and I think that David would agree. Based on my reading habits, though, my main concern is the length of the paragraphs and trying to link all of these very disjointed concepts. Personally, six short paragraphs are much easier to read (in the lead) then three long paragraphs.

I disagree with magnetic monopoles being in the lead. It is curious but not necessary to understand the magnetic field and David is right about the lead needing to be trimmed of fat. TStein (talk) 19:59, 8 December 2010 (UTC)

FyzixFighter, I'm totally amazed that you think that there should be separate articles for two sides of the same equation. We have the equation B = μH. It's actually one of the original Maxwell's equations in his 1873 paper, and yet you are curious about the rationale for not having separate articles for B and H?

It's quite simple. Apply an E field to material and we get a D field inside the material. D = εE, and that is one of Maxwell's original equations. Likewise, apply an H field to material and we get a B field inside the material. B = μ₀(H + M).

M of course, just like P in electrostatic polarization, is a later concept subsequent to Maxwell's papers of the 1860's. Once you understand A, B, H, M, D, E, and P you will realize that we don't need separate articles for B and H. David Tombe (talk) 19:17, 8 December 2010 (UTC)

I agree that we don't need separate articles. I am sorry for bringing that up. TStein (talk) 19:47, 8 December 2010 (UTC)

The B field and the H field

Tstein, Very well, let's then discuss the issue of B and H. I have in front of me a modern textbook called 'Electromagnetism' by I.S. Grant and W.R. Phillips. It confirms the relationship between B, H, and M that appears in the main article here. However, reading on, it also confirms my long standing belief that the relationship between B and H issue, in most cases, is nothing less than a straight B = μH where μ is the product of the relative permeability and the permeability of free space. In other words, B is analogous to D in electrostatics. When a material is magnetized, the magnetic field inside it, B, is equal to the applied magnetic field H (analogous to E in electrostatics) multiplied by the permeability.

In electrostatics, we never expect the linear polarization to be in a different direction from the applied E. In magnetization however, there may be an ingrained ferromagnetization which means that the final magnetization is not aligned with the applied H, and so in this respect magnetization is somewhat more tricky.

But I do not see two topics here. I see one topic. The topic is 'magnetic field' and the sub-topic is magnetization in material mediums, and that involves the use of three parameters, B, H and M. That does not mean that we have two different magnetic fields requiring two different articles.

We do however need a section on magnetization which clearly lays these inter-relationships out. That section could be vastly simplified, based on what I have said above. It could read something like the magnetic field B inside a material is the sum of the applied field H and the internal magnetization M. Hence B = μ₀(H + M). What else could we need? David Tombe (talk) 15:58, 8 December 2010 (UTC)

Yikes! I apologize for opening this can of worms. I am not trying to split the article into B and H. That battle has already been fought and I definitely don't want to fight it again and again.

I would argue that the most common case is that B = μH is NOT valid. It is automatically incorrect for any magnet that has a pole for example. (If it has a pole then H has a divergence.) Therefore it is not valid for any 'permanent' magnet or finite sized electromagnet with an magnetic core. It is approximately valid for a linear material if it forms a loop. It can be assumed to be valid in magnetic circuits even when there are air gaps (that definitely have poles) because the quantity of interest is not H but a line integral around the loop of H. (A similar thing happens with electric fields and EMF-the electrostatic E field that is needed to push the charge around is completely ignored.)

I highly recommend Grifith's to understand the difference between B and H. For example on page 273 he states: 'Only when the divergence of M vanishes is the parallel between B and μH_o faithful.' Then on page 276 he states that this defect is not fixed with a linear material because the divergence of M becomes infinite at a boundary. (See demagnetizing field for a better explanation.)

Perhaps I am being overly technical. I have spent a lot of time looking up the relationship between B and H because the inconsistencies of B = μ_o(H + M) with B = μH drove me up the wall. For example, if B = μH were true then the divergence of B would be infinite at the poles. Perhaps, I skewed the article too much to explain this. Not everybody would be driven as crazy by it as I was. On the other hand, it is relevant to understanding articles like the aforementioned demagnetizing field.

I will see what I can do to simplify the magnetization section further. I have never truly been in favor of the magnetism section either. More precisely I don't like how it doesn't integrate well with the article. TStein (talk) 19:37, 8 December 2010 (UTC)

Tstein, I see your point now. You are looking at the apparent inconsistency between B = μ_o(H + M) on the one hand and B = μH on the other hand. Well of course B = μ_o(H + M) will only ever simplify to B = μH in the special case when H and M are aligned. So it's probably best that we use B = μ_o(H + M) as being the more general case. Do you have a problem with the special case where H and M are aligned?

As regards poles, remember that there are no magnetic monopoles. Magnetic field lines will always close on themselves. DivH and DivB will always be zero.

And one final point. Can you by any chance give me a case scenario in which the magnetization M will not be exactly aligned with the applied H field? If we apply an H field across a non-aligned ferromagnetic material, this will cause a torque which will lead to an alignment. Prior to the alignment being reached, obviously M and H will not be aligned. But I would have taken it that B = μ_o(H + M) applies to the static equilibrium situation. Perhaps if a third force were to prevent the ferromagnetic material from aligning, then we would have a non-aligned case scenario. But in that case, the internal dipoles would be aligned as per the resultant of the two H fields. One applied H field and one H field from the ferromagnetic material. Can you elaborate on any of this? David Tombe (talk) 21:27, 8 December 2010 (UTC)

I may have explained my thoughts wrong above. I will try to better explain it here. If B = μH in a magnet and B = μ_oH outside the magnet then either H is different inside and outside the magnet or Guass's law for magnetism is violated across the pole. The former is of course true. Depending on the relative size of μ and whether it is para or diamagnetic H_inside can be in the same or opposite direction to either B or M but it is definitely different than H_out and both of them may be different than the H_applied. My problem with B = μH is that it should be B = μH_inside when most people, including myself wrongly above, interpret it as B = μH_applied. (The problem with using H_inside is that it is hard to get while H_applied is easy. Demagnetizing factors can help get H_inside from H_applied but it is non-trivial.)

That being said, I am coming more and more to appreciate your point of view. I have skewed the article too much to deal with this subtlety. I am starting to try and bring it back without taking it too far in the other direction. It may take a while. Some of the sections will require some though. TStein (talk) 21:57, 8 December 2010 (UTC)

Tstein, This is certainly a tricky subject. So let's take it very slowly, one piece at a time. I want you to look at your statement,

If B = μH in a magnet and B = μ_oH outside the magnet then either H is different inside and outside the magnet or Guass's law for magnetism is violated across the pole. Tstein

Certainly, H will vary throughout space. But B = μH is merely giving the relationship between B and H at a specific chosen point in space. Hence inside the material, B will become substantially different that outside the material, because the relative permeability changes. But as regards H, I can't see any variations as between inside or outside the material, other than those related to the function which determines H. And of course it will be a solenoidal function. I don't see where you see a violation of divH = 0. David Tombe (talk) 10:54, 9 December 2010 (UTC)

We are arguing in circles, when I am not sure it is relevant. divH = - divM but divM is non-zero at the poles where the magnetization ends or begins. Further, B cannot be substantially different inside than outside of the magnet and remain solenoidal. This is reflected by the boundary condition that B_perp-in = B_perp-out which means that μH_perp-in = μ_oH_perp-out. This guarantees that H_perp-in cannot equal H_perp-out unless μ=μ_o or H = 0. The end result is that H has a solenoidal part due to the free current and a conservative (definitely not solenoidal) part due to divM at the poles. This second part is called the demagnetizing field.

In any case, though, I do agree that this article emphasizes this too much. I am still working to better integrate the two. I think that in the end, we will both be pleased by the result. Further, it is obvious, since all my above explanation is in the article, that it needs not only a shorter explanation but a better explanation as well. TStein (talk) 17:41, 9 December 2010 (UTC)

TStein, I see what you are saying now. M ends abruptly at the boundary of the material and so it cannot be solenoidal. Let's see now if we can solve this riddle. But first of all, let's distinguish between magnetization M as an induced effect of an applied field on the one hand, and the source magnetization that exists in a ferromagnetic material on the other hand. And let's first of all concentrate on the non-ferromagnetic materials. In the non-ferromagnetic materials, M is in many ways analogous to P in linear polarization. It is an effect which is induced by an applied field. E induces P, while H induces M. M is not therefore a magnetic field as such, but rather an effect of a magnetic field, just as linear polarization is an effect of an electric field. H is the actual magnetic field, and H is solenoidal. B will also be solenoidal, because since it is equal to μ_o(H + M) it will close on itself as per H, whether or not M disappears along the line.

So perhaps we ought to alter our language slightly. Rather than talking about B and H as being two distinct magnetic fields, we should maybe be talking in terms of B and H being two distinct vectors which are used in the mathematical analysis of a magnetic field. David Tombe (talk) 19:25, 9 December 2010 (UTC)

The article intro says "There are two separate but closely related fields to which the name 'magnetic field' can refer: a magnetic B field and a magnetic H field." This is correct, clear, and consistent with reliable sources, and I emphatically oppose David's suggestion to imply that B and H are somehow two aspects of just one "magnetic field". "Field" means vector field or quantum field, it does not mean "phenomenon". Maybe you could argue that there is just one "phenomenon of magnetism", but you cannot say that there is just one "magnetic field".

If the field lines of M and H end, then M and H are not solenoidal vector fields. There is nothing subtle or tricky here, it's very simple. M and H are not solenoidal, and the equations div M=0 and div H=0 are false equations (false in general, true only under restricted circumstances). This is clearly explained in every textbook on magnetism, and certainly we should not say otherwise the article. --Steve (talk) 23:10, 10 December 2010 (UTC)

Steve, At the moment, I am specifically focusing on magnetic induction scenarios, and not permanent magnet scenarios. In induction scenarios, the H lines never end. As for M, it is only an induced effect of the H field inside a medium. The magnetic field is solenoidal. H is the magnetic field, and I can think of no induction situation in which divH is not equal to zero. B is the magnetic induction field (or magnetic flux density), which arises from the sum of the magnetic field H and an effect M which is induced by the magnetic field H, such that B = μ_o(H + M).

However, if we move on to permanent magnets, it becomes a different ball game. The magnetization then takes on the role of a kind of magnetic source charge. So the first thing that we need to do is to segregate these two issues. At the moment, we have a section on permament magnets, yet some of the material in the section above it also refers to permant magnet scenarios where there is no applied H field. This all needs to be tidied up. David Tombe (talk) 23:44, 10 December 2010 (UTC)

David -- I want to be clear. I just stated a fact which is the universal consensus of modern physicists and engineers. "div H = 0" and "div M = 0" are false equations when there are permanent magnets present, they are false equations when there are paramagnets present, they are false equations when there are diamagnets present. I was not trying to enter into a debate on the merits of this issue. I have no interest in that, sorry. --Steve (talk) 01:12, 11 December 2010 (UTC)

Steve, I see what has happened. We are all agreed that B = μ_o(H + M) for induction scenarios. However, if we reverse cause and effect and consider a permanent magnet, one might expect that we should at least reverse the sign on the magnetization term M. But the textbooks don't seem to do that. They apply exactly the same equation. The result is that the H field, being only a mathematical tool used for analysis, reverses directions inside the magnet, hence giving rise to fictitious magnetic monopoles at each end of the magnet. Forget about what I just said there about reversing the sign of M. I have now striked it out. Let's accept that B = μ_o(H + M) holds for both induced magnetization and source magnetization. The bit that I am interested in is where the magnetic H field reverses its direction inside a permament magnet. I checked Grant and Philipps again, and this fact is rationalized on the basis that if we do a line integral on H which goes through the magnet, the result will be zero. From this they reason that the H field's direction must be reversed inside the magnet, giving rise to magnetic monoploes at each end of the magnet. This seems to be a case of Ampère's circuital law with a zero current. Yet, to me it would appear that there neverthless must be a magnetization current involved. So I have my doubts about this reversal of the H field. Can you show me the mathematical function (Biot-Savart law equivalent) for such an H field which reverses directions inside a permanent magnet giving rise to fictitious monopoles poles at each end of the magnet? At any rate, the actual physical magnetic field is solenoidal, and so if there are any situations in which divH is not equal to zero, then it follows that the divergence of one of the other two terms in the equation must be the negative of that non-zero value, such as to exactly cancel with it. It seems to me that all of this is an issue of mathematics which is being given far too much emphasis at the expense of obscuring the physical picture. David Tombe (talk) 11:17, 11 December 2010 (UTC)

segregating induced magnetization from source magnetization

Based on the above discussions, it is clear that we need to have a section on 'induced magnetization', and a section on 'source magnetization'. The latter will be about permanent magnets.

It would seem that the equation B = μ_o(H + M) is ideally suited to 'induced magnetization'. In modern textbooks, the vector B is introduced first, often defined through F = qv×B. Then they introduce induced magnetization M. And finally they introduce H. However, there is never any attempt to hide the fact that H is the driving force, and that it is analogous to E, and historically, H came first and Maxwell's papers use μH. It should also be remembered that when we use the equation B = μ_o(H + M) it is only a broad macroscopic equation which deals in averages and simplifications. Molecules are considered to be rotating dipoles which all align in sympathy with the magnetic field.

Permanent magnets are a different topic because the magnetization is the actual source of H.

And as regards the dilemma that divB = 0, whereas M, which is part of the B function ends abruptly at the boundaries, this is not a problem. The M lines may end, but they don't end at sources or sinks. They just end. They are solenoidal where they exist, in sympathy with the H lines.

And finally, the idea of two magnetic fields, B and H, should be dropped. There is one magnetic field and the vectors B and H are both used in the analysis. David Tombe (talk) 12:04, 10 December 2010 (UTC)

"Molecules are considered to be rotating dipoles which all align in sympathy with the magnetic field." But what about diamagnetism? Extremely small electron eddy currents are produced in atoms of a diamagnetic material when brought towards a magnetic field, and this is obvious when dealing with superconducting materials. The result of diamagnetism is not attraction, but repulsion, upon approach. Perhaps the only way to overcome diamagnetism to allow for paramagnetism in materials in general is to switch the field on and off at a rate much quicker than the time it takes to develop the extremely small electron eddy currents, which is relative to the inductance/resistance time constant of charge circuits in atoms. Such a time constant, due to the tiny size of each atom, is ridiculously small, and thus it is not possible that atoms, except those with paramagnetism or ferromagnetism, generally possess magnetic attraction towards magnetic fields.Kmarinas86 (Expert Sectioneer of Wikipedia) ^{19+9+14 + karma = 19+9+14 + talk = 86} 20:15, 10 December 2010 (UTC)

Kmarinas86, Diamagnetism is of course yet another topic. In my suggestion for segregation, I was really only thinking about a segregation as between paramagnetic and ferromagnetic induction on the one hand, and permanent magnets on the other hand. Feel free to write what you know about diamganetism in the article, but make sure you keep it in a separate section if such a section hasn't already been started. David Tombe (talk) 20:59, 10 December 2010 (UTC)

I am strongly opposed to almost everything David is saying here. The equation B = μ_o(H + M) is not "ideally suited" to one thing or another, it is a universally true equation for any macroscopic system, including ferromagnets, diamagnets, paramagnets, or whatever. We should not imply that it is something restricted to certain applications. And we should not draw distinctions between "induced magnetization" and "source magnetization" unless that distinction is in the literature. (If it is, I haven't ever seen it, at least not the way David describes it.) --Steve (talk) 00:20, 11 December 2010 (UTC)

For it to be a "universally true equation" would prohibit limiting its validity to macroscopic systems.Kmarinas86 (Expert Sectioneer of Wikipedia) ^{19+9+14 + karma = 19+9+14 + talk = 86} 18:02, 11 December 2010 (UTC)

Steve, the distinction is quite basic. We can have magnetization as caused by an external magnetic field. That topic is known as 'magnetic induction'. On the other hand, we can have a magnetic field caused by an alignment within a ferromagnetic material. That comes within the topic of permanent magnets. There is no induction involved in the latter, and both of these topics are in the literature and discussed separately. They are two reciprocal topics, and it merely confuses cause and effect if we try to mix them together in the same section. As regards 'induction', the equation B = μ_o(H + M) refers to the fact that within the material there will be an induced magnetization, and that the vector B is connected to the sum of the applied H field and the induced M field. As regards a permanent magnet, the magnetization is actually the source of the magnetic field. So even if we have one section to deal with these two reverse scenarios, we at least need to get the chronology correct and make it clear when have have moved on from talking about 'induction' to talking about permanent magnets where there is no applied field involved. David Tombe (talk) 00:44, 11 December 2010 (UTC)

Because B only makes sense in terms a point in space and time, the equation should really express itself as B(x,y,z,t) = μ_o(H(x,y,z,t) + M(x,y,z,t)), if using rectangular coordinates for example, and thus M(x,y,z,t) is the magnetization at point (x,y,z) at time t, and H(x,y,z,t) is the background magnetizing field at point (x,y,z) at time t. These are instantaneous. It is not as though H(x,y,z,t) causes M(x,y,z,t). You can say that H(x,y,z,t) allows M'(x,y,z,t) to be non-zero, such that it affects the difference between M(x,y,z,t+α) and M(x,y,z,t-α), where α is some arbitrarily small positive real number. Induced magnetization is what you talk about when you speak of generating a magnetic field. This implies a change between two different times. What is left when the magnetic field is not being generated anymore is the remanence, which you cannot simply refer to as the "M field". To find the remanence, you remove the H-field (possibly a bar magnet) at time t, making H(x,y,z,t) effectively 0.

Of course, if you have two permanent magnets, the one outside the borders of the page could be treated as the source and sink of the H-field, and the one inside the page could be treated as the block in which the M-field resides. But interestingly enough, that permanent magnet outside the page can easily have its own M field. This further emphasizes the need to treat B, H, and M as intensive properties, not extensive properties (see Intensive and extensive properties).

The distinction between H and M can be simplified the following way:

• The source and sink of H(x,y,z,t) is a set of points.
• The source and sink of M(x,y,z,t) is point (x,y,z).

Kmarinas86 (Expert Sectioneer of Wikipedia) ^{19+9+14 + karma = 19+9+14 + talk = 86} 15:30, 11 December 2010 (UTC)

Kmarinas86, The scenarios which we have been discussing are all frozen in time. The issue of inducing actual magnetic fields and time varying magnetic field would normally come in the next chapter. The magnetization which we have been talking about, and which we have been using the symbol M for, has been exclsuively about the alignment of the dipoles within a material, and not about the actual magnetic fields themselves. I think we have now identified the root of the controversy. It is with regard to the issue that the H field reverses its direction inside a permanent magnet, giving rise to magnetic H field monopoles at each end of the magnet. The reasoning for this seems to be that Ampère's circuital law, when applied through a permanent magnet does not have a source current. If we accept that argument, then H will indeed reverse and we will have magnetic monopoles. But these magnetic monopoles will only be a mathematical construct with no relationship to the actual physical magnetic field which is always solenoidal. And besides that, I don't understand why the above argument neglects the source magnetization current. David Tombe (talk) 17:01, 11 December 2010 (UTC)

An M-field is basically a microscopic H-field unit with an extremely small range beyond the source magnetization currents, which themselves are smaller than the magnetic domains. The shape of the M-field is basically the sum of all such units. This is why the M-field has the appearance of terminating at both ends of a bar magnet, which is merely due to the simplifying use of the M-field concept. In reality, only H-fields exist, but the M-field approximation is still useful physics, considering the uncertainty of the shape of H-fields at atomic dimensions or smaller. Monopoles do not even enter the situation. Also, saying that:

• "The scenarios which we have been discussing are all frozen in time."

....contradicts the latter statement:

• "It is with regard to the issue that the H field reverses its direction inside a permanent magnet, giving rise to magnetic H field monopoles at each end of the magnet."

....due to latter statement's need to imply a movement, which obviously cannot be described as "frozen in time".

Kmarinas86 (Expert Sectioneer of Wikipedia) ^{19+9+14 + karma = 19+9+14 + talk = 86} 17:48, 11 December 2010 (UTC)

Kmarinas86, The microscopic details of magnetization are not altogether clear. As in all matters when we penetrate inside the dark and dirty jungles of atomic and molecular matter, we need to do alot of second guessing, and that of course leads to many varying opinions. The purpose of the equation B = μ_o(H + M) was to by-pass those details and simplify the matter by concentrating on the broader principles. The problem however is, that in doing so, it seems to have led to no end of confusion, in that the maths now seems to have confused the underlying physics. The bit in particular which I would like to hear your opinion on relates to the reversal of the direction of the H field inside a permanent magnet. You will no doubt agree that if we integrate an H field around a loop which goes through the middle of a closed electric circuit, that we will end up with Ampère's circuital law, and we will have a distinct value for electric current in the equation. Can you please explain to me why this should not be so if we replace the source electric current with a permanent magnet. The textbooks argue that there will be no current in the permanent magnet scenario, and they hence conclude that H reverses inside a permanent magnet. This in turn leads to the idea of H lines beginning and ending at the ends of the magnet. This seems to be what is causing all the confusion. Can you explain to me why we could not have the basic Ampère's circuital law for a permanent magnet using a source magnetization current? David Tombe (talk) 14:17, 12 December 2010 (UTC)

Ampère's circuital law#Extending the original law: the Maxwell–Ampère equationKmarinas86 (Expert Sectioneer of Wikipedia) ^{19+9+14 + karma = 19+9+14 + talk = 86} 14:59, 12 December 2010 (UTC)

Kmarinas86, The Maxwell addition to Ampère's circuital law is not the issue here, unless of course you think that 'magnetization current' is what is behind the additional Maxwell term. I do actually believe that, but the conventional belief is that Maxwell's additional term is tied up with conservation of charge. But let's not get side tracked into all that. At the moment we are focused on 'magnetization current', and the question is 'why are textbooks such as Grant and Philipps disregarding the magnetization current in a permament magnet when they are making the argument that the integral of H around a closed loop which passes through a magnet will be zero?'. This is the key point which supposedly turns H upside down inside a permanent magnet, hence leading to the idea that divH does not equal zero at the poles. Can you shed any light on this? It is the issue which is the source of most of the confusion in the topic. [As a historical aside, when Maxwell introduced displacement current in the preamble of part III of his 1861 paper, it did rather look as if he was aiming at a rotatory/magnetization type effect. But it seems that by 1864 he was looking more at a linear polarization effect. Nowadays, the polarization idea prevails in issues to do with dielectric materials, whereas in the vacuum, the idea has changed completely from its historical origins.] David Tombe (talk) 19:58, 12 December 2010 (UTC)

"You will no doubt agree that if we integrate an H field around a loop which goes through the middle of a closed electric circuit, that we will end up with Ampère's circuital law, and we will have a distinct value for electric current in the equation. Can you please explain to me why this should not be so if we replace the source electric current with a permanent magnet." "At the moment we are focused on 'magnetization current', and the question is 'why are textbooks such as Grant and Philipps disregarding the magnetization current in a permament magnet when they are making the argument that the integral of H around a closed loop which passes through a magnet will be zero?'."

Answer: The area of an H loop in a permanent magnet cuts through both sides of each magnetization current loop, not just one. So the currents cancel out. However, if one is nit-picky, one might include the currents at the very edge of the loop which are only cut by the area of the H loop at one side.Kmarinas86 (Expert Sectioneer of Wikipedia) ^{19+9+14 + karma = 19+9+14 + talk = 86} 02:52, 13 December 2010 (UTC)

Kmarinas86, Thanks for answering the question. However, the currents at the very edge of the loop, which do not cancel, are a reality, and we have no way of putting a numerical figure to them. But it only takes that figure to be non-zero and then we have Ampère's circuital law in conjunction with a magnetization current, and hence there can be no basis for the argument that the H field must reverse its direction inside the magnet. This would all tie in with Maxwell's initial hunch that displacement current is a magnetization current associated with a rotatory effect, and also with one of his original equations, B = μH, which appeared in his 1873 paper. But since the modern textbooks have now decided to ignore the magnetization current in a permanent magnet, leading to a claim that H lines inside a permanent magnet are cut out and re-joined upside down, I will depart from this discussion. I can see now exactly what is going on. David Tombe (talk) 00:07, 14 December 2010 (UTC)

Is discussion about whether magnetic fields do work necessary?

I am coming more and more to the conclusion that the following discussion about magnetic fields doing work is irrelevant for this article.

"Because the magnetic force is always perpendicular to the motion, the magnetic fields can do no work on an isolated charge. It can and does, however, change the particle's direction, even to the extent that a force applied in one direction can cause the particle to drift in a perpendicular direction. It is often claimed that the magnetic force can do work to a non-elementary magnetic dipole, or to charged particles whose motion is constrained by other forces, but this is not the case[11] because the work in those cases is performed by the electric forces of the charges deflected by the magnetic field.

I understand that Griffith's and I think earlier texts make a big deal about this. It seems to me that it causes more trouble then it is worth, though. TStein (talk) 17:04, 2 August 2010 (UTC)

The interesting thing about this concept is that it says that that a side acting maqnetic field will change the direction of the path of a moving electrified particle, but not the velocity, and therefor will not do any work. This is opposed to the theory that a side acting applied electrostatic force applied to an electrified particle will add an additional side component of velocity to the particle and thus will do work. However a vector analysis of this situation would not allow the magnetic field side applied force to be absolutely perpendicular to the forward velocity because the resultant velocity would then also be increased as the result of the applied magnetic force.WFPM (talk) 13:29, 5 August 2010 (UTC)

"However a vector analysis of this situation would not allow the magnetic field side applied force to be absolutely perpendicular to the forward velocity because the resultant velocity would then also be increased as the result of the applied magnetic force."

This is incorrect. If the force is always perpendicular to the velocity, then that force will never change the speed. However, if the force you apply does not change with the direction of the particle, only then would you expect that the velocity to change. Because the direction will change with the force applied, the stronger the force applied, the quicker it must rotate to compensate for the deflection it causes, otherwise it will no longer be perpendicular to the motion.siNkarma86—Expert Sectioneer of Wikipedia
^{86 = 19+9+14 + karma = 19+9+14 + talk} 20:54, 22 March 2011 (UTC)

I dunno... I think it is a rather notable point to make, even though I would not say "magnetic field LINES cannot do work" and just say "magnetic FIELDS cannot do work." On the other hand, the important caveats required to make this statement accurate might end up neutering it: first, magnetic fields that cannot do work in one reference frame transform to electric fields in other reference frames that CAN do work, and secondly, this statement is only strictly and unproblematically true in classical physics, as in quantum physics it's not so clearly the case (as far as I'm aware... though of course, what is analogous to work in quantum mechanics sometimes becomes problematic too! Nonetheless, I think that there are enough situations in quantum mechanics where work can be reasonably defined that violate this).

So basically, the statement is: classically, magnetic fields cannot do work, though this principle does not hold at all in relativity or quantum mechanics. If that distinction is too technical for an article such as this one, then this property of magnetic fields may need not be mentioned.--Scyldscefing (talk) 21:59, 23 September 2010 (UTC)

Tstein, I would agree with you that that paragraph badly needs to be tidied up, as it contains some serious inaccuracies. It's true that in the particular case of a charged particle moving in a steady state magnetic field, that it moves with uniform speed in a helix, and that as such, no work is done. But it is not true in general that a magnetic force does no work. The F = qv×B force does have a Lagrangian which is given by the A.v dot product, where A is the magnetic vector potential. And on this web link here at equation (8), [4] the author has unusually decided to write the F = qv×B force in terms of the gradient of the Lagrangian expression. And at any rate, we know that work is done when two magnets repel each other. David Tombe (talk) 11:27, 21 October 2010 (UTC)

My main objection is not that I think that magnetic fields can do work. (Right now I am leaning toward Scyldscefing's position, but it is hardly a thing that I am an expert on or think about much.) I was hoping that the question was irrelevant enough that I can ditch it altogether. Sadly, I must confess that a good portion of my motivation behind that hope was that I didn't want to deal with any controversy. The potential for good articles to be ruined by squabbles over details like this is too high for my comfort. Like you I find the A⋅v dot term in the Lagrangian to be compelling. (On the other hand A is also a source of electric field.) I am more troubled by the magnetic torque on a dipole. I see a lot of good arguments on both sides, though. I wish I had time to sort through ALL of the subtleties. There are just too many other things that I think are more important. TStein (talk) 19:35, 21 October 2010 (UTC)

Static magnetic fields do no work, they simply rotate the direction of motion of the particle. That's obvious from the equation. However, dynamic magnetic fields do do work, as in an electric motor. However, even then, the magnetic field still doesn't actually do the work; that equation is absolute. What happens is that the changing magnetic field generates an electric field and that electric field does the work.Rememberway (talk) 22:04, 21 October 2010 (UTC)

A paperclip gets lifted up by a bar magnet. How is the magnetic field not doing work? Well, maybe there's some technical argument..."really it's ultimately the electron kinetic energy in the bar magnet that does work", or whatever it is. But isn't it sort of obscure trivia? One indication that it is obscure trivia is the fact that I can't find any reliable source that goes through a quantum-mechanical example (like bar magnets lifting paper clips) in detail. Therefore I say we shouldn't make a general statement. We should only say that a magnetic field cannot change the speed of a classical point charge...an important point that every textbook explains and everyone agrees on. --Steve (talk) 22:56, 21 October 2010 (UTC)

It's easier and more to the point to understand what happens in an electromagnet attracted to a magnet, in that case the energy to raise up/accelerate towards the magnet comes from the circuit for fairly obvious geometric reasons. I think that for a paperclip it's related to the magnetocaloric effect, so the energy comes from the thermal motion, but my Feynman is in my other jacket.Rememberway (talk) 02:42, 22 October 2010 (UTC)

"What happens is that the changing magnetic field generates an electric field and that electric field does the work."

-Changing magnetic fields can only lead to work along magnetic field lines if there is an external electric field to interact with: A translating or growing magnetic field may lead to electromagnetic induction, such as what occurs when a magnet passes a closed copper loop, or when a transformer is being operated. However, if we only pay attention to first-order effects, the electrical forces produced by a changing magnetic field exist only at a right angle to the magnetic field lines, which does not allow work to be done up and down the magnetic field lines. If these first-order effects interact with external electric fields, only then may that cause acceleration along the magnetic field lines.

-Electromagnetic induction is biased in favor of magnetic forces which reduce the relative motion of magnets: If the magnets are not allowed to grow in strength but are allowed to translate, the first-order effect will be electromagnetic induction, but without a good conducting loop in the vicinity, just other matter, then this effect is small and is known as diamagnetism. The electromagnetic induction actually serves to change the magnetism of objects it interacts with. In fact, this electromagnetic induction only serves to slow down the magnets. It cannot speed them up regardless of what direction it is headed. Thus it cannot explain magnetic attraction upon approach nor magnetic repulsion upon leave. For ferromagnets, the magnetization is left pretty much unchanged whether the magnets are brought together, separated, or kept at a fixed distance. Diamagnetic effects are orders of magnitude weaker.

-Work is not needed to cause acceleration of magnets anyway: In reality, no "work" is necessarily involved in causing magnets to accelerate. All you need to have is deflection of pre-existing charge motion in such a way that they gather towards a net direction. The magnetic attraction of charges is not what changes the speed of the charges; they are only capable of deflecting charges, yet that is sufficient for explaining why permanent magnets attract or repel.

-How magnets can accelerate even when all the forces are at right angles to the path of their constituent particles: The condition required for this to occur is that charges are deflected from one magnetic field line to the next, on and on, until they find a magnetic field line that they are parallel to. The background electric field may be involved in that process. Because magnetic field lines are not straight, each charge will end up running into a magnetic field line that is it not parallel to. They will do this periodically, and as a result, they will travel in straighter paths along magnetic field lines and more curled paths when traveling across them. Depending on the sequence of magnetic fields lines intercepted by a charge, their orientation, and their polarity, acceleration may occur along the magnetic field in a preferred direction (i.e. towards or away from another source of magnetic fields). In the absence of a background electric field, redirected motion down a set of magnetic field lines is only possible if these field lines are not strictly parallel; otherwise, the magnetic field may only cause motions within a single plane. This allows attraction and repulsion forces to occur between magnets even when they are held in place and maintained at the same strength.siNkarma86—Expert Sectioneer of Wikipedia
^{86 = 19+9+14 + karma = 19+9+14 + talk} 23:48, 21 March 2011 (UTC)

Steve, Of course you are correct in observing that a static magnetic field can do work. And we know that v×B is the grad of the A.v Lagrangian. What we need to ask is why do some people think that a static magnetic field can't do any work. The reason is that they point to the fact that a charged particle moving in a static magnetic field maintains a constant speed. But the same could be said about a circular gravity orbit. We all know that gravity can do work, but that in the special case of a circular orbit, it is not doing any work and the speed remains constant. Likewise with the v×B force when it is acting as a centripetal force in a circular motion. But that doesn't mean that in general the v×B force does no work. Anyway, I will now reduce the paragraph to a statement of fact which is not in dispute and which avoids the issue of work done. David Tombe (talk) 23:43, 21 October 2010 (UTC)

This article has an interesting perspective. This issue comes up in Appendix B on page 49. Count Iblis (talk) 03:13, 22 October 2010 (UTC)

Count Iblis, thanks for supplying this interesting paper. I checked out page 49 and the author certainly raised the relevant issue. Why does a magnetic force do no work when a charged particle moves in a magnetic field, when we all know that it can do work in general. The problem of course was never about how the work would be done, because we know that there is a potential energy given by the A.v scalar. The problem was more one of why no work is done in the special case of a charged particle moving in a static magnetic field. The solution is a helix with constant speed. Likewise with gravity, no work is done in the special case of a circular orbit, even though gravity in general does work. The only difference between the gravity orbit and the v×B orbit is that the gravity orbit could be an ellipse, a parabola, or a hyerbola, whereas the v×B orbit is always a circle/helix. David Tombe (talk) 12:24, 22 October 2010 (UTC)

The example you're giving of gravity and a stable closed orbit vs. any other trajectory is not analogous to what we're discussing here. In purely CLASSICAL cases, it's absolutely true that static magnetic fields do no work, and even in the case of time varying magnetic fields it's really the current or time-varying electric field that's doing the work. As I said above, it's only in relativity and quantum mechanics(?) that magnetic fields can do work.

There are no cases in classical physics in which a magnetic field can do work, unlike with gravity. Now if you want to call classical physics a "special case" of more generalized formulations of physics, I'll buy that I suppose. But in classicla physics, magnetic fields CANNOT do work, whereas there are a subset of orbits in which gravity DOES NOT do any work. I think that's a substantial difference.Scyldscefing (talk) 22:44, 26 January 2011 (UTC)

So many are led to believe that whole magnets perform work because whole magnets are seen as accelerating along the path of motion. However, the very essences of these magnets, the subatomic particles, only need to have their motions partially-deflected toward a common direction to explain the collective motion. The magnetic force is always at a right angle to the motion of a particle, so magnetic fields merely deflect energy. Magnetic forces do not and cannot change the speed of charges. Yet magnetic fields by themselves can explain how a large mass "accelerates". With magnetic fields already provided in the system, no "work" is involved in converting subatomic kinetic energies to a visible kind of kinetic energy common to everyday experience.siNkarma86—Expert Sectioneer of Wikipedia
^{86 = 19+9+14 + karma = 19+9+14 + talk} 04:12, 3 March 2011 (UTC)

Field Lines

Could someone please explicitly confirm somewhere appropriate whether or not the 'field' between the field lines (as seen typically eminating from a bar magnet/iron filings demonstration) is zero. If the 'field' between the lines is not zero, could someone please explain why the filings arrange themseles in lines instead of a gradated 'spread'?

Field lines are only a graphical technique for visualizing vector fields like the magnetic field. In a drawing of field lines the lines are only intended to represent the direction of the magnetic field at "typical" points. The assumption of such drawings is that there is nothing "special" about the points on the lines, and the field is "smoothly varying" and has an equal strength at points between the lines as on the lines.

When iron filings are sprinkled on a paper in a magnetic field, they tend to clump together and form "strings" that follow the direction of the magnetic field, so they look like field lines. The filings are mostly shaped like tiny needles (that's why they use filings, not iron powder). In a magnetic field they acquire an induced magnetization, with a N pole at one end and a S pole at the other. The external field exerts a force on them that tends to turn them to align with their long axis parallel to the field, like compass needles. Since they are magnets they attract one another. When they hit the paper they don't stay spread out evenly but clump together in strings with their ends oriented N to S, N to S. So the "lines" that can be seen in a pattern of iron filings over a magnet are not a feature of the underlying magnetic field, which is "smooth" and has an equal strength between the lines as on the lines. They are a random result of the attraction of the filings when they are sprinkled. --Chetvorno^TALK 11:28, 12 March 2011 (UTC)

Comment

Good job on the comprehensive article. Very informative, indeed. —Preceding unsigned comment added by 129.97.120.139 (talk) 06:09, 6 April 2011 (UTC)

B-field and H-field are not two different fields

This article makes a major mistake right in the introduction. B-field and H-field are not two different fields they different descriptions of the same field...a magnetic field. —Preceding unsigned comment added by 67.241.83.46 (talk) 01:24, 12 April 2011 (UTC)

"Field" is a technical term with a specific meaning: In this case, it means vector field. A vector field is a mathematical function whose domain is the points in spacetime, and whose range is the set of vectors in 3D Euclidean space. Two fields are "the same field" when the functions are equal. We agree, I hope, that the equation B(r) = H(r) is generally false. Therefore B and H are not "the same field". Instead, since B≠H, they are "two different fields". Two different mathematical functions means two different fields.

But there's a different statement you can make: "B-field and H-field are different descriptions of the same phenomenon". I actually agree with this statement (more or less). Certainly, there is only one "magnetism phenomenon". Nobody would ever argue, "This refrigerator magnet is held up by B-field magnetism," ... "No I disagree, it's held up by H-field magnetism!" They just say, "It's held up by magnetism!" :-)

If you think the article gives the wrong impression, implying there is "B-field magnetism" and there is "H-field magnetism" and they are different phenomena, then we should certainly edit it to be clearer! :-) --Steve (talk) 05:21, 12 April 2011 (UTC)

Exactly. The key to the difficulty in my opinion is that the terms 'magnetic field', 'magnetism', and 'magnetization' are nebulous and mean essentially the same thing to someone who hasn't studied them. Yet, they have very precise and very different meanings. Part of the problem is that all three of these terms can be used for the general "phenomenon of magnetism" for which there is no agreed upon name as far as I am aware.

To me the sentence in question is adequate as it stands. I agree with Steve, though, that if it truly causes confusion and if there is a simple fix that doesn't cause its own set of problems, then lets get it done.TStein (talk) 22:12, 12 April 2011 (UTC)

Currents vs poles

In Magnetic_field#Magnetization, there is the following quote: "The physically correct way to represent magnetization is to add all of the currents of the dipole moments that produce the magnetization," implying that other methods (in particular, representing the magnetization by charges) are incorrect. This view is reinforced in several Wikipedia pages related to magnetism, for example Magnet#Two models for magnets: magnetic poles and atomic currents and Force between magnets, where a magnetic charge model is referred to as the Gilbert model and called "physically incorrect."

This view of magnetization is wrong, for two reasons:

1. The magnetization in hard magnets such as ferromagnets is not carried by currents. It is carried by spin magnetic moments of electrons. At best, in a ferromagnetic conductor like iron, currents might make a small contribution, but it is generally small enough to ignore. There is nothing "physically correct" about representing a magnetic spin by a nonexistent current loop.
2. The Gilbert model is a caricature of accurate models that represent the magnetization by magnetic poles (a description of which can be found in Demagnetizing field).

I do not blame the Wikipedia authors for promulgating this warped view of magnetism because it can be found in a number of respected textbooks on electromagnetism, for example Griffiths (cited in Force between magnets) and even Jackson. However, you won't find it in any textbook that specializes in magnetism. It is a wonder to me that the authors of electromagnetism books have such a blind spot when it comes to magnetism. RockMagnetist (talk) 18:36, 23 July 2011 (UTC)

I agree that current loop model is sometimes incorrect as well, in cases when intrinsic moments of spin predominates. But that does not make magnetic charge view "physically correct"; it is always just a shortcut to solve the problem.—Netheril96 (talk) 00:28, 24 July 2011 (UTC)

Sure. The magnetic charges don't represent real magnetic monopoles, but they are also not representing some deeper reality involving currents. A calculation that makes use of them is accurate to the extent that the magnetization can be represented by a classical field. A thorough discussion of the applicability of the magnetic charge approximation can be found in Magnetostatic Principles in Ferromagnetism by William Fuller Brown. RockMagnetist (talk) 01:33, 24 July 2011 (UTC)

The B-field of a point magnetic dipole is

$\mathbf {B} (\mathbf {x} )={\frac {\mu _{0}}{4\pi }}\left[{\frac {3\mathbf {n} (\mathbf {n} \cdot \mathbf {m} )-\mathbf {m} }{|\mathbf {x} |^{3}}}+{\frac {8\pi }{3}}\mathbf {m} \delta (\mathbf {x} )\right]$

The magnetization is obviously

$\mathbf {M} (\mathbf {x} )=\mathbf {m} \delta (\mathbf {x} )$

Therefore the H-field of a point magnetic dipole is

$\mathbf {H} (\mathbf {x} )=\mathbf {B} (\mathbf {x} )/\mu _{0}-\mathbf {M} (\mathbf {x} )={\frac {\mu _{0}}{4\pi }}\left[{\frac {3\mathbf {n} (\mathbf {n} \cdot \mathbf {m} )-\mathbf {m} }{|\mathbf {x} |^{3}}}-{\frac {4\pi }{3}}\mathbf {m} \delta (\mathbf {x} )\right]$

If you form a magnetic dipole by making a current loop smaller and smaller, but keeping the product of current and area constant, you get a field in the form of the B expression. If you form a magnetic dipole by taking a "north pole" and a "south pole" monopole, bringing them closer and closer together but keeping the product of magnetic pole-charge and distance constant, you get a field in the form of the H expression. (The H expression is mathematically identical to the expression for the E-field of a point electric dipole.)

An electron's intrinsic spin magnetic moment is neither an infinitesimal current loop, nor is it two point poles infinitesimally close together. But the B-field agrees with the former not the latter, while the H-field agrees with the latter not the former. Griffiths takes the view that B is more fundamental and important than H--we can discuss the merits of that separately. But given that he's talking about B, it's absolutely correct to say that the infinitesimal-current-loop model is right and the magnetic-poles model is wrong. The magnetic-poles model gives the wrong coefficient of the delta-function, which has observable consequences (eg the average field inside a uniformly-magnetized sphere comes straight from the delta-function term). Most magnetism books focus on H, and therefore they are completely justified in modeling an intrinsic spin magnetic moment as two close-together poles that source the H-field. Then larger magnetized materials can be consistently treated as having pole distributions in different places, which act as a source for H (but not B). You cannot directly model H using the current loop model for spins.

Does everyone agree with that background? If so, it shouldn't be too hard to rewrite the article in an improved way :-) --Steve (talk) 00:16, 24 July 2011 (UTC)

B-field and H-field are just two ways of description for magnetic field, so I don't get what you were saying.—Netheril96 (talk) 00:33, 24 July 2011 (UTC)

B and H are related but they're certainly not the same: B≠H. What I'm saying is, B always has the mathematical properties of a field generated by current loops...even when it is not literally generated by current loops. OTOH, H has the mathematical properties of a field generated by spatially-separated poles...even though it is not literally generated by spatially-separated poles. (For example, div B=0, but div H ≠ 0.) --Steve (talk) 00:48, 24 July 2011 (UTC)

Steve, your discussion is intriguing, but I think that it is essential to remember that magnetization is a purely classical concept. Looked at closely enough, a magnet is a collection of spin magnetic moments and currents with empty space between them, and in that space $\mathbf {B} =\mu _{0}\mathbf {H} .$ It is only when you start averaging over the moments to get a continuous function of position that the magnetization arises and the two fields are no longer proportional to each other (as Brown discusses in the book I mentioned above). From that perspective, the delta functions (though often useful) are pushing the continuum theory too far. RockMagnetist (talk) 01:46, 24 July 2011 (UTC)

Steve - on second thought, I have decided your discussion is just right for Magnetic moment#Magnetic dipoles, and I have shamelessly expropriated it. I hope you don't mind. RockMagnetist (talk) 22:49, 2 August 2011 (UTC)

Treatments of the magnetic dipole field

I have started a general discussion of the many treatments of the magnetic dipole field at Wikipedia talk:WikiProject Physics#Treatments of the magnetic dipole field. RockMagnetist (talk) 03:11, 3 August 2011 (UTC)

"a small magnet placed inside of a larger magnet..."

"a small magnet placed inside of a larger magnet is twisted in the opposite direction to that expected from the H-field". This is not true. Right now it's tagged "clarification needed", but it should just be deleted because it's the opposite of the truth!

If you put a B-field in free space and a small magnet in the field, it rotates so that the magnetic moment is parallel to the B-field (U=-m⋅B, so potential energy is minimized when m and B are parallel). Inside a bar magnet, the B-field points parallel to the m's inside the magnet, while the H-field points in the opposite direction to the m's. Each unpaired electron in the bar magnet is a little magnet...this electron is "a small magnet placed inside of a larger magnet". The real magnetic force is to flip the m's (see demagnetizing field). So it seems to me that the "small magnet placed inside of a larger magnet is twisted in the SAME direction as expected from the H-field and OPPOSITE as expected from B-field"!! --Steve (talk) 15:42, 12 August 2011 (UTC)

I just removed that statement. If I recall correctly, I inserted that statement based on the torque = mxB and Griffith's statement that it was always correct. I am still conflicted about what the truth is, I trust that the torque=mxB but I also understand about the demagnetizing field. There is some subtlety that eludes me yet; which is highly frustrating. I am coming to see the error of my ways in trusting Griffith's too much in this area. I am working to fix this and other problems. I have always suspected that H would work just as well as B for magnetostatics as long as it was done properly using magnetic charges. I just don't have the proper reference yet. Even the magnetism books that I have that emphasize H use the amperian loops. TStein (talk) 05:53, 8 November 2011 (UTC)

The lead again.

It seems like periodically, the lead needs to be pruned and simplified. I propose the following:

A magnetic field is a mathematical description of the magnetic influence of an electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude (or strength); as such it is a vector field. The magnetic field is most commonly defined in terms of the Lorentz force it exerts on moving electric charges. There are two separate but closely related fields to which the name 'magnetic field' can refer: a magnetic B field and a magnetic H field.

The relationship between the magnetic and electric fields, and the currents and charges that create them, is described by the set of Maxwell's equations. In special relativity, electric and magnetic fields are two interrelated aspects of a single object, called the electromagnetic field tensor; the aspect of the electromagnetic field that is seen as a magnetic field is dependent on the reference frame of the observer. In quantum physics, the electromagnetic field is quantized and electromagnetic interactions result from the exchange of photons.

Magnetic fields have had many uses in ancient and modern society. The Earth produces its own magnetic field, which is important in navigation. Rotating magnetic fields are utilized in both electric motors and generators. Magnetic forces give information about the charge carriers in a material through the Hall effect. The interaction of magnetic fields in electric devices such as transformers is studied in the discipline of magnetic circuits.

Most of my changes are in the first paragraph where I removed the details of what creates the magnetic field. (This has the additional benefit of avoiding saying that a changing electric field creates a magnetic field; it appears in the Maxwell's equations but the Jifimenko equations don't have that term. Further it postpones the debate about whether it is better to represent the magnetization of a magnet using the amperian model of current loops or the magnetic dipole.) I did not change the second paragraph. I only cut a little from the third.

Normally, I would just make the changes, but I know how contentious changes like this can be.

TStein (talk) 21:38, 31 October 2011 (UTC)

Looks like an improvement, but I suggest reinstating a discussion of sources in a fourth paragraph. Here is one possible wording:

Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin. RockMagnetist (talk) 21:58, 31 October 2011 (UTC)

I really like that formulation of the sentence. It addresses all of my concerns above. The question is where to put it. It also probably needs better discussion someplace in the article itself. The only change I would make is to link quantum. TStein (talk) 22:21, 31 October 2011 (UTC)

I made the modification with the addition of replacing the line about Maxwell's equations with the one suggested by RockMagnetist. Mentioning Maxwell's equations in the lede, just doesn't seem as important as it once did to me; plus it has the additional benefit of flowing a lot better now, IMO. I also modified the table about the different names for B and H. I am not trying to force my own view in doing so but am merely experimenting around trying to find something that makes everybody comfortable. My goals were to make it less busy and to not obscure the navbox, which I find personally very helpful. I plan to expand the section about the names (not in the lede) to say something like:

The term 'magnetic field' is historically used to describe a magnetic 'H-field' whereas other terms were used to describe a related magnetic 'B-field'. Informally, and formally for some recent textbooks mostly in physics, the term 'magnetic field' is used to describe the magnetic 'B-field' as well as or in place of H.

Thoughts? TStein (talk) 05:39, 8 November 2011 (UTC)

The lead looks good. I only have one concern - the second paragraph makes it sound like there are two realities (quantum and relativistic) instead of two views of the same reality. Your statement about H and B fields sounds fine to me. RockMagnetist (talk) 06:01, 8 November 2011 (UTC)

Interesting thought about the two realities. We could replace 'in special relativity' by 'as described by special relativity' and remove the 'in quantum mechanics'. The main problem seems to be using 'In x' as a short cut for saying 'x shows that'. On the other hand, this may be a subtle enough of a point that ignoring it might be the best option; being too subtle can sometimes cause more trouble than good. TStein (talk) 06:19, 8 November 2011 (UTC)

Help with resources for current (Amperian model) versus magnetic charge models of the dipole, etc..

I want to contribute this page again, but I need some more resources. (That doesn't cost too much. I teach at a university, but they don't pay near enough to afford to buy books just for a project such as this.) Does anyone have a list of books, papers, etc that can help me get a better understanding of the current model versus the magnetic charge model. I liked the discussion above and have always felt that something like it must be true and have derived some things like it myself. But there are still a lot of questions I have where I don't want to reinvent the wheel.

I have a number of textbooks some of which are magnetic engineering oriented. But even all of the engineering oriented ones use the amperian description of the magnetic dipole. This cause particular problems, because the amperian formulation is designed such that the fundamental field is the B-field; yet these textbooks treat the H-field as being the most fundamental. Worse a lot of them seem to think that the true H-field is just that due to the free currents. The demagnetizing field is treated as something mysterious and an afterthought; rather than being a true source of H. It always drove me nuts that in the absence of an applied magnetic field the demagnetizing field is the field produced by a magnet.

This article still has a mess of confusing issues with regard to the relation between B and H and the magnetic dipole that I would like to address. (To be fair I have created some of these issues myself by being too trusting of Griffiths which is a very good text book in a lot of ways but has some strange and large weaknesses in others. Some of these ways are listed above. I still haven't found anyone else who references a 'Gilbert model'.)

I apologize for the rambling. I am uncertain that anyone can help, but any help would be greatly appreciated. TStein (talk) 22:15, 31 October 2011 (UTC)

I have found it extraordinarily difficult to find a good reference that compares the models. The authors of electromagnetism textbooks, for example Griffiths and Jackson, seem to have a blind spot for magnetism, while books on magnetism mostly ignore Amperian currents except in defining the B-field. The only book I know of that discusses their relation is Brown's book on magnetostatics. All of these are referenced in Demagnetizing field. It would be nice to have some online source, but I don't know of any. RockMagnetist (talk) 22:57, 31 October 2011 (UTC)

Well, I guess I have to pony up for Brown or maybe do an inter-library loan. I will check out your references in demagnetizing field as well. Currently, I don't even have a single book that uses the alternate model using magnetic charges. Maybe if I can find one that does, as in the ones you reference in demagnetizing field, that would be sufficient. Thanks. TStein (talk) 16:17, 1 November 2011 (UTC)

More quantitative

It would be nice if someone can edit more mathematical contents into the article. Right now, it's mostly descriptive. There are only a few sprinklings of equations and very little proofs and derivations. Hopefully, this will make the article more substantive and informative, perhaps raise the rating from B to A.--LaoChen (talk) 00:45, 6 November 2011 (UTC)

We already have a tag saying it's too technical. I have written articles with more equations than this, and they are not very well received. RockMagnetist (talk) 01:22, 6 November 2011 (UTC)

To add to what RockMagnetist said. The question of substantive and informative is a different question than how many equations and derivations is included. It is harder but not impossible to be substantive without equations. Yet in my opinion, it is well worth the effort for an article like this; one that is primarily aimed at people who have little mathematical background. If we have failed to be substantive and informative it is not because of a lack of equations, but because we haven't yet succeeded in the difficult task of explaining a complex physical phenomenon in a way that Feynman's barmaid would understand. Further proofs and derivations are way beyond the scope of this article, its length is already quite large. Such proofs and derivations are better left to the various articles that this article links to. That is not to say that there is NO room for a few additional equations, just that I think we should be very selective about how we use them. TStein (talk) 04:27, 6 November 2011 (UTC)

I agree with what both of you were saying. From the rating received, it's obvious that we have not been able to successfully explain the concept so that those high school students or average readers can learn it without difficulties. I am not sure what can be done to make the article better. Based on the pageview data, this article is very important and definitely needs to be improved. --LaoChen (talk) 06:10, 7 November 2011 (UTC)

Thanks for your input. We are aware of the problems and are working on it, even if the process is slower than we would like. TStein (talk) 15:29, 7 November 2011 (UTC)

Defining H in terms of B

The following paragraph, that I want to drastically trim, is in the Definitions, units, and measurement section.

"The H-field is defined as a modification of B due to magnetic fields produced by material media. See H and B inside and outside of magnetic materials below for the relationship between B and H. Outside of a material (i.e., in vacuum) the B and H fields are indistinguishable. (They only differ by a multiplicative constant.) Inside a material, though, they may differ in relative magnitude and even direction. Often, though, they differ only by a material dependent multiplicative constant."

My question is: is it appropriate to say that the H-field is defined in terms of B. I am coming to the opinion that Maxwell's equations don't say which is more fundamental B or H; only that they are related in a certain way. Is it too subtle of a question to worry about? Perhaps we should punt on this until later in the article by removing that sentence entirely. But then we don't have a definition in the definition section.

I am trying to make this article a little more 'agnostic' in the area of which is more 'fundamental' the H-field (based on magnetic charge dipoles) or B-field (based on amperian current loops). But, this will come close to wp:or which is why I am posting so many changes here before implementing them. TStein (talk) 20:20, 17 November 2011 (UTC)

Some people try to claim either H or B are fundamental, but that just leads to unproductive arguments. How about this:

There are two magnetic fields, H and B. In a vacuum they are indistinguishable, differing only by a multiplicative constant that depends on the physical units. Inside a material they are different (see H and B inside and outside of magnetic materials ).

That doesn't involve any WP:OR. RockMagnetist (talk) 21:24, 17 November 2011 (UTC)

That statement is similar to what I was thinking. The temptation to write something down about how they are related is strong, though.

I don't think that arguing about which is more fundamental (H or B) is unproductive. I have found that that argument and thought-experiments about that argument has helped me to understand the topic and to understand other discipline's views about E&M. I agree, though, that any such debate has to be kept out of the article, where it would be very counterproductive. TStein (talk) 21:42, 17 November 2011 (UTC)

I used your suggestion, but then felt that it should go before where B and H are introduced. After some more reflection, I thought that the definition and measurement section did not need to distinguish between B & H since we are not measuring a magnetic field inside a magnetic material for the most part (any subtlety about whether the Hall effect measures B or H if the material is magnetic is too subtle). Therefore, I moved the introduction of two fields being called magnetic field down. It still seems a little unsettled to me. (I have a strong desire to place the discussion about H being historical magnetic field, etc in a foot note. The only reason I don't is because then we would have a foot note in a footnote, else one really big footnote.) Over all I am happy with it, though. Please let me know or fix it yourself where you disagree. TStein (talk) 22:24, 17 November 2011 (UTC)

Neither field is more fundamental unless if there is a way to express permeability in closed form in terms of one of the fields but not the other. For example, if permeability was a function of H but not B, then that makes H more fundamental than B. Unfortunately, there isn't much said about mathematical models for the origins of permeability, at the level of undergraduate understanding anyway.siNkarma86—Expert Sectioneer of Wikipedia
^{86 = 19+9+14 + karma = 19+9+14 + talk} 02:57, 25 November 2011 (UTC)

You'll find more about the origins in Magnetism. RockMagnetist (talk) 04:04, 25 November 2011 (UTC)

We probably need something about the origins of the magnetic field in this article as well. (There seems to be a fair amount of curiosity and misinformation about what is the 'microscopic' origin of the magnetic field.) But there are so many clean-up issues that need to be taken care of first. Plus, the exact origin of the spin component of the magnetic field is not clear to me. I have heard that it is relativistic in origin but I haven't seen a proof of it. IIRC, the factor of 2 for the ratio of the magnetic moment to the angular momentum is predicted to a large number of digits by QED which suggests that spin has its origins in QED.

I don't buy that H is just as fundamental as B for 3 reasons

1. H needs both magnetic charge and amperian current loops, B only needs current loops; occam's razor
2. H and magnetic charges cannot explain the relationship between spin and angular momentum
3. Amperian loops and the B field explain as a consequence of how they are formed why there are no isolated 'magnetic charges'

None of these reasons make B fundamental, just more fundamental. The fact still remains that electrons are point charges and NOT current loops. Don't get me wrong, I am still planning to make this article more agnostic about which field is more fundamental. As RockMagnetist alluded to above, statements that speak about (or even hint at) whether or not something is fundamental (or physical) have a tendency of causing arguments which are usually as futile and as useless as they are loud. The only reason I bring it up here is that I still don't think I have a great handle on it and if we can keep this discussion civil and on the talk page then it could be quite profitable. TStein (talk) 05:06, 25 November 2011 (UTC)

Snap... Snarl... Must be civil... Howl... aargh... Seriously, though:

1. What do you mean, H "needs" both magnetic charge and amperian current loops?
2. You're taking these magnetic charges too literally. The actual sources of B and H are quantum spins and currents. And while the relationship between spin and angular momentum is analogous to the relation between the magnetic moment of a current loop and its angular momentum, this is in no way an explanation. Think about it - a classical explanation of a quantum phenomenon?
3. What kind of an explanation is that? We posit a current loop, therefore there is no isolated charge? Actually, Dirac showed that the quantization of electronic charge could follow from the existence of a single magnetic monopole in the Universe, and physicists are still searching for one (see Magnetic_monopole#Searches_for_magnetic_monopoles). RockMagnetist (talk) 06:27, 25 November 2011 (UTC)

Some would argue that it is the electric and magnetic potentials, A and φ, that are fundamental, not the fields (see Aharonov-Bohm effect). RockMagnetist (talk) 06:34, 25 November 2011 (UTC)

Maybe this debate isn't as useful as I hoped. I can see your point. Perhaps I am taking things too literally. But physicists tend to push a model as far as it can go. And the amperian loop model which naturally produces a B field can be pushed further (even into the semi-classical regime) than the magnetic charge model which naturally leads to the H field. You can refactor the description of H to avoid magnetic charges, but in my mind it feels strained. I am not quite sure how I feel about magnetic monopoles. It would be cool physics, but right now electricity and magnetism are wrapped up in a neat package where they are united as a single force. The magnetic monopole would send that reeling. What would it mean physically? As a theoretically minded physicist I am one of those who like to think that A and &phi are the most fundamental and since B = curl A ;) ... (I know, I know. You can replace B with H since these equations are 'microscopic')

On the other hand, I did learn something from this; that even though we know and understand the exact same facts we disagree completely about their interpretation. This is of course proof why we should avoid terms like fundamental; further it gave me a better perspective about how other people from different fields see things, which is greatly appreciated. Therefore, I will repent of my ways and try not to refer to B as being more fundamental again. TStein (talk) 07:08, 25 November 2011 (UTC)

I know how you feel about monopoles. Dirac's proof is on my list of things that I really should get around to reading some day (there is a summary of it in Jackson's textbook). I don't know how it would change Maxwell's equations either. As for H vs B, what do you think of my approach in Magnetic dipole? RockMagnetist (talk) 16:46, 25 November 2011 (UTC)

Griffith's has dirac's proof as a homework problem, iirc. It leads you through the process fairly well. Having the solutions manual helps of course ;) . As far as magnetic dipole, I will leave some comments there. As far as that approach affects this article, though... I do like the fact that you avoided using the term magnetic charge. I also like the simplicity of it. Unfortunately, magnetic field needs to be more accessible to non-technical readers in my opinion which makes it significantly more difficult. That is not to say that we cannot do something similar in Magnetic field (starting with the potentials then deriving B and H then showing that they are related by B = u_o (H + M) ). It will be tricky to implement, though. TStein (talk) 19:44, 25 November 2011 (UTC)

I think B is more fundamental than H because if Alice says that the orbital current of a certain electron contributes to M but not J, and Bob says it contributes to J but not M, then Alice and Bob will agree on the value of B but disagree on H.

Well anyway, I agree the article should not favor or advocate B over H or vice-versa. It's just fun to offer my own opinion ;-) --Steve (talk) 02:15, 6 December 2011 (UTC)