Talk:Magnetic vector potential

Untitled
I've never heard of "magnetic potential" as defined in the opening paragraph of this article, sounds very dubious. The vector and scalar magnetic potential formulations seem correct, but the article also lacks sources and is written in an informal tone. Let's clean it up and get an expert on this page. RyanC. 12:05, 7 March 2007 (UTC)

I had never either but it is used in the literature. e.g. Nonlinear dynamics of the firehose insatbility in a mangetic dipole geotail, W.Horton et al, Journal of Geophysical Reasearch, Vol 109, A09216, 2004. Paragraph 23. M.Rosin

The magnetic potential is real, and it is equal to the curl of B, as claimed. The talk about gauge choices is sensible as well. I've never heard of a magnetic scalar potential, though. It sounds weird, but the cut explanation seems to work. I think this article is accurate enough, but it could use some references. Dpeldon 05:28, 17 May 2007 (UTC)

Added my undergrad electromagnetics book as a reference. Omnispace 04:10, 2 June 2007 (UTC)

(Almost) Everything in this article is correct. However, the explanation could use work, I will try to add more explanations. As for references, I agree that that more E&M textbooks should be listed. 74.102.181.37 07:20, 2 June 2007 (UTC)

I've added references to Jackson and Duffin which are both well known EM texts. I would agree with the above both the magnetic vector and scalar potential exist in the literature. Unfortunately I don't have access to textbooks to give pages numbers. Christopherlumb

From what I gather the A-potential is often referred to as an unphysical modification to Maxwell's Equations, because of the gauge invariance condition, and so its use is to define the B-field rather than to represent anything physical. This is a rather unsatisfying explanation and a physical meaning can be given to A in the form of an electromagnetic momentum, as written in arXiv ( http://arxiv.org/abs/1303.5619 ) or an older journal article Am. J. Phys. 46, 499 (1978); doi: 10.1119/1.11298 --70.79.150.161 (talk) 06:15, 28 March 2013 (UTC)
 * And who would be doing this referring of the A-potential as unphysical? I'm not aware of any physics text written in the least 50 years that says that.Constant314 (talk) 22:54, 28 March 2013 (UTC)
 * For starters, my quantum electrodynamics professor. --70.79.150.161 (talk) 02:54, 29 March 2013 (UTC)
 * Does your prof refer to A as unphysical or does he say that others refer to it as unphysical?Constant314 (talk) 04:04, 29 March 2013 (UTC)
 * Prof did. From the point of view of QED in particular, A simply sets the behavior of the force carrier and if you have zero mass, there's the photon. In terms of classical ED, it is used to set the gauge for the field equations but does not have a physical meaning outside of being used to give the form of the B-field. Thus my understanding that at least some E&M texts follow this pedagogy. --70.79.150.161 (talk) 04:26, 30 March 2013 (UTC)
 * In the text (all classical E&M) books that I have, -dA/dt is responsible for the electric field produced by currents. It is the principal actor responsible for transformer action with B relegated to causing skin effect and proximity effect.  If you have perfect conductors, you go from J (current density) to A to E without ever computing B.  To me, that makes A physical, or at least dA/dt is physical.  Feynman in volume 2 of his lecture series does a fine job of explaining this.  I have seen H referred to as unphysical because H would operate on magnetic monopoles, of which there are none.  Feynman has a special definition of a "real field" which is a set of numbers, local to a point, that allow you to calculate all the forces on the particle at that point.  The electric scalar potential and the A potential taken together, satisfy this requirement.  If your prof says A is unphysical, he probably has a specific technical definition for physical.  It is probably more productive to ask him why he says A is unphysical can to try to get the answer here.  On the other hand, it would not surprise me for the prof of a QED class to declare all fields to be unphysical.Constant314 (talk) 16:25, 30 March 2013 (UTC)

Too much material
More explanation is good and more references are good, but 74.102.181.37 has added lots of new material including new concepts such as Decoupling Maxwell's Equations and four-dimensional potentials. This makes an already difficult subject, even more difficult to understand. My suggestion is that anything four dimensional should be given a separate article. Also, this is about the MAGNETIC potential so any reference to the ELECTRIC field should be minimal. Some simple magnetostatic examples using the magnetic vector and magnetic scalar potential would be nice (with diagrams even). Yes, there's more to life than magnetostatics but a reader is unable to learn the whole of physics in a single sitting... an article must be simple enough to be approachable and ultimately that implies deferring more complex concepts to other articles.

Possibly some references from the Maxwell's Equations page could be used here. Possibly also the material on the Maxwell's Equations page could benefit from being better organised. There must be text books covering magnetostatics surely?


 * I think you're right. The part on "Decoupling Maxwell's Equation" may be better moved - though it's one main motivation for using the magnetic potential. The magnetic field B is more intuitive, but harder to deal with mathematically, that's why A is used. The stuff on "Four Dimensional potential" seems like it should also be moved off to electromagnetic potential. And "Reality of potential fields" needs to be improved/removed. 74.102.181.37 02:15, 13 June 2007 (UTC)

Aharonov-Bohm effect
Perhaps someone should add a description of the A-B effect and the consequences on the understanding of the vector potential. Or at least a link to the article on the effect. I don't feel confident to describe the effect myself.

--Larssl (talk) 17:38, 24 May 2008 (UTC)

In fact the magnetic vector potential IS directly detectable through the Aharonov-Bohm effect (the phase of an electron can be altered by it). The part in this article stating it is a non-observable mathematical artifact is rubish. The effect is used in SQUID devices and is used in several patented devices to create communications devices with far better range and lower interferance. It is far more fundamental than the magnetic field, which is in fact just a secondary effect of it. The article needs to be corrected. --Jamey 14:15, 4 November 2008 (UTC) —Preceding unsigned comment added by 70.221.68.213 (talk)


 * Are you familiar with the concept of gauge freedom? If so, you would understand why it's wrong to say the "magnetic vector potential is directly detectable". Only gauge-independent quantities can be measured, by simple logic.


 * In the A-B effect, the line integral of A around a closed curve is the only thing you can measure; this quantity is gauge-independent and no one would argue that it's measurable. It's also, by the way, expressible solely in terms of B; it's proportional to the magnetic flux through the curve. (See Aharonov-Bohm effect.) --Steve (talk) 15:25, 4 November 2008 (UTC)

Propose split
I propose that this article be split so that the magnetic scalar potential and magnetic vector potential are in different articles. Putting them both in the same place, at least as it's done now, ends up sorta implying that each is equally valid and equally widely used, when really the magnetic vector potential is way more important. Moreover, there's virtually no overlap between the two topics, and you can understand either of them perfectly without ever having heard of the other. Thoughts? --Steve (talk) 20:26, 21 July 2008 (UTC)


 * Support gOOd idea. David J Griffiths's 3rd edition supports what Steve is saying. Pages 234-246, 252 describe quite a bit about magnetic vector potential, while magnetic scalar potential is only mentioned in passing. --Firefly322 (talk) 15:05, 22 July 2008 (UTC)


 * Weak Oppose If the term 'magnetic potential' is used for both then I prefer to use one page to include both for now. With the lengths of the 2 sections as they are now, I believe it is slightly better to have magnetic vector potential point to Magnetic potential then to create an disambig page for magnetic potential.  This way the scalar vector potential may get more attention.  Plus, I hate disambig pages since they add extra clicks.  It is easy enough to point out that the magnetic vector potential is much more useful in the article.  If on the other hand the magnetic vector potential section grows to something approaching its stature in physics then it may need to be separated out. TStein (talk) 05:47, 26 July 2008 (UTC)


 * I guess I was inclined to believe that "magnetic potential" isn't actually used for both. But after google-searching, I see that it is. (In physics "magnetic potential" always means vector, but in other disciplines like geology it often means scalar). So under those circumstances I'll agree that, until the page is longer, it need not be split. --Steve (talk) 05:16, 29 July 2008 (UTC)

The page has almost tripled in size since this discussion and I think it is time to split the page. I followed a link to this page and it was some time before I found there was some relevant information on the scalar potential at the bottom of the page. This is highly confusing. More to the point, these are two entirely separate topics and it is against Wikipedia guidelines to have two different topics on the same page. SpinningSpark 08:50, 5 April 2020 (UTC)


 * Support splitting. Constant314 (talk) 15:18, 5 April 2020 (UTC)

It's been a week and no one else seems interested so I'm going to carry out the split. SpinningSpark 13:47, 12 April 2020 (UTC)

4-potential nonsense?
I've never heard of the idea of merging a "scalar magnetic potential with a vector electric potential" to get a weird type of 4-potential. Is there a source for it? Otherwise I'm deleting it, and making it clear that the one and only electromagnetic 4-potential is the vector magnetic potential and scalar electric potential. --Steve (talk) 20:29, 21 July 2008 (UTC)


 * In a world with magnetic monopoles, but no electric charges, this is what you would have to do. A possible advantage is that a scalar field is easier to deal with than a vector field, so if you only have magnetic stuff, it is simpler. JRSpriggs (talk) 19:32, 22 July 2008 (UTC)


 * Sure. But in this universe, we rarely if ever would have occasion to use this backwards 4-potential. It's highly obscure at best, outright original research at worst. I'll wait a bit longer for someone to find a reliable source attesting to its notability, but otherwise I'm taking it out. --Steve (talk) 21:01, 22 July 2008 (UTC)


 * Aww come on the phrase 'the concept of vector electric potential is just too weird to exist in the same universe as decent common-sense folks.' is too funny to remove. I can't imagine this is notable, though.  Jackson does discuss this in terms of the fields (E,B) but not in terms of the potentials.  This is known as a 'duality transformation'.  It is discussed in 6.11 (On the question of Magnetic Monopoles) pp 273-5 in Jackson 3rd edition.TStein (talk) 05:34, 26 July 2008 (UTC)


 * Kulkarni & Khaparde, Transformer Engineering: Design and Practice, 2004, CRC Press, page 180. As a computational artifice, sometimes the numerical solution of transformer simulation uses a vector electric potential and a scalar magnetic potential.Constant314 (talk) 18:08, 20 November 2010 (UTC)


 * I have no clue how notable that is for the purpose of this article. It is intriguing, though. In retrospect it shouldn't surprise me, though. With only my cursory knowledge of the field of transformer engineering, it appears to me that the field largely uses something akin to the duality transformation working with H the same way that electrostatics deals with E.


 * Balanis, Antenna Theory 2nd ed 1997 mentions this in chapter 3 has a lot to say about it starting on page 119. Constant314 (talk) 00:23, 23 November 2010 (UTC)
 * Harrington, Time-harmonic Electromagnetic Fields 1961, page 7 observes that  $$  {  \partial \mathbf{D}   \over \partial t }   \,  $$  is called the electric displacement current and acts like an electric current, so $$  {  \partial \mathbf{B}   \over \partial t }   \,  $$ must be magnetic displacement current and then on page 99 introduces F, the electic vector potential as a function of magnetic currents.  After only a quick look, I get the notion that he uses a distribution magnetic currents to replace a distribution of electric charge.Constant314 (talk) 00:23, 23 November 2010 (UTC)
 * I don't know if it is important at all, but Balanis is fairly common and Jackson suggests Harrington at the end of chapter 8.Constant314 (talk) 00:23, 23 November 2010 (UTC)

Calculation of potentials from source distributions
I need to have the equations for A and phi for an article on transformers. This article seems like the perfect place to put them.

I'll start by adding some references so they will be there when the new section is inserted.

And speaking of references, I have Jackson third edition in my hands and it says copyright 1999 instead of 1998. Of course that doesn't mean there isn't a third edition out there with a 1998 copyright. I think I can add a reference that is the same except for the year without breaking anything, so I'll just add a refernce that says 1999. I'll leave it to someone else to delete the 1998 version if they are sure there is no such version. Constant314 (talk) 01:50, 2 November 2010 (UTC)


 * In principle I think the equations for A and phi in the Lorenz gauge should be primarily in the Lorenz gauge article (which they're not right now, instead the formulas were split off into a separate article retarded potential), the formula for A and phi in the Coulomb gauge should be primarily in the Coulomb gauge article (right now Coulomb gauge is a section not an article, but the equations are there), etc. They should be here too, in all those forms, but perhaps discussed more briefly. :-) --Steve (talk) 20:26, 3 November 2010 (UTC)

First sentence use of "fields"
The first sentence says "In electromagnetism the physical effects can be expressed by either fields or potentials"

Aren't the potentials also fields? Constant314 (talk) 15:04, 3 November 2010 (UTC)


 * I rewrote to clarify... --Steve (talk) 20:21, 3 November 2010 (UTC)

Depiction of the A field
I have a depiction of the A field around a toroid shaped inductor for another article. I think it could be useful here. The lines are just drawn to look good and impart general look of the A field. Constant314 (talk) 21:46, 20 November 2010 (UTC)


 * Looks good to me. :-) --Steve (talk) 23:33, 20 November 2010 (UTC)
 * thanks for the feedback and the edits.Constant314 (talk) 13:44, 21 November 2010 (UTC)
 * I see you added that the depiction was for the columb guage instead of the Lorenz gauge. Can you tell why it is one and not the other?Constant314 (talk) 14:06, 21 November 2010 (UTC)

Well Coulomb gauge and Lorenz gauge are the same in this case. It's either of those. But there are other possibilities, so I thought it's good to be specific!

When you solve for the B-field given a J-field, you solve two equations: Both the picture and its description say that the A field was inferred from B in the same way that B would be inferred from J. That means you were solving: Of course, $$\nabla\cdot A = 0$$ means Coulomb gauge. (However, as you mentioned, the Lorenz gauge is the same for this case.) :-) --Steve (talk) 19:30, 21 November 2010 (UTC)
 * $$\nabla\times B \propto J$$
 * $$\nabla\cdot B = 0$$
 * $$\nabla\times A = B$$
 * $$\nabla\cdot A = 0$$
 * And are the two gauges are the same because the charge distribution is zero? I suppose I ought to mention that. I suppose I should also mention quasi-static assumption? Constant314 (talk) 20:36, 21 November 2010 (UTC)

Hmm, the Coulomb gauge condition is $$\nabla\cdot A = 0$$, and the Lorenz gauge condition is $$\nabla\cdot{\mathbf A} + \frac{1}{c^2}\frac{\partial\varphi}{\partial t}=0$$ So they're the same if $$\frac{\partial\varphi}{\partial t}=0$$ in the Lorenz gauge. The formula for $$\varphi$$ in the Lorenz gauge is given here, and $$\varphi$$ is time-independent if the charge distribution $$\rho$$ is unchanging in time. So it seems to me, if the charge distribution $$\rho$$ is unchanging in time, then the Lorenz and Coulomb gauge are the same, and vice-versa. :-) --Steve (talk) 01:54, 22 November 2010 (UTC)
 * I think that I will change the caption to say div A = 0 is assumed then on the side say why that might be so. —Preceding unsigned comment added by Constant314 (talk • contribs) 17:04, 22 November 2010 (UTC)

clean up
If its ok ---


 * I cleaned up the article,
 * changed the notation to be consistent with most other EM articles (including retarded time, retarded potential, Jefimenko's equations etc),
 * introduced the characters ∇ • for clearer divergence (why use " "?)
 * cut down on prosy wordyness in some places
 * moved the big image of the A field to the right so the bullet points are visable and its clearer to read on the left anyway

F = q(E+v×B) ⇄ ∑ici 16:49, 26 May 2012 (UTC)




 * If its also ok - I redrew the image by Constant314 in SVG form, I like the originality so kept all the colours and everything (except maybe some shading for the toroidal core, as I couldn't quite get it to work, maybe I can edit this with inkscape later, sorry)...


 * It has replaced the jpeg version in the article. Thanks, =) F = q(E+v×B) ⇄ ∑ici 20:17, 26 May 2012 (UTC)

Reference is wrong
The author of one of the references reads "Davd" instead of "David" — Preceding unsigned comment added by 18.51.3.219 (talk) 02:26, 22 November 2013 (UTC)

Depiction of the A field
Is the diagram in this section correct? Martin Hogbin (talk) 15:44, 27 February 2014 (UTC)

OK, I get it now. I wonder if + and. are the best symbols for the direction of the B field inside the toroid. What about using N and S?  Do we have a source for this diagram? Martin Hogbin (talk) 15:44, 27 February 2014 (UTC)
 * There is a long history of using dots and crosses for this purpose. The crosses are interpreted as the tail feathers of the arrows entering the figure and the dots are interpreted as the tip of the arrows emerging from the figure.Constant314 (talk) 00:30, 28 February 2014 (UTC)
 * I have seen that usage for the electric field, that is what first confused me before I read the section more carefully, but I have not seen it used for a magnetic field before. Three respected text books that I have to hand do not use that convention and this search does not seem to show it being used for the magnetic field, although it does show that usage for the electric field/current. It may seem rather old fashioned but what is the objection to using N and S? This makes it immediately apparent to most people that we are showing a magnetic field. Martin Hogbin (talk) 09:52, 28 February 2014 (UTC)
 * Dots and crosses can be used for any vector field. I don't think N and S would convey which was in and which was out.  Also, what would N and S mean when there was no obvious pole?  This is just lines of flux running in a circle around an axis.  Time Harmonic Electromagnetic Fields by Harrington and Principles of Radar by M.I.T. Radar School Staff both use dots and crosses for H field and E field depending on the point of view.  I've never seen N and S used for this purpose.Constant314 (talk) 00:40, 1 March 2014 (UTC)
 * Also Lectures on Physics by Feynman uses dots and crosses for the B-field in figure 23-16 of volume 2.Constant314 (talk) 00:57, 1 March 2014 (UTC)
 * Yes, you are right Feynman does use it in one place. Martin Hogbin (talk) 10:02, 1 March 2014 (UTC)
 * Regarding those three respected text books: do they have any depiction that has B or H flux going directly into the page or coming directly out of the page? If yes, what convention do they use? Constant314 (talk) 17:40, 1 March 2014 (UTC)
 * I could not find any examples where the magnetic field direction going into the page was shown, but I should say that one of the books was Feynman, so maybe I did not look hard enough. Martin Hogbin (talk) 21:14, 1 March 2014 (UTC)

Assessment comment
Substituted at 22:50, 29 April 2016 (UTC)

"Tesla-metre" listed at Redirects for discussion
An editor has asked for a discussion to address the redirect Tesla-metre. Please participate in the redirect discussion if you wish to do so. signed,Rosguill talk 17:25, 8 April 2020 (UTC)
 * I suppose Tesla-metre is a metre that measures magnetic flux density. Perhaps it should redirect to Magnetometer. Constant314 (talk) 17:54, 8 April 2020 (UTC)

Depiction of the A-field
Since $$\nabla \times \mathbf{B} = \mu_0\mathbf{J}$$ assuming quasi-static conditions...

...the lines and contours of A relate to B like the lines and contours of B relate to j.

Should this last j be a capital J?


 * Yes and fixed. Constant314 (talk) 13:17, 18 May 2022 (UTC)