Talk:Maxwell's equations/Archive 2

Maxwell's equations or Maxwell equations
I think modern usage would have the Maxwell equations rather than Maxwell's equations. Here I quote J. D. Jackson in the preface to the 2nd edition of "Classical Electrodynamics"
 * Of minor note is the change from Maxwell's equations and a Green's function to the Maxwell equations and a Green function. The latter boggles some minds, but is in conformity with other usage (Bessel function, for example).

He then uses the term Maxwell equations throughout this book, which is pretty authoritative. Thus in my opinion the article should be changed to reflect this modern usage. DMB 13th December 2005


 * As much as I respect Jackson, neither he nor any authority can dictate the English language, and "Maxwell's equations" is still far more widespread as far as I can tell. When it comes to things like this (where there is no "right" or "wrong", only convention), the safest thing is for Wikipedia to simply follow the most common usage and to note widespread alternate usages. —Steven G. Johnson 16:55, 13 December 2005 (UTC)
 * You have some heavyweights on the side of the apostrophe.
 * "The special theory of relativity owes its origins to Maxwell's equations of the electromagnetic field" — Albert Einstein
 * The Feynman Lectures on Physics chapter headings have 1 heading for Maxwell Equations and 2 headings for Maxwell's equations --Ancheta Wis 01:55, 14 December 2005 (UTC)
 * Albert einstein might have been a genius, but how could he use the modern form when writing 100 years ago DMB 14th Dec 2005

This entire discussion is irrelevant and a complete waste of time. Wikipedia is an encyclopedia, not a cutting edge journal. The purpose of Wikipedia is not to make new propositions or to change existing conventions. The purpose is to report things the way they are, not the way they ought to be. Right, wrong, or indifferent, the currently accepted and only correct terminology as of today is Maxwell's equations and not the Maxwell equations. If you don't think that is correct or proper, then write an article and publish it on Wikibooks or the Wiki Commons, but not on Wikipedia. -- Metacomet 17:48, 14 December 2005 (UTC)


 * Metacomet, you're overstating the case. "The Maxwell equations", while not the most common terminology currently, is certainly used by some prominent authorities (e.g. Jackson), and you can find it in journal articles, etcetera &mdash; it is also accepted as "correct".  While I don't think we should change the title of the Wikipedia page, we should probably also "report things the way they are", in your words, and say that this is a common alternative name.  In fact, I'll do that now.  —Steven G. Johnson 23:19, 14 December 2005 (UTC)

Some more explanations please, Cleanup
I think this page is not accessible for people who don't know the subject already. Please help to explain the equations for lay people with basic knowledge of mathematics and physics. Andries 19:44, 2 Jun 2004 (UTC


 * I presume you don't think that "basic knowledge of mathematics" includes partial differential equations, and that "basic knowledge of physics" does not include electromagnetism. In that case, see my comment below for all the articles that need work. Maxwell's equations are not the laws of electromagnetism, they are a particular mathematical formulation of them. Being technical, anyone who knows the mathematical and physical prerequisites (of multivariate calculus and electromagnetism) should have no problem with them. But the prerequisites should not be explained here but linked. That's what's great about hypertext: not everything has to be in the same article. Miguel 18:11, 5 Jun 2004 (UTC)


 * I have put the page on cleanup, not because the article bad in itself but it needs to be made more accessible. Andries 12:20, 5 Jun 2004 (UTC)


 * Could you be specific about what parts you think are unclear? or do you think the whole article should be rewritten?  Bear in mind that the article is not meant to be a course in electrodynamics, but rather just an explanation of Maxwells equations. Lethe


 * At least the symbols should be explained e.g. B in the equations. It is not that I can't find out but one should not have to go other articles to find them. Wikipedia is not written by experts for experts but by experts for everybody with basic knowledge of physics and mathematics. I can do it too but I need some time, if you could help then that would be great Andries 15:23, 5 Jun 2004 (UTC)


 * We could insert little wiki links before each of the 4 equations, which point directly to the article which is in the right side-bar on Electromagnetism; would that help you out? Ancheta Wis 16:09, 5 Jun 2004 (UTC)


 * Yes, I think that will be sufficient.Andries 16:16, 5 Jun 2004 (UTC)


 * Maxwell's equations really cannot be understood without a lot of math and a physical intuition for the laws of electromagnetism that they encode: Gauss' law, the Faraday-Lenz law, Ampère's law (or Maxwell-Ampère law) and the absence of magnetic charge. Those four laws of electromagnetism can and should be discussed in intuitive physical and geometrical terms without the need for partial differential equations. Lay readers should be directed to those articles, assuming they are accessible. Do you think they are? Miguel 18:05, 5 Jun 2004 (UTC)


 * One can still try to improve the introduction, to make it a little clearer what quantities and concepts the equations describe, as well as their broad implications and historical significance. I've rewritten the introduction accordingly. &mdash;Steven G. Johnson 20:56, Jun 5, 2004 (UTC)


 * Note: The partial differential equations expressed in the article represent centuries of human thought and development. Researchers have literally given their lives investigating the phenomena they represent. Please spend a little time on this article if you wish to gain some insight into the physical phenomena and the attendant notation which represents the phenomena.


 * StevenJ, Miguel and Ancheta_Wis, thanks for all your help. The article is quite okay now. I think I got a bit spoilt by the accessibility of encarta. Andries
 * I don't think there is any reason that we shouldn't be as accessible or more so than encarta. if you have more suggestions, i guess we should hear them.  Lethe

This division of Maxwell's equations is derived from tensor representation, it is also relativistic expression. Therefore, this division is essential and clearer. e.g. Landau "The Classical Theory of Fields".L-H

This article is not for speculative physics
User:Reddi insists on including, without explanation, the following citation:


 * Jack, Peter Michael, "Maxwell-equations: A Brief Note". Physical space as a quaternion structure - I.

This is an unpublished, unrefereed article, on a site (apparently) by the author, advancing a speculative "new theory [that] now links thermal, electric, and magnetic phenomena alltogether in one set of elementary equations. This result is based on an initial hypothesis, named 'The Quaternion Axiom,' that postulates physical space is a quaternion structure."

This sort of speculative pseudo or proto-science is not appropriate for an encyclopedia article on Maxwell's equations, where a reader looking at the citations for places to go for more information should expect to find only authoritative and well-established material.

&mdash;Steven G. Johnson 02:37, Jun 22, 2004 (UTC)


 * i think Stevenj is correct, i removed the linkLethe 02:51, Jun 22, 2004 (UTC)

Do all external lnks need to be published and refereed article for articles in wikipedia? It may be a site on a speculative "new theory", but the link deals specifically with one topic. Just because you don't "approve" of the information [you POV is pretty clear from "speculative pseudo or proto-science"] does not mean the iinformation is not appropriate for A EXTERNAL LINK (not a reference) in an encyclopedia article on Maxwell's equations. The citations section should be for the reference that the article uses to construct that article. I'll be adding more external links for places to go for more information. JDR

Author's Note: Given that the "accepted vector analysis" originally derived from Hamilton's Theory of Quaternions, and these same quaternions motivated James C. Maxwell in his mathematical formulation of Electromagnetic Theory, (vector analysis did not exist in Maxwell's time in 1873, only Quaternions) it is probably appropriate to cite some sources that lead researchers to consider what sort of ideas Maxwell himself needed to grapple with at the time his Electromagnetic Equations were being formulated. From this point of view, the Quaternion paper could be considered very relevant. A revised version of the html article can also be officially referenced through the ARXIV archives here [math-ph/0307038],&mdash;pmj 02:35 pm, Aug 27, 2004 (EST)


 * This is false. Maxwell's original 1864 work (I have the paper) did not use quaternions in any shape or form.  Second, your paper is not a merely historical discussion, nor do you use simply the 1870's quaternion formalism &mdash; you introduce a new scalar component "T" into the field quaternion, introducing speculative new physics beyond the standard Maxwell's equations.  Wikipedia is not for promotion of original research, especially unpublished and non-peer-reviewed research. &mdash;Steven G. Johnson 18:58, Aug 27, 2004 (UTC)


 * I think you misinterpreted what I said. Or, perhaps I wasn't clear enough. So let me clarify a few points. First of all, many of Maxwell's private papers and letters for the period 1860-1879 were lost soon after his death. So, nobody knows today exactly what Maxwell's original thoughts were on his formulation of EM, since this was the period when he was working on the mathematical formulation (He dies in 1879). Maxwell was discouraged from publishing his Quaternion ideas, so much of what he thought about this would mostly be found only in his private papers which are now lost. Harman discusses this in his book, and tells us that it is believed these papers were destroyed in a fire that burnt down the Maxwell's House at Glenlair (sometime around 1886). We know that by 1873 Maxwell had decided to re-cast the formulation of EM using Hamilton's Quaternions, and he published "some" of his ideas in that year in his now famous text. We know that Maxwell was thinking about Quaternions at least as early as 1867, because he wrote to Tait asking him about the reasons for the shape of the nabla symbol in a letter dated 11th December of that year. This was an important question, which Tait seems not to have understood at all from his response. Reading many of the other surviving letters and publications written by Maxwell, suggests to us that Maxwell himself did in deed "get it," while Tait did not. However, there's a hint in Maxwell's writings that the ideas of left and right nablas may have originated with Hamilton, although there is no published work from Hamilton, nor anyone else of that period, that show both forms of nabla. Indeed, Hamilton himself had to "insist" that some of his ideas on the applications of Quaternions be included in the records. As far back as the June 1845 meeting of the British Association for The Advancement of Science (the organization that held discussions on these things back then) we find Hamilton making a "special request" to have his idea (His Quote--"Is there not an analogy between the fundamental pair of equations ij=k ji=-k, and the facts of opposite currents of electricity corresponding to opposite rotations?") put in the records. This suggests to us that many things were discussed and presented "off the record," but obviously Hamilton wanted the future generations to know that he'd thought of it first, he'd seen the beautiful connection between EM and quaternions, but he too was discouraged from publishing his ideas. This mystery continues up to today. People are still being discouraged from publishing their quaternion application ideas. However, the ideas are so simple and clear, that anyone who understands a bit of math and physics can see that there is a hole in the historical literature of physics. And that hole is right around these ideas that utilize Quaternions in EM theory. To give another example, of how mysterious this phenomenon is, we note that all the private letters between Maxwell and Stokes and Maxwell and Thomson (Lord Kelvin), of that critical formative period, are missing. To understand the significance of this, recall that Stokes was the Cambridge Professor who was the leading expert on Hydrodynamics in his time, the same hydrodynamics that Maxwell borrows mathematical ideas from to formulate his theory. And Thomson was the leading expert on Thermodynamics and Heat at that same time. These were the very two men, to whom Maxwell would turn to discuss any ideas that linked Thermoelectricity with Electromagnetism (Maxwell was well aquainted with both men). Indeed, Thomson had succeeded in uniting the two phenomena, 1822 Seebeck Effect and 1834 Peltier Effect, and had proposed and discovered another Thermoelectric Effect, now called the Thomson Effect, all by the year 1854. So, the subject of thermolectricity was well known by 1873 when Maxwell brings together "Electricity" and "Magnetism" under one beautiful simple mathematical theory. So, if Maxwell was preoccupied with the question of uniting "Electric" and "Magnetic" phenomena under one roof, how is it that he missed considering the inclusion of "Thermal" phenomena into the one simple beautiful theory, when Thermoelectricity was sitting right there telling everyone that "Electric" and "Thermal" phenomena were also connected too? Where are the discussions between Maxwell and his contemporaries on the "idea" of linking Thermoelectric and Electromagnetic effects? "Electric" effects are "vector" effects, "Magnetic" effects are "vector" effects, but "Thermal" effects are "scalar". And what is a Quaternion? The union of a "vector" and a "scalar." Note, that the very first publication by Hamilton on the application of Quaternion nabla was to thermal phemonena. (again, this paper mysteriously, wasn't published...the record says it was "misdirected" by accident, and so Hamilton has to mention it in another brief footnote (see Graves, discussion of the year 1846)) so, this mysterious hole in physics continues to propagate through time.  It is true that I introduce a new scalar term "T", but even using the 3-vector quaternion form of nabla back then, Maxwell must have dealt with the related "scalar" term that is just a special case of what I call "T". This is because the product of two vectors, in quaterion theory, is a 4-dimentional quaternion, (a1.i+a2.j+a3.k)(b1.i+b2.j+b3.k) = -a.b + axb, (in modern notation), that includes a scalar part. So you have to include this scalar term in the mathematical formulation. I just extend it and give it a meaning related to the current physics we already know. It's simple. Now, I would like to think that I am the original discoverer of this elementary theory that links thermal and electromagnetic phenomena, that would be nice. However, after I had discovered these things, the simplicity of it puzzled me, since someone must have done this before. So, I started to search the historical literature to find out more information, but drew blank! Yet, I could see from what is in the historical records, the hints and suggestions of thoughts having traversed the path before me. But still, there are no official writings that clearly discuss the links my paper does. Not even to shoot it down! So, I'm not just promoting "my" idea, but those of "Hamilton" and "Maxwell" too. Not many people are aware that Hamilton was the first to see the links between Quaternions and Electromagnetism, and that was way back in 1845-6, long before Maxwell thought about these things. Maxwell was really completing Hamiltons work, when he sought to cast Elecromagnetic Theory in Quaternions, it wasn't Maxwell's original idea to do this. ]],&mdash;pmj 11:04 pm EST, Sep 30, 2004 (EST)

Meaning of citations
If you think that "external links" are significantly different from references, then you don't understand how citations are used in practice. Regardless of whether you call them references, a bibliography, or external links, they are places the reader will go to better understand the material, as well as to have additional sources with which the reader can convince herself of the veracity of the material. This is why I think that a separate "external links" heading here is misguided. &mdash;Steven G. Johnson 03:04, Jun 22, 2004 (UTC)

(If you are writing in your field, you may not need to consult any references at all to write something. You still look for references, though, to give the reader pointers on places to go for more depth/breadth.)


 * If you think that "External links" don't "significantly differ" from references but there some differences. Your "attack" on my understanding does nothing to the point. Citations are used in practice to cite material used. IT IS IMPORTANT to call them references, a bibliography, or external links ... pending on the links and how it related to that article. How can a reader can convince herself of the veracity of the material if all the information is not provided? A separate "external links" heading here is not misguided (only if you want to exclude information that does't fits you POV). A reader will go to better understand the material if the reader is given all the information [not half of it). JDR 03:38, 22 Jun 2004 (UTC) (BTW, this isn't NuPedia)


 * Citations are used for far more than to list "material used" in writing an article. In fact, for most articles using citations in the real world (not homework assignments), the vast majority of citations are not material used so much as pointers to sources of more information and breadth, as I said.   &mdash;Steven G. Johnson 03:44, Jun 22, 2004 (UTC)


 * Encyclopedias are not for new research, they are for well-established material. Especially on a well-established subject like Maxwell's equations, it is misleading to the reader to direct him/her at such a speculative article, especially when the link is right next to an authoritative reference like Landau.  &mdash;Steven G. Johnson 03:44, Jun 22, 2004 (UTC)


 * Wikipedia is a secondary or a tertiary source. Encyclopedias are not for new research (I did write alil about that article on that, IIRC). If you don't understant what kinds of sources should be used in Wikipedia ... then mabey tyou should read up on the types.
 * Wikipedia is for established material ... as well as current research and so-called "speculative" information. Providing information on the "well-established" subject like Maxwell's equations [more appropriately the "Heaviside-Gibbs equations"] is not misleading the reader ... it's providing the reader information (you seem to have a problem with that). Directing the reader to external articles is not "harmful", but I gues YMMV on that. JDR

Introduction before TOC
Please keep the high-level introduction before the table of contents. It is important to distinguish it from the later material, which is much more technical.

&mdash;Steven G. Johnson 03:04, Jun 22, 2004 (UTC)


 * The introduction after the table of contents helps the readability of the page. To distinguish it from the more technical material ... nest the subheadings. JDR 03:10, 22 Jun 2004 (UTC)


 * Nested subheadings do not improve readability either. I don't feel too strongly about this formatting issue, but I would like to hear other opinions besides yours.  (PS. Write what you want in the talk section, but please don't edit my text.  Including my headings.) &mdash;Steven G. Johnson 03:17, Jun 22, 2004 (UTC)


 * Whoa, there seems to be an edit war going on here! -Lethe 03:11, Jun 22, 2004 (UTC)


 * Welcome to the wonderful world of Reddi's edits. He's been periodically garbling physics articles he doesn't understand for ages now, leaving it to the rest of us to clean up his messes, and he usually fights with insistent reverts/insertions, with scant answer to criticisms, until several people start to complain.  &mdash;Steven G. Johnson 03:17, Jun 22, 2004 (UTC)


 * Nice attack, Stevie. I respond [not "fight"]. I also provide information and links (more than most do; eg., your "scant answers") ... if the factual information and references are ignored, I guess I can't do anything about that. JDR 03:31, 22 Jun 2004 (UTC) (Disdains pompous donkeys)


 * Reddi, I initially tried to be understanding to you, way back when, but you persist in editing articles you don't have the technical or mathematical background to understand, and you ignore the fact that essentially everyone disagrees with your arguments regarding technical additions. On balance, you do more harm than good on Wikipedia.  &mdash;Steven G. Johnson 03:36, Jun 22, 2004 (UTC)


 * Stevenj, you don't "understand" me nor have we agreed on many things ... and I try to avoid articles you edit [if they interest me]. I will continue to do this where I can ... but sometimes that is not possible. I will continue edit articles, adding information ... I'm glad you know what my understanding of the technical or mathematical background is [/end sacasm]. I do not ignore the facts ... and mob rule does not make the state of wikipedia "better".
 * I do more harm than good on Wikipedia? IYNSHO ...
 * JDR 03:44, 22 Jun 2004 (UTC)

Anyone object to restoring the tensor equations
The Revision as of 23:18, 24 Jul 2004 removed the tensor equations. Anyone object if we restore them Ancheta Wis 21:42, 10 Aug 2004 (UTC)


 * Yeah, It looks like User:205.188.116.206 deleted the special relativistic formulation and the differential forms formulation without justification. Let's get those back into the article - Lethe | Talk

Inaccuracy in the equations
I'm not a physicist or a mathematician, however, I do know that Otto Schmitt stated privately if not publicly in his last year of life that Maxwell's equations are inaccurate. Please consider this statement hearsay as I was not told directly by Otto, rather a friend was. I would hate to be responsible for marking Mr. Schmitt's name in the negative. However, if there is truth to the statement it would be an important scientific piece of information.

I wanted to find reference to this statement before posting and could find none. I did find reference to Otto Schmitt and Maxwell in a paper:

http://www.nebic.org/icebi/schwan1.htm

Specifically, the "Maxwell-Wagner effect".

Digging a bit more I found a Russian publication of 1995 which may or may not be relevant:

http://eos.wdcb.rssi.ru/transl/izve/9509/pap05.ps

"Geoelectrical problems covering sonic and infrasonic frequencies commonly deal with a quasi-stationary approximation, which essentially simplifies solving the Maxwell equations. To what extent does this approximation ignore the displacement current applicable to the model involving macroanisotropic media?"


 * I haven't read this paper, but the quote describes the accuracy of an approximate solution of Maxwell's equations (by dropping the displacement-current term), not the accuracy of the full equations themselves. &mdash;Steven G. Johnson

My guess is that Otto Schmitt was seeing some indications of a poor fit for Maxwell's equations in the research he was doing. Experimental was not matching theoretical with a high enough degree of correlation. As a result he knew either that his measurements were wrong or that Maxwell's equations were wrong. Considering the weight Otto's life's work carries, it is probable that Otto had good reason to believe problems exist within the equations.


 * Wikipedia does not report unpublished speculations, much less rumors of unpublished deathbed speculations. If you find an unrefuted paper in a mainstream scientific journal that seriously questions the validity of Maxwell's equations (other than known corrections for quantum effects and GR), please post it here. &mdash;Steven G. Johnson 14:59, Dec 1, 2004 (UTC)

Examples section?
Is it okay to add an examples section straight after the detailed formulas one? With some simple stuff like a point charge and the infinite wire with current in it?
 * That is what would be in a textbook, but not under Maxwell's equations, rather as applications in electrodynamics or electricity and magnetism. How about creating a new article with links to the electromagnetism series, as well as the appropriate link to the new page in this article? It might be useful to electrical and electronics engineering students as well, and as examples in applied mathematics, as the solutions to equations. Ancheta Wis 02:26, 22 Dec 2004 (UTC)


 * Textbook-style tutorials are more appropriate for WikiBooks than for an encyclopedia. Please add examples to the physics textbook there.  The only exceptions might be some example that is relevant to a particular article (e.g. capacitor or light) or some problem that has historical importance for other reasons.  &mdash;Steven G. Johnson 02:44, Dec 22, 2004 (UTC)

Maxwell's equations in terms of differential forms
This section looks to me like the key for a deeper understanding, but it is very very short at the moment. Does anyone have more information about that? 84.160.214.150 13:40, 19 Feb 2005 (UTC)
 * Like you, we are eagerly awaiting mathematicians who can develop more structure which expresses the differential forms which may be applied to the manifolds currently contemplated for use in physics. For example, we need forms which can handle the presence of matter in all its forms (probably a pun, but maybe there is some physics in it), not just vacuum. Ancheta Wis 00:57, 16 Mar 2005 (UTC)

old four-vector notation
Any chance of having my favourite four-vector Maxwell's equation, namely

d'Alembertian of (four potential (A,phi) = four current (j,rho)

in the older notation that most of us physicists learnt a few years back.Linuxlad 18:33, 9 Apr 2005 (UTC)
 * see Electromagnetic four-potential for more links. Ancheta Wis 10:25, 11 Apr 2005 (UTC)

Thanks (I had in fact just found it! and had come to post a link here :-)). I've added a few tiny mods for those of us used to the older vector operators. Linuxlad 10:48, 11 Apr 2005 (UTC)

Equation Form
can someone who is familiar with the mathtype used on wikipedia please add the constants onto maxwell's equations? This would be very useful as the current form of the equations is totally unusable for any practical application. Cpl.Luke 19:59, 25 Jun 2005 (UTC)

also the differentials are mislabeled, for instance in gauss's law it should be da not ds Cpl.Luke 20:02, 25 Jun 2005 (UTC)


 * Currently looks good to me. If you scroll down a bit you get the simple version


 * $$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$


 * which is only good in free space, but


 * $$\nabla \cdot \mathbf{D} = \rho$$


 * is the general form and therefore belongs in the box near the top as it is more generally useful. Also, ds is a rather standard alternative to da as a is used for many things such as acceleration.  See the notation in surface integral. --Laura Scudder | Talk 20:16, 25 Jun 2005 (UTC)

However in every physics textbook I've read (only talking about the integral version here) da is used (also missed the version of the equations with constants apparently)

Also it would agree more with the gauss's law article to use da in the gauss's law entry, also looking in a textbook right now I see da used for the gauss's law entries and ds used for faradays and ampere's law. It would be wise to avoid confusion by changing it to da. Also we can say what the differentials mean in the "where:" entry directly below the table. since D and H seem to be used souly to make the equations appear simpler we should attempt to avoid confusion by reducing the number of variables down to 2 E, and B, later on in the article it is explained what the relationship between B,E and H,D is and thus we can continue using them for the rest of the article, but it would seem that it is far simpler to only use B and E in the original table. I made the relevant edits however they were promptly reverted, I would appreciate some feedback as to why it was reverted so that we can come to a compromise. Cpl.Luke 05:19, 12 July 2005 (UTC)
 * See the comment for 18:06, 27 May 2005 by Stevenj:
 * "(the equations can include interactions with non-charged matter as well (e.g. spin effects), although in any case epsilon and mu have to come from experiment (or quantum theory) and aren't given by ME)". That is what LauraScudder meant above. BTW, the thread should be in temporal order. Right now, this 2005 entry is on top of the 2004 entries below. After this all settles down, we should cut and paste this entry to the bottom of the thread. Ancheta Wis 05:50, 12 July 2005 (UTC)


 * I still don't see the relevence of wheather or not mu and epsilon come from experiment or not, as all your doing by using D, and H is moving the mu or epsilon over to the other side of the equation. Also just in case I'm missing something in the above statement, this still doesn't disclude us from using da instead of dsCpl.Luke 06:43, 12 July 2005 (UTC)


 * You often can't move the &mu; and &epsilon; through the derivative as they can be spatially dependent. Think of a non-uniform material or a boundary between materials.  There's also special cases for nonlinear and anisotropic materials where in general $$ D_i = \epsilon_i,j E_j$$.  So until you know the problem you're working with, you cannot move &epsilon; and &mu;.  --Laura Scudder | Talk 14:40, 12 July 2005 (UTC)


 * The choice of ds for line integrals I've always found very unfortunate, but I think it arises from wanting to generalize length as the surface area of a line. --Laura Scudder | Talk 14:40, 12 July 2005 (UTC)


 * yes that would seem to make sense, but since we are talking about area here specifically, and the gauss's law article already uses da we should make the switchCpl.Luke 16:53, 12 July 2005 (UTC)


 * A can also mean magnetic vector potential. Thus Area could be confused with an important electromagnetic concept. S has the handy mnemonic Surface, with lowercase s for surface element. Ancheta Wis 17:09, 12 July 2005 (UTC)


 * however we can say that its the differential of area in the "where:" entry directly below the table, we actually should already have what the differentials mean in that entry.
 * also whats the problem with using flux in faradays law?Cpl.Luke 18:55, 12 July 2005 (UTC)


 * Again, the problem with Faraday's Law is whether the derivative can commute, in this case with the integral. It is possible to have a changing surface of integration (i.e. a railgun, a closing loop of wire, etc.).  So the time derivative can only pass through the integral sign if the particular problem consists of a non-changing surface.  This is actually also a problem with Ampere's Law, but the changing surface there comes up much less often.  --Laura Scudder | Talk 19:49, 12 July 2005 (UTC)


 * ok, but we should at least change the differential term to agree with the gauss's law article, da. Then just label what the da stands forCpl.Luke 23:17, 12 July 2005 (UTC)

Clifford Algebra Notation
Maybe it's interesting to add the notation in Clifford Algebra, it's very concise. Andy 13:48, 5 April 2006 (UTC)

Meaning of symbols
Please note that the table in the General case section contains symbols that are not defined in the key underneath. In particular, Qencl, Iencl, and &Phi;D are not explained (until the Detail section, where slightly different notation is used). - dcljr (talk) 05:08, 25 July 2005 (UTC)

Solutions ???
Is there a list of some important solutions of Maxwell's equations on WP ? I think there should be. The general relativity pages have a page on exact solutions of Einstein's field equations and I think it would be good if the same was done here. :)--Mpatel 13:28, 31 July 2005 (UTC)
 * As Feynman said, the same equations have the same solutions - what do you say to a set of links to equations of the form of xxx. Then it becomes a reference in mathematical physics. Probably the electrical engineers have a say in this as well. Ancheta Wis 13:37, 31 July 2005 (UTC)
 * To illustrate, every electrical engineer has to learn Maxwell's equations, but the situation is not symmetrical: not every physics student has to learn about the practical issues involved in a circuit.
 * Oops. I just remembered how Kurt Lehovec (one of the 4 founders of the integrated circuit) would derive the fundamental physics for a flash memory. He would start from electrostatics. But that is a nit in the machinery for Maxwell's equations. Maybe I should withdraw the suggestion. Ancheta Wis 14:01, 31 July 2005 (UTC)

Proca's Extended Maxwell Equations with magnetic monopoles?
Proca's Extended Maxwell Equations can be found here http://www.innopro.de/maxwell_equations.htm#maxwell_quantum.

Could someone make a page about Proca's Extended Maxwell Equations with magnetic monopoles? I mean Maxwell equations with Proca's extensions and hypothetical magnetic monopoles. Henri Tapani Heinonen 14:07, 6 November 2005 (UTC)


 * Perhaps you are thinking of Dirac monopoles. The general theory of electromagnetic fields in the presence of monopoles is that of cohomology and Hodge theory. linas 23:33, 14 December 2005 (UTC)