Talk:A Dynamical Theory of the Electromagnetic Field

Web links
Here are web links that give the complete paper in question,


 * http://www.zpenergy.com/downloads/Maxwell_1864_1.pdf
 * http://www.zpenergy.com/downloads/Maxwell_1864_2.pdf
 * http://www.zpenergy.com/downloads/Maxwell_1864_3.pdf
 * http://www.zpenergy.com/downloads/Maxwell_1864_4.pdf
 * http://www.zpenergy.com/downloads/Maxwell_1864_5.pdf
 * http://www.zpenergy.com/downloads/Maxwell_1864_6.pdf

These should be helpful for the purposes of discussing the paper 'A Dynamical Theory of the Electromagnetic Field', by James Clerk-Maxwell 1864

math translation
Correct errors and insert conversions, thanks; make a note below equation if this is done. JDR 05:56, 24 September 2005 (UTC) [PS., math hates me]


 * $$\nabla \times \mathbf{H} = \mu_0 \mathbf{J}_{tot}$$

The curl of the "magnetic intensity" equals the permeability of total current (including displacement current).


 * $$\mathbf{J}_{tot} = \mathbf{J} + \frac{\partial\mathbf{D}}{\partial t}$$

The total current (including displacement current) equals the electric current density plus the partial derivative of the "electric displacement" over the partial derivative of time.


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

The divergence of the electric displacement field is equal to the electric charge density.


 * $$\mu \mathbf{H} = \nabla \times \mathbf{A}$$

the permeability of the magnetic field equals the curl of the electromagnetic momentum.

I have corrected the symbol 'E' (electric field) into 'f' (force per unit charge). That this should be so is clear from Maxwell's paper where he uses the vector in question in the expression for emf in the place of 'force per unit charge'.131.180.35.186 (talk) 07:41, 27 May 2013 (UTC)


 * $$\mathbf{f} = \mu \mathbf{v} \times \mathbf{H} - \frac{\partial\mathbf{A}}{\partial t}-\nabla \phi $$


 * $$\mathbf{f} = \frac{1}{\epsilon} \mathbf{D}$$


 * $$\mathbf{f} = \frac{1}{\sigma} \mathbf{J}$$


 * $$\nabla \cdot \mathbf{J} = -\frac{\partial\rho}{\partial t}$$


 * notes
 * put in some vector operator names. JDR 04:20, 25 September 2005 (UTC)

Asking for a translation

 * Reddi, since you don't understand math, please don't propose "translations". Your translations are nonsensical.  (Also, discussions of the consequences and interpretations of these equations can be found already in Maxwell's equations and elsewhere.)  &mdash;Steven G. Johnson 18:17, 24 September 2005 (UTC)


 * My mathematical skills are not great ... but that is exactly why I have asked for a translation. (BTW, I do understand some math, but I am not a mathematician.)
 * I think one great mathemetician once said, "equations that can be translated into english are a good ones, Those that cannot be, are not ... Clifford mabey or someone else ...
 * Thanks for the direction to the article, though. JDR (PS., I'm not asking for a interpertation or consequences, I'm asking for the reading ot the equation. Such as, 1+1=2; one plus one equals two)

The link to the online version of the document is only available to subscribers.

no div B equation?
The list doesn't include div B = 0. Is that an error, or did Maxwell actually not include it in his paper?--75.83.140.254 17:02, 13 December 2006 (UTC)

Maxwell didn't include the div B = 0 equation in his list of eight in his 1864 paper. Neither did he include Faradays's law of electromagnetic induction. These two equations did however both appear in Maxwell's 1861 paper, and Heaviside included them in his four modified Maxwell's equations in 1884. It is also a point of interest that the Lorentz force was one of the original eight Maxwell's equations. It first appeared as equation (77) in Maxwell's 1861 paper, long before Lorentz produced it. (222.126.43.98 19:33, 15 February 2007 (UTC))


 * It's not an error. Maxwell didn't need to include it, because it is implied by the $$\mathbf{B} = \nabla \times \mathbf{A}$$ equation.  (The divergence of a curl is zero.) —Steven G. Johnson 21:28, 13 December 2006 (UTC)

Error in article?
Equation (G), Gauss's Law should probably have del. D = rho, not del. D = - rho. Right? As in Gauss's_law. Common sense as well, because electric field radiates out from a positive charge. — Preceding unsigned comment added by 128.250.38.191 (talk) 03:04, 6 September 2012 (UTC)


 * Fixed. — Gavin R Putland (talk) 11:49, 30 May 2018 (UTC).

Improve "translation"
There was a request to improve the translation above from 6 years ago and a rather arrogant reply. In reviewing the mathematical formula I notice a number of deficiencies in the definitions e.g. Upside-down triangle Nabla_symbol is not defined, neither is the epsilon, and there are a couple of other deficiencies. I notice that the previous requester did not specify the deficiencies in the symbolic key/legend. So now these are specified and please correct them. I noticed from the sources of the mathematical papers that the equations are different. It is up to the person who substitute the symbolism to define the symbols that he is using completely (less the widely known symbols like +, -, /, . . . . . --PB666 yap 15:42, 2 June 2014 (UTC)

Thanks Hasratpreet Brar (talk) 06:20, 3 March 2017 (UTC)

Publishing Details
The Royal Society has records of the timeline between the paper being read on 8 December 1664 and its publication in 1865 in its register of papers, including original correspondence. Perhaps notable is that it was peer-reviewed by William Thomson, later Lord Kelvin, and George Gabriel Stokes. It was approved for publication, according with the Society's statutes on such matters, by the committee of papers on 15 June 1865, and sent to the printer the day after. While Philosophical Transactions was only published annually in 1865 (in time for the Society's anniversary day, so some time in later November), offprints, which were given to the author for personal use and usually distributed by them to their peers, would have appeared shortly after this date. 16 June 1865 would seem to be the date from which the paper would be widely distributed. I'm happy to add this info if others think it is relevant. (Sjanusz&#124;talk)(COI) 15:14, 4 June 2015 (UTC)

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Can we have more about Maxwell's actual paper?
Why is there a long section called "Heaviside's equations" in this article, which is supposed to be about Maxwell's 1864 paper? Maybe the idea is that Heaviside "vectorized" Maxwell's equations, and that equations (A)-(G) are modern versions of Maxwell's original 20 equations, some being vectorized. But calling them "Heaviside's equations" is confusing to people who want to find Maxwell's equations, especially since the article seems to say Heaviside did not write these equations (A)-(G):


 * Heaviside's versions of Maxwell's equations are distinct by virtue of the fact that they are written in modern vector notation. They actually only contain one of the original eight—equation "G" (Gauss's Law). Another of Heaviside's four equations is an amalgamation of Maxwell's law of total currents (equation "A") with Ampère's circuital law (equation "C").

All in all, the way the article is written makes it difficult to sort out what are Maxwell's equations and what is Heaviside's later work. I think this article should clarify Maxwell's paper "A Dynamical Theory of the Electromagnetic Field" and other articles should explain the history of modern work on electromagnetism by Heaviside and others. John Baez (talk) 08:26, 23 July 2023 (UTC)