# Talk:Gauss's law

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## Disambiguation

There's a hatnote with 3 different disambiguation links. I think this is messy and it's time to make Gauss's Law a disambiguation page and move this article to the explicitly named Gauss's Law for Electric fields or something similar.Larryisgood (talk) 16:35, 5 February 2011 (UTC)

I shortened it a bit, I don't think it's too bad. Renaming would be OK, but I would suggest that "Gauss's law" redirects to this article and not to a disambiguation page, per WP:PRIMARYTOPIC. As for whether the hatnote should say
(A) "Gauss's law redirects here. For analogous laws concerning different fields, see Gauss's law for magnetism or Gauss's law for gravity. For Gauss's theorem, a mathematical theorem relevant to all of these laws, see Divergence theorem."
or
(B) "Gauss's law redirects here. For other uses see Gauss's law (disambiguation)"
I prefer (A) to (B) because the text in the hatnote is actually important educational material that a reader should know. --Steve (talk) 20:03, 5 February 2011 (UTC)
I think I see what you mean, readers may not be aware of the analogous laws and not bother checking the disambiguation page? Larryisgood (talk) 15:05, 6 February 2011 (UTC)

## Permittivity

Maybe $\epsilon_0$ should be replaced by $\epsilon$ for gaining a general statement. Profangas —Preceding unsigned comment added by 141.7.211.81 (talk) 11:34, 9 March 2010 (UTC)

See sections 2 and 3... --Steve (talk) 19:11, 9 March 2010 (UTC)

## Path integrals, integration symbols

It doesn't make sense to speak of a path integral over a surface. A path or curve is by definition one-dimensional; a surface is by definition two-dimensional. Michael Hardy 01:24 Mar 21, 2003 (UTC)

indeed, must we still use the \oint symbol then?
yes, the \oint symbol is still appropriate. It's not just notation for one-dimensional closed-paths, it's also used for the integral taken over any closed manifold, a closed path is just the one-dimensional case, here, it means a closed 2-mainfold, or surface. Revolver
What we really need is the symbol for an integral over a closed surface, which is two integral signs with a loop through both of them: sort of an \oiint, which doesn't exist in standard TeX and LaTeX. (It's in Unicode: U+222F (insert pitch for MathML here).) Mike 21:11, 29 March 2006 (UTC)

## Differential Form

Shouldn't we include it in differential form too? I am too afraid to make mistakes myself to do it.

### Partial form

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

$\nabla \cdot$ is the divergence

D is the electric displacement field (in units of C/m2).

ρ is the free electric charge density (in units of C/m3), not including dipole charges bound in a material

Andries 09:29, 4 Sep 2004 (UTC)

### The divervence notation

∇ · E is not displayed correctly in some computers. Could be the   code replaced by a normal space? -- Fernando Estel ☆ · 星 (Talk: here- commons- es) 09:41, 20 June 2010 (UTC)

Today's edits by User:128.6.83.17 should be carefully vetted. --Wetman 00:12, 10 Jun 2005 (UTC)

2.000? o_O what's the point --210.6.198.242 15:34, 16 Jun 2005 (UTC)

Reply: I believe that there are certain theoretical reasons for insisting that the square be exactly 2, and not just approximately 2. One, I think, has to do with the central nature of the electric force which does not show up with 1/(r^n) type dependence if n is not equal to 2. I could be wrong, so take this with a chunk of salt.

--24.84.203.193 28 June 2005 06:45 (UTC)

solve gauss's law for a sherical charge its just 2, with no reason to insist on a decimal Cpl.Luke 00:04, 13 July 2005 (UTC)

## Symbols

The symbol $\Phi$ should be introduced after the first equation (the integral form). Curiously, all other symbols are introduced.

Could somebody add something about the history of the law? I don't really know much about it, but the only indication that Gauss had anything to do with it (it could just be a name) is the link on the bottom of the page. 134.10.12.13 10:50, 13 February 2007 (UTC)

## Incorrect Equation

Hello. I am looking in my physics text book right now, and it appears the integral for Guass's Law is incorrect. The integral should take the sum of the Magnetic Field not the Electric field as stated in this article. My knowledge is just first year physics, so I wish not to change this article.

134.117.254.250 17:32, 2 March 2007 (UTC) Dave Hawkins

## Correction Not Needed

The statment I made in the last thread was incorrect and I dont know how to dealete it. I apologize for the mistake. Thanks

134.117.254.250Dave Hawkins

• You're not entirely wrong. The integral form of Gauss's Law for a magnetic field can be constructed, but it's equal to zero, always. This is a consequence of the fact that magnetic monopoles don't exist (so magnetic fields go in loops and the net magnetic flux - in the static case - is zero because all field lines that exit the Gaussian surface must re-enter it somewhere else. 24.80.118.29 04:36, 4 June 2007 (UTC)

## Change to intro

Although the introductory paragraph is correct, it's a bit convoluted. Perhaps we could add a couple consice definitions like:

In electrostatics: The electrical flux through an arbituary closed surface is proportional to the electric charge enclosed by that surface.

In gavitation: The gravitational flux through an arbituary closed surface is proportional to the mass enclosed by that surface.

How about simply stating clearly what it means? The article completely fails to do this. Like all too many math/physics articles. Maury 20:17, 28 September 2007 (UTC)

## Template:Electromagnetism vs Template:Electromagnetism2

I have thought for a while that the electromagnetism template is too long. I feel it gives a better overview of the subject if all of the main topics can be seen together. I created a new template and gave an explanation on the old template talk page, however I don't think many people are watching that page.

I have modified this article to demonstrate the new template and I would appreciate people's thoughts on it: constructive criticism, arguments for or against the change, suggestions for different layouts, etc.

To see an example of a similar template style, check out Template:Thermodynamic_equations. This example expands the sublist associated with the main topic article currently being viewed, then has a separate template for each main topic once you are viewing articles within that topic. My personal preference (at least for electromagnetism) would be to remain with just one template and expand the main topic sublist for all articles associated with that topic.--DJIndica 16:35, 6 November 2007 (UTC)

## Move

Shouldn't this article be called "Gauss' Law"?Bless sins 13:37, 14 November 2007 (UTC)

I just came here thinking the same thing...Random89 (talk) 22:06, 31 January 2008 (UTC)
Actually, it's a bit more ambiguous than you might think. This might be an interesting read. Personally, I prefer putting the "s" afterward just for consistency's sake. -142.151.163.237 (talk) 04:26, 27 February 2008 (UTC)
I came here thinking the exact opposite thing, that it should be Gauss's, and I think the article cited above clearly backs me up: everyone I've ever heard say it pronounces it "Gauss's", with an extra "ess" sound versus what one would normally hear when referring to Gauss himself. Fantusta (talk) 23:20, 17 March 2008 (UTC)

## Scope of article?

My impression (borne out by my quick search of Google and textbooks) is that what everyone calls "Gauss's law" is an empirical law that relates D (or E) to electric charge. It has a differential and an integral form, and these are related by the divergence theorem. There's also something called "Gauss's law for magnetism", an empirical law that says that B is divergenceless (again, this law comes in two different forms), and "Gauss's law for gravity", an empirical law equivalent to Newton's law of gravity (again, with two different forms). The only unifying theme among these is that all of them state that the divergence of something is something else, and hence all of them have two forms (differential and integral) related by the divergence theorem.

The article divergence theorem already shows the general form of these equations, and lists out all of these as specific examples. Therefore, I propose:

1. Create dedicated articles for Gauss's law for magnetism and Gauss's law for gravity
3. Put a disambiguating note at the top of the article, directing readers to both the divergence theorem (aka "Gauss's theorem"), and Gauss's law for magnetism and gravity.
4. Add any remaining good content and/or links to the appropriate part of Divergence theorem.

What do people think? --Steve (talk) 20:39, 27 March 2008 (UTC)

All done. --Steve (talk) 04:31, 1 April 2008 (UTC)

In fact, any "inverse-square law" can be formulated in a way similar to Gauss' law: For example, Gauss' law itself follows from the inverse-square Coulomb's law, and Gauss' law for gravity follows from the inverse-square Newton's law of gravity. This implies that you can derive Gauss' law from Coulomb's law yet there is a section called "Deriving Coulomb's law from Gauss' law". Given that you derive Gauss' law from Coulombs law it would make more sense for the article to have "Deriving Gauss' law from Coulomb's law"? See Gauss'_law_for_gravity for what I mean. Perhaps this could be clarified?. --Omnieiunium (talk) 08:02, 23 August 2008 (UTC)

Either follows from the other, more or less. I think I was too lazy to put in the "Deriving Gauss' law from Coulomb's law" section, although I did put in the almost-identical section in the gravity one. I'll put it in when I get a chance, unless someone else does so first. Also, you're right that the text you cite is misleading in putting one over the other. I'll fix that too. --Steve (talk) 16:25, 23 August 2008 (UTC)
Thanks! I'm taking my first E&M class in the fall and was doing a bit of reading/deriving ahead of time and it just seemed weird. Glad to see it fixed! --Omnieiunium (talk) 07:57, 25 August 2008 (UTC)

## Gauss's law

This should be gauss's law not gauss' law. Not only do all the E&M books that I have handy say this, but the Chicago Manual of Style and The Elements of Style, both prefer to add 's to singular nouns ending in an s. 75.177.84.51 (talk) 17:03, 20 April 2008 (UTC)

See the conversation two sections above. It appears that it was changed from Gauss's to Gauss' a few months ago. I think both forms are pretty widely used, and as such, I think either way is probably fine. :-) --Steve (talk) 16:29, 21 April 2008 (UTC)
FYI: I checked both Jackson (Classical Electrodynamics) and Purcell (E&M) and they both use "Gauss's". I would vote for this. Davidofithaca (talk) 21:19, 13 August 2008 (UTC)
Right, but you don't have to look far before you find respectable sources that use "Gauss'". Yes, Gauss's is somewhat better and Gauss' is somewhat worse. But they're both OK. Is it worth your time to move the page back, change the spelling in the text, do the same with all the related articles like Gauss' law for magnetism and the back-links across wikipedia, argue with everyone who wants to move it back again, etc.? I, for one, am on the side of Stare decisis here. :-) --Steve (talk) 22:31, 13 August 2008 (UTC)
This is not a matter of what is used where. It's a matter of English grammar, which dictates that Gauss's is the correct form. --Lingwitt (talk) 18:53, 11 September 2008 (UTC)
If you think that changing the spelling is a good use of your time, be my guest. By the way, I posted a note at Wikipedia talk:WikiProject Physics, to help make sure that any objections are dealt with before, not after, you spend all the time making the changes. I recommend that you wait a week to make sure that there's consensus for the change; I'd really hate to see it changed then changed back yet again.
It also would be worthwhile, I think, if you put a footnote in the first sentence saying that some people spell it "Gauss'" instead of "Gauss's", but this article uses "Gauss's" because [blah] reliable physics sources use "Gauss's", and also [blah] reliable grammar sources say it should be "Gauss's". This might further help ensure that no one comes along and changes it back to "Gauss'" next year. --Steve (talk) 00:42, 12 September 2008 (UTC)
I agree that grammatically it should be Gauss's Law. I would certainly defend against changing it from Gauss's to Gauss' but considering that it has already been changed before and this will eventually come up again, I personally wouldn't go to the trouble it. If however, someone is willing to do it then I'm for it. —Fiziker t c 00:50, 12 September 2008 (UTC)
I'm for whatever's grammatically correct. I'm French is my native tongue, and the apostrophe rule always confused me. I'm under the impression that it's Gauss's law because Gauss is not plural. Jimmy's toothpick vs. The two boys' cake. If it's Gauss's law, then move it to Gauss's law.Headbomb {ταλκWP Physics: PotW} 14:42, 15 September 2008 (UTC)
The more correct form is ’s although is somewhat tolerated (or preferred in applications such as newspaper titles). —Fiziker t c 16:27, 15 September 2008 (UTC)
You are correct about the newspapers, if only because journalists (and their editors) often place style over grammar. If this is to be a reputable source, I feel that style must come second to the proper rules of English. 69.199.23.90 (talk) 20:51, 26 June 2009 (UTC)
It's a moot point all the way, as our own encyclopedia manual of style dictates that so long as everything is consistent within the article, it doesn't matter if there is a 's or an '. Shrug. I learned to in general leave off the s, but I have no opinion in this specific case. --Izno (talk) 21:45, 25 August 2009 (UTC)

## Deriving Gauss's law from Coulomb's law

The identity

$\nabla \cdot \left(\frac{\mathbf{s}}{|\mathbf{s}|^3}\right) = 4\pi \delta(\mathbf{s})$

is not an obvious result to me. I think it would be helpful if this were derived as a lemma possibly placed in a show/hide box. Alternatively, if this derivation exists in another article a link would be useful. I can't find it anywhere and can't come up with a proof just now. Help? Rboesch (talk) 20:56, 25 August 2009 (UTC)

The one currently cited in the article (Griffiths) is particularly clear and explicit. Here's one I found online: [1]. --Steve (talk) 06:01, 26 August 2009 (UTC)

The link above doesn't prove that div $\frac{r}{|r|^3}=4/pi\delta(r)$ The derivation of gauss' law from coulomb's (newton's) law everywhere on wikipedia give this proof, but it ignores, what seems to me, a chunk of functional analysis without a readily available reference. —Preceding unsigned comment added by 76.181.77.201 (talk) 14:45, 13 July 2010 (UTC)

Summary of proof: Let $f(\mathbf{s}) = \nabla \cdot \left(\frac{\mathbf{s}}{|\mathbf{s}|^3}\right)$. By straightforward differentiation, $f(\mathbf{s})=0$ whenever $\mathbf{s} \neq 0$. By the divergence theorem, $\int_V f(\mathbf{s}) d \mathbf{s} = 4\pi$, where V is the unit ball (the set of points in 3D space whose distance from the origin is 1 or less). The only function f that satisfies these two equations is $f(\mathbf{s}) = 4\pi \delta(\mathbf{s})$. :-) --Steve (talk) 23:17, 23 December 2010 (UTC)

## Incorrect Statement

"The law was formulated by Carl Friedrich Gauss in 1835, but was not published until 1867." This is an incredibly misleading statement. In many senses, it's extremely incorrect. If the source does say this it's anachronistic/junk history. Here's an abstract of a paper (positive evidence) that I found: http://adsabs.harvard.edu/abs/2009APS..4CF.F8005S . I haven't read this paper (Now I'm unsure that this abstract completely captures the historical subtleness and nuance) in particular, but I know enough about electromagnetic history to realize how science-fiction-some the current (initially quoted) statement, as written, is. 63.200.214.151 (talk) 18:44, 22 December 2010 (UTC)

If the current source is no good, we need a better one...Can you suggest any? (Your link is the abstract of a talk, not the abstract of a paper. There is no paper as far as I can tell.) I suppose we could just cite the abstract if there's nothing better. :-) --Steve (talk) 12:49, 23 December 2010 (UTC)

## Original references would be highly desirable

The article has several references, but all are to modern books or papers. Does anyone have references to the original publications? Drkirkby (talk) 10:01, 29 November 2011 (UTC)

## clean up

Main changes were:

• Add oiint template to flux surface integrals
• removed redundancy in sections 1 and 2,
• simplify $\Phi_{E,S},\, \Phi_{D,S}$ to $\Phi_E,\, \Phi_D$ - why include the S when flux already known to pass through surface S?? There is no need - its just a clutter of symbols.
• removed the over-repeated "integral and diff. form are related by the div theorem", said almost each time they are quoted.
• moved some general statements about the law into the first section, such as the similarity between Gauss' law in other areas and inverse square laws. Why leave them till later?
• removed flowery "there is a nice, simple relationship between E and D". Really?
• also added more show/hide boxes for the proofs/derivations - "lets not scare readers" and all that......
• re-formatted the blank line for nothing in the Linear materials section - it doesn't take much to re-write the text so that the equations are not "cluttered up", also added links within the section (will a reader know what the terms homogeneous, isotropic, linear mean?).

-- 15:14, 25 February 2012 (UTC)

## Useing Gauss's Law derive the formula for electic field and dew to infinity long strait charged wire?

ʃɛ.da = ɛq/ɛo

2∏ ˠ lɛ = ʎL/ɛo

      ɛ = ʎL/2∏ ˠlɛo

      ɛ = ʎ/2∏ ˠɛo . 1/ˠ  — Preceding unsigned comment added by Badshahfaiyaz (talk • contribs) 13:47, 24 March 2012 (UTC)

What is your point? Could you explain what ∏, ˠ and ʎ are? (do you mean lambda λ for linear charge density?) Also in this equation ʃɛ.da = ɛq/ɛo, what are you doing? You mean
$\oint\limits_\mathrm{surface}\mathbf{E}\cdot d\mathbf{A} = q/\epsilon_0 \,\!$
for free space right? In your version ɛ is used on both sides, so the expression ɛq/ɛo is unclear (and wrong if you use ɛ0 for vacumm permittivity and ɛ for ... another pernittivity/field?).
To calculate the electric field due to an infinite line of charge of uniform linear charge density, see Gaussian surface#Cylindrical surface. The solution is
$\mathbf{E} = \frac{\lambda}{2 \pi\varepsilon_0 |\mathbf{r}|} \mathbf{\hat{e}}_r$
where r is position and $\mathbf{\hat{e}}_r$ is a unit vector, both are directed radially outwards from the line of charge. Does this help?-- F=q(E+v×B) ⇄ ici 14:10, 24 March 2012 (UTC)

## Shouldn't it be "Gauss' Law"?

The New York Public Library Writer's Guide to Style and Usage suggests that one would write "the boss' memos[;] the witness' statement[; or] the hostess' chair" (268). Why would the same not be true for "Gauss' Law"? 129.22.1.10 (talk) 04:09, 25 February 2013 (UTC)