Talk:Gauss's law

message: 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)
replies: text: See sections 2 and 3... --Steve (talk) 19:11, 9 March 2010 (UTC)
thread_title: Permittivity

message: 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)
thread_title: Path integrals, integration symbols

message: 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)
thread_title: Differential Form

message: \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)
thread_title: '''Partial  form'''

message: ∇ · 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)
thread_title:  The divervence notation 

message: Today's edits by User:128.6.83.17 should be carefully vetted. --Wetman 00:12, 10 Jun 2005 (UTC)
replies: text: 2.000? o_O what's the point --210.6.198.242 15:34, 16 Jun 2005 (UTC)

text: 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)
thread_title: Please vet

message: 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)
thread_title:  Symbols 

message: 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)
thread_title:  Incorrect Equation 

message: 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)
thread_title:  Correction Not Needed 

message: 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)
thread_title:  Change to intro 

message: 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)
thread_title:  [[Template:Electromagnetism]] vs [[Template:Electromagnetism2]] 

message: Shouldn't this article be called "Gauss' Law"?Bless sins 13:37, 14 November 2007 (UTC)
replies: text: I just came here thinking the same thing...Random89 (talk) 22:06, 31 January 2008 (UTC)
replies: text: 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)
replies: text: 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)
thread_title: Move

message: 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:
# Create dedicated articles for Gauss's law for magnetism and Gauss's law for gravity
# Make this article specifically about the law relating D or E to electric charge, in accordance with common usage, and delete all the content not about this law
# 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.
# 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)
replies: text: All done. --Steve (talk) 04:31, 1 April 2008 (UTC)
thread_title:  Scope of article? 

message: 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)
replies: text: 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)
replies: text:  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)
thread_title: Contradiction?

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

text: 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)
thread_title:  Deriving Gauss's law from Coulomb's law 

message: "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)
replies: text: 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)
thread_title: Incorrect Statement

message: 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)
replies: text: I've included them in my recent edits.--Geremia (talk) 16:51, 3 August 2016 (UTC)
thread_title:  Original references would be highly desirable 

message: 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?).
--  F = q(E + v × B) 15:14, 25 February 2012 (UTC)
thread_title: clean up

message: I am new here so I'm hesitant whether I should make modifications myself, but I feel like this section needs an overhaul and I'm not sure how to indicate this. First of all, when describing electric field lines one shouldn't be calling them "power lines" as electric field lines AFAIK are not a measure of power (Js^-1). Secondly, the section has obviously been duplicated with some modifications to the second copy displayed. Thirdly, the section is written in very poor English and is lacking clarity (for instance the third sentance "...the direction of - field lines..." should read "...the direction of negative field lines..."). Fourthly, it is incorrectly referenced.  — Preceding unsigned comment added by BeNZealand (talk • contribs) 05:03, 29 September 2016 (UTC)
thread_title:  Interpretations section needs an overhaul 

message: In the section entitled "In terms of fields of force" we find this sentence fragment:
Of course, meant keeping signs,
I am not sure if this was supposed to read "*This*, of course, meant keeping signs," or what so maybe someone who understand the material better can correct or clarify here.--Jrm2007 (talk) 06:41, 10 September 2017 (UTC)
thread_title:  Possible typo 

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thread_title:  External links modified 

message: Shouldn't we make it clear that "the" electric field mentioned in the current article is only that part of the total electric field that is due to the charge enclosed by the surface.  Charges outside the surface make no contribution to the net flux through the surface, but they can can contribute to the electric field at any point.  
For example, the passage:
:
"where  is the electric field,..."
doesn't make it clear that E is only that part of the electric field due to charges inside the surface. 
Tashiro~enwiki (talk) 08:29, 26 January 2018 (UTC)
thread_title: Which electric field is "the" electric field?

message: I would adjust the title of this article. This one's too broad!  — Preceding unsigned comment added by Koitus~nlwiki (talk • contribs) 18:30, 7 October 2019 (UTC)
thread_title:  As if Gauss' law for gravity does not exist! 

message: The differential form of Gauss Law is written as 
\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0 \varepsilon_r}
in the article. However, there is no \varepsilon_r relative permittivity dependence in the actual equation. The article on Maxwell's equations has it in its correct form.
Hamzh-19 (talk) 02:26, 6 April 2022 (UTC)
replies: text: I think that the article is correct.  I'll try to get back to you soon to explain my thinking.  Constant314 (talk) 02:57, 6 April 2022 (UTC)

text: As promised:  Take a parallel plate, vacuum capacitor of 1F (it is a big capacitor) with plate separation of 1mm.  You put a 1V source across the plates, you get an E field of 1000kV/m and +1C on one plate and -1C on the other plate.  Put the Gaussian surface around the positive plate.  All good.  Now you replace the vacuum with a dielectric material have a relative permittivity of 2.  The E field is unchanged, but now the positive plate has +2C.  Since the E-field is the same, then the surface integral is the same, but there is twice as much charge.  Hence, you have to reduce the charge by the relative permittivity to make the equation valid. Constant314 (talk) 03:14, 6 April 2022 (UTC)
replies: text: Ah yes, you are correct. My apologies; I guess for completeness the relative permittivity is needed for cases where it is not equal to 1, like dielectrics as you have said. However then, Gauss Law as written in https://en.wikipedia.org/wiki/Maxwell%27s_equations#Differential_equations differs from this, and does not included relative permittivity. Do you think it would require changing? Hamzh-19 (talk) 22:46, 6 April 2022 (UTC)
replies: text: No.  That section of that article explicitly calls out a vacuum. Constant314 (talk) 22:55, 6 April 2022 (UTC)
thread_title:  Incorrect Differential form of Gauss Law 

message: The codes such as
 
do not show correctly in dark theme. The integral sign is invisible. -- Jähmefyysikko (talk) 11:51, 12 February 2023 (UTC)
thread_title:  Equations are broken in dark theme 

message: I need explanation 223.227.32.178 (talk) 14:08, 10 October 2023 (UTC)
thread_title:  Potential point charge