Talk:Continuity equation

confusion between current density of moving charges/mass/... and charge/mass/... density
the current article brings the traditional confusion of the current density carrying "mobile" density (rho(r,t) with non null speed field v(r,t)) and the density that is the *sum* of both "static"(rho(r,t) with null speed field) and "mobile" density. In others words the current density j(r,t)= rho_mobile.v(r,t) =/= (rho_mobile + rho_static).v(r,t)= rho.v(r,t), where the last one is explicitly stated in different sections of this wikipage. can this be corrected/made explicit ? (remove/correct the definition of the current) See, for example, reference: Electromagnetic theory, 1941, J.A. Stratton, Mc Graw-Hills. wiki charge conservation seems OK — Preceding unsigned comment added by 81.245.114.72 (talk) 09:21, 19 April 2014 (UTC)


 * In the continuity equation for electric charge, v would be the average velocity of particles, weighted by the charge of each particle. In the continuity equation for mass, v would be the average velocity of particles, weighted by the mass of each particle.


 * Certainly there are situations with two subpopulations (e.g. conduction electrons vs immobile ion charges in a metal) with different average velocities, where it would be wise to treat each subpopulation separately instead of lumping them together into a single continuity equation. That is basically what you're suggesting by splitting the charge density into mobile vs immobile, each with its own velocity. I would not say that lumping them together is incorrect exactly. The lumped-together equation is true -- but not as useful as the two split-up equations. (The "v" in the lumped-together equation would be a weighted average of the mobile charge velocity and the immobile charge velocity (which is 0).)


 * Likewise, there are also situations with three subpopulations (e.g. conduction electrons vs holes vs immobile ions in a semiconductor), or four or five or more subpopulations (e.g. charge continuity in an electrolytic solution). In all these cases it is wise (but not strictly required) to write separate continuity equations instead of lumping them together.


 * If you're saying that the article does not make it clear that v is an average, then I agree! It's not mentioned at all in the article right now, but it's an important point. The multiple-subpopulation situation is one where it is especially important ... but even when there are not multiple subpopulations, there is still a distribution of different particle velocities, and v is still an average. :-D --Steve (talk) 03:09, 21 April 2014 (UTC)

[reply 01.05.2014] unfortunately, average speed does not resolve the highlighted problem. To make it more explicit than the mobile and immobile charges case (or mobile versus immobile matter, or ...), formally we have a scalar field (rho(r,t)) and a vector field (j(r,t)) and they are independant (in the general case). The continuity equation add a loose coupling between them. As soon as we implicitly say (for the general case) j(r,t)=rho.v, we just end with errors (see below,ohms law example). Taking formally an integral form of an average volume of the continuity equation will not change the point: we have a scalar field (rho(r,t)) and a vector field (j(r,t)).

To hilight my point:

first, we can have rho(r,t) = 0 and j(r,t)=/=0 and the continuity equation. This is incompatible with stating (in the "general case") j(r,t)=rho.v = 0.

Second, (our computers work, we have power): an electric conductor and the ohms law (finite conductivity): j=sigma.E. If one apply formally the continuity equation and maxwell equations and resolve it, one will get rho(r,t>>1) = 0, except at the boundary of the conductor, leading to an almost infinite resistance even for a copper conductor, a contradiction. On all my known good reference books, we can see how the author pay attention to the definition of the current (example reference: Electromagnetic theory, 1941, J.A. Stratton, Mc Graw-Hills) and avoid the trap (section 1.2, charge and current). — Preceding unsigned comment added by 81.247.97.77 (talk) 07:43, 1 May 2014 (UTC)


 * I was editing those sections recently. In the current version, I don't think the article implies that you can or should use the equation "j=rho.v" for electric current. It presents that equation essentially only in the context of fluid flow. The equation j=rho.v is not mentioned during the discussions of electric current--just j is used, not v. Do you agree that the article is OK now? --Steve (talk) 15:10, 1 May 2014 (UTC)

[reply 05.05.2014] unfortunatly no as long as there is j= rho v without the explicit restrictions statements. The main difference between elecotromangetism and fluid dynamics regarding the continuity equation is the positive only(or null) density (e.g. mass). Unfortunately, I have no references on my mind, but I assume (please note i have not checked this one so i can be wrong) if ones take a pipe where the moving fluid is with a partial phase transition (e.g. from a liquid to a non moving solid attached to some parts of the pipe), ones may end with the problem of j= rho_mobile.v(r,t) =/= (rho_mobile+rho_immobile).v(r,t).

If you really want to keep j=rho.v (in the section general equation),I will suggest to add a patch: to express the limitations (with the risk of creating another contradiction), something like: if there is a closed "sufficently regular" volume were the density has a non null speed for all t within a defined closed interval,then J= rho.v within this volume and time interval (i let you find a better wording / mathematical expression), however wihtout a proper reference this could be questionable. — Preceding unsigned comment added by 81.247.82.241 (talk) 19:47, 5 May 2014 (UTC)


 * It says "If there is a velocity field v which describes the relevant flow...". That is an "explicit restrictions statement", isn't it? Any example you come up with where j=rho v is not applicable is either a system where there is no velocity field, or else it's a system with a velocity field which does not describe the relevant flow.


 * If water freezes to the side of the pipe, then the velocity field is zero in the ice regions.


 * How about
 * "If there is a velocity field v which describes the relevant flow--in other words, if all of the quantity q at a point r is moving with velocity v(r)--then..."
 * maybe that helps? :-D --Steve (talk) 14:46, 6 May 2014 (UTC)

[reply 05.05.2014] ok for the comments on my example as I have to push too much in getting an analogy with the em (mixing the "mobile" matter with the non "mobile" matter and we will forget our main topic that is to avoid the reader to stick to the special case where j=rho.v. I really appreciate you effort to my comments so thanks for that. in conclusion, i will prefer to say, "if we have j = rho. v then ..." however looking at this wiki article it will change too many sections. so let's look more on this article.

so rewording your "how about" i would try to propose the following based on the above labels
 * from reading the continuity article, I understand the implicits (please correct me if you do not agree)
 * flow and density (of a quantity). -- it would be better enforce those labels along the whole article (or the ones you prefer like the current and the density,...) to ensure a better consistency (nice to have)
 * where the quanity is implicitly the physical observable
 * "If on a given volume, the density has a velocity field v which describes the flow then the flow j=rho.v --in other words, if all of the density around a point r and time t, rho(r,t) is moving with a velocity v(r,t)
 * however in that case you need a reference to proove it ... (it becomes a mathematical proof "if ...then")
 * reading again the article, i can see there is also the term "flux" used several time and that can contradicts (and it does not point to) the wiki page http://en.wikipedia.org/wiki/Flux. — Preceding unsigned comment added by 91.179.53.212 (talk) 16:03, 17 May 2014 (UTC)


 * Sorry, I don't really understand what you're saying...


 * What would "change too many sections"? Velocity is barely mentioned in the article right now. It's just mentioned in the fluid flow section (where it is clearly applicable), and in the section that says "if there is a velocity field...", where it defines exactly what that means.


 * I don't think the terminology is inconsistent or confusing. Can you clarify? "Flow" is a colloquial term that any English speaker will understand. "Flux" is a specific scientific term which is defined in the article. There is a whole section going through that definition of "flux" in great detail.


 * You are unhappy that there are no links to the Flux article. Actually, there are a couple of links. But there's no real point in linking. This article already has a thorough definition and explanation of flux, as thorough as the one in flux. I would say it's better. One reason it's better is because the flux article lists multiple definitions of flux, not only the definition that we use in the continuity equation, but also totally unrelated definitions. (Do you agree? You say that they "contradict", but I don't think they do. Why do you say that?) Therefore, a reader trying to understand the continuity equation is much better off learning about flux from the flux section of this article than from the flux article.


 * Are you complaining that the article uses several context-specific synonyms of "flux"? For example, "heat flow", "current density", etc. The reason for that is, that's how it is in the real world. When you're talking about electricity, everyone calls it "current"; when you're talking about heat, everyone calls it "flow" or "flux". We should use the terminology that everyone else uses, even if it's not as perfectly consistent as we might like. I think the article makes it quite clear that "current density" (for example) is a special case of the general concept of "flux". Do you agree? If you think something like that is not clear, please point it out, I can add more text.


 * When you say I "need a reference to prove it", it sounds like you are skeptical. Do you believe that the equation j = rho.v is never ever correct??? If not, what do you personally believe? If you just want a reference, you can open up any fluid dynamics book, and you will probably find an explanation of j=rho.v somewhere in the book. --Steve (talk) 20:41, 17 May 2014 (UTC)

Brownian motion and probability continuity
Suggest introducing Brownian motion as a first example of probability continuity, before bringing up quantum mechanics. A Brownian particle is closer to a classical one and its explanation would be more intuitive as to how mass flow becomes probabalized, and this example could then help clarify the QM example. --69.126.41.101 (talk) 15:48, 23 October 2014 (UTC)


 * I think that's a good idea. I rewrote it a bit, I hope you don't mind. :-D --Steve (talk) 02:05, 24 October 2014 (UTC)

Can we have a better sentence than the following?
<<>>

I am not saying that this is a bad sentence. It is perfectly okay when you are describing it to anyone. But I think it doesn't fit at the very beginning of an encyclopedic article. A good (and of course a simple) rephrasing would be preferable.

There are several other instances where it is advisable to revise the literature. Such as,
 * nor can it "teleport" from one place to another
 * the laws of physics in Brazil are the same as the laws of physics in Argentina. Ahmedafifkhan 07:07, 27 December 2017 (UTC)


 * In my opinion, the tone and wording of those sentences is sufficiently formal / professional / encyclopedic as is. But if you have a better alternative I'm happy to hear it. I will be pleasantly surprised if you propose an alternative that is actually equally easy to read and understand. My experience instead has been that the people who go around trying to make things sound more professional are usually doing terrible, counterproductive things like replacing common words with their jargon-y synonyms, replacing concrete descriptions with harder-to-follow abstract descriptions, and so on. (I hope that that stereotype does not apply to you!) --Steve (talk) 16:01, 27 December 2017 (UTC)

Heat flow?
Heat doesn't 'flow', it is not a fluid. The example of heat in a solid is particularly troublesome. One of Fourier's many great contributions to science was to show that heat diffuses in solids. The situtation in fluids is much more complicated because fluids really do flow (!), as in central heating. But this is flow of mass and the evidence is that heat does not have mass. Any analysis that proposes heat 'flowing' is just an unfortunate use of language.--Damorbel (talk) 05:57, 5 August 2019 (UTC)
 * Electric current isn’t a fluid either, but we say an electric current flows in a circuit. Why do you say anything that isn’t a fluid cannot flow? Dolphin ( t ) 11:08, 5 August 2019 (UTC)

Who first apply current continuity equation?
I thought this page should make it clear who is the first one applied current continuity equation. In Maxwell's equations of Maxwell himself, the continuity equation is included. current continuity equation is also the reason for Maxwell to introduce the displacement current which led correct Maxwell's equation.

As I know Gustav Robert Kirchhoff in his 1857 paper "On the Motion of Electricity in Conductors" has applied current continuity equation, but I do not know whether has some one before him has applied current continuity equation. Imrecons (talk) 02:39, 6 June 2021 (UTC)