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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)
[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)
[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)
[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
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)
<<<This statement does not immediately rule out the possibility that energy could disappear from a field in Canada while simultaneously appearing in a room in Indonesia.>>>
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,
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)
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)
This article is rated C-class on Wikipedia's
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Daily pageviews of this article
A graph should have been displayed here but
graphs are temporarily disabled. Until they are enabled again, visit the interactive graph at
pageviews.wmcloud.org |
|
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This page has archives. Sections older than 365 days may be automatically archived by Lowercase sigmabot III when more than 5 sections are present. |
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)
[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)
[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)
[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
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)
<<<This statement does not immediately rule out the possibility that energy could disappear from a field in Canada while simultaneously appearing in a room in Indonesia.>>>
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,
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)
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)