Talk:Poynting's theorem

Old Comments

Isn't the right side the negative of the total power done by the electric field? Not work... --Bmk 15:01, 25 July 2006 (UTC)

Oh, and isn't it actually power per unit volume? --Bmk 15:02, 25 July 2006 (UTC)

Yes. Fixed now. JRSpriggs 05:30, 26 July 2006 (UTC)

I think phasor poynting's theorem should also be mentioned in this page. --139.179.12.105 (talk) 23:20, 1 January 2008 (UTC)Özgür

wrong

Hello, this statement is totally wrong : "Poynting's theorem takes into account the case when the electric and magnetic fields are coupled – static or stationary electric and magnetic fields are not coupled. In other words, Poynting theorem is valid only in electrodynamics." take a look at the feynman course. Wwe can define a poynting vector for a single particle with constant velocity, all the discussiàon bout electrodynamic momentum talks about that. — Preceding unsigned comment added by 134.158.23.246 (talk) 09:34, 24 June 2011 (UTC)

Where is E × B ?

Near the bottom the article says "Instead of the flux vector E × B as above ...". Where does E × B appear above? (I was hoping to be able to refer to it.) Vaughan Pratt (talk) 02:41, 10 January 2014 (UTC)

Cumbersome derivation in "Derivation" section

The derivation in the section entitled "Derivation" could be done simply by differentiation. Going back and forth between the integral statements and the pointwise statements (several times!) is a red herring. It subjects the reader to a pedagogical rehash of the geometric justification for the divergence theorem, whether he wants it or not.

Inconsistencies throughout article

(1) The article defines the Poynting vector S to be "the energy flux vector", rather than giving a specific formula. That is fine. But the definition is not made "out loud", but only implicitly -- one is forced to infer it from the proof of Poynting's theorem. That is not so good.

(2) The main problem I have with this article: it goes back and forth several times between S = E x B and S = E x H, between J and J_f, and between a vacuum and a medium.

For example, early in the article we hear about "free" current, but then we switch to just E and B, then suddenly we have constitutive relations, but they are merely the constitutive relations of empty space. Then we proceed to derive (to prove) that S = E x H. Then we're told that we really did S = E x B (!!!). This does not match the S = E x H definition given under Poynting vector.

What is the correct setting for proving the theorem? Do I need to consult a medium, or decide in a vacuum?

(3) At the end we are told that we could have gotten S = E x H, S = D x B, or even S = D x H, and that the content of Poynting's theorem is different depending on what we got. In the words of the text:

It is possible to derive alternative versions of Poynting's theorem. Instead of the flux vector E × B as above, it is possible to follow the same style of derivation, but instead choose the Abraham form E × H, the Minkowski form D × B, or perhaps D × H.

Choose?

The Poynting theorem we proved here was established independently of these conclusions. It made no commitment as to whether S = E x B or S = E x H. How can the theorem have different versions depending on the formula we later discover for S? Is Poynting's theorem the "continuity"-type statement

$-{\frac {\partial u}{\partial t}}=\nabla \cdot \mathbf {S} +\mathbf {J} _{f}\cdot \mathbf {E}$

where S is defined to be the energy flux, or is it the conclusion S = E x B, where S is defined to be the energy flux? Or is it the formula that's obtained by substituting E x B for S in the boxed formula?

Are the hypotheses or definitions different, to get different theorems? In that case, what are these variable hypotheses?

Why don't we get S = E x H, like in the article Poynting vector? Or do we?

It seems that the definitions and background assumptions are constantly oscillating back and forth in this article.

178.38.181.216 (talk) 00:44, 24 May 2015 (UTC)

Pretty devastating takedown, if I say so myself. Is there such a thing as a C-class article? 84.226.185.221 (talk) 20:47, 15 October 2015 (UTC)

There is. I'm going to try to wade through the subject to figure out what the correct form of the equations should be. --Ipatrol (talk) 19:58, 18 October 2017 (UTC)

(4) (82.71.19.188 (talk) 11:43, 8 April 2021 (UTC)) Amongst physicists, there tends to be a difference of opinion between definitions of the Poynting vector, and this difference often isn't very important (and hence is often not explained) because most materials are non-magnetic (and hence B and H differ only by a constant). Which is best has generated debate in the optics (and quantum optics) communities, often on grounds that make sense in optics, but not necessarily in a pure EM theory context.

In optics, ExH is usually preferred, because it makes spatial boundary conditions clearer, and because E and H are the most useful EM fields in that context. Thus just as a dielectric response generates D from a driving E field, so it is regarded that a magnetic response generates a B from a driving H. This point of view is largely based on practicality, and survives because of that, and because things like relativity and fully spacetime descriptions would almost always an irrelevant distraction and unnecessary complication; there is a sensible lab frame, so you just use it and get on with the calculation.

In contrast, physicists from a pure EM or relativistic background consider E and B the fundamental fields on the basis of the structure of Maxwell's equations (with the source-free equation linking E & B, and the sourced equation linking D & H. Thus they would say that H is generated in a magnetic medium from a driving B field. The relativists are of course absolutely correct, but they are not usually stuck with the problem of making calculations in optics, where using E & H is much more convenient. (as an aside, it is possible to claim that D & H are merely gauge fields for the current, and cannot (should not) be considered to be real physical fields)

Perhaps the point is this: is this article about Poynting *original* theorem, or about possible Poynting-style conservationish theorems in EM (as e.g. enumerated in ref[6])? What is the article trying to communicate? Maybe the bulk of the article should ruthlessly stick to original Poynting, and leave remarks on variants and controversies to a discussion subsection at the end.

Importance rating

I'm fairly new here (sorry if I'm wrong) but reading the guidelines for importance scale I think the "low" rating is too low. Poynting's theorem is covered in at least some undergraduate physics degrees (that's actually how I ended up at this page) which would put it comfortably in the "high" category. Griffith's Introduction to Electrodynamics is a standard undergraduate text that discusses it in chapter 8. I would recommend medium after reading the guidelines.

Alich1881 (talk) 23:23, 2 September 2021 (UTC)

Agreed PianoDan (talk) 22:22, 2 December 2021 (UTC)

References