Talk:Displacement current/Archive 1

Archive 1

Archive 2

Archive 3

Dispersion in dielectrics

Dielectric constant not time independent?? Never heard of this one. Would someone care to explain?? Light current 00:27, 4 September 2005 (UTC)

The word dispersive is the explanation. Clearly any change in the density of a fluid medium could cause a change in its dielectric constant. DFH 15:26:59, 2005-09-06 (UTC)

Can anyone tell me where I can get time dependent dielectric material to be used as a PCB substrate. I could really do with some. I'm not joking! Light current 00:21, 7 September 2005 (UTC)

Pseudocurrent?

A definition which uses an undefined word is hardly an adequate description. Anyone care to attempt to explain what the word pseudocurrent really means? DFH 16:06:13, 2005-09-06 (UTC)

Not worth it. Ive just changed it! Light current 22:47, 6 September 2005 (UTC)

Stored Current?

How can current be stored (unless in a superconducting ring) para 3?? Light current 23:07, 6 September 2005 (UTC)

Paragraph 3 repeats the commonly taught error that something is stored in the dielectric material. Is it not rather obvious that for a capacitor in which the space between the plates is a vacuum, such an explanation is nonsense? The best that can be said is that it is a poor analogy to bring in the word elastic. DFH 07:06:58, 2005-09-07 (UTC)

Sorry. I just couldn't stand seeing this nonsense any more - so I changed it Light current 14:03, 7 September 2005 (UTC)

The Catt Anomaly, etc

Have you read any of Ivor Catt's work on electromagnetism?
(including his 1978 Wireless World article: Displacement Current — and how to get rid of it)
DFH 21:45:52, 2005-09-07 (UTC)

Yes I did read it, but unfortunately my dad threw out all my magazines with these articles/letters in . I would love to be able to read them again. Has Catt published all his articles on this website? Light current 01:25, 8 September 2005 (UTC)

Yes, he has — just follow the above links. He has more than one website. Site navigation is rather messy, and many of the articles appear more than once in various forms. DFH 07:04:59, 2005-09-08 (UTC)

LC: Now I know what you are up to over in Talk:Capacitor. Alfred Centauri 22:06, 13 September 2005 (UTC)

AC: Having a ding-dong in various talk pages is all very interesting, but a proper NPOV article about Catt would be more useful for the encyclopedia. DFH 18:19, 16 September 2005 (UTC)

David: I'm unfamiliar with the term ding-dong in this context but I'm assuming it is equivalent to a 'knockdown-dragout' :) Regarding an article about Catt - what's holding it up? Since I know nothing about Mr. Catt other than that he appears to exhibit all the hallmarks of a 'crank', I'll leave that article up to you and LC. I've got to go now and see what Tom Bearden is up to ;<) Alfred Centauri 21:12, 16 September 2005 (UTC)

Just looked up the two terms:

A)Ding -dong is a hammering exchange of blows,

B)knockdown dragout is a particularly violent and acrimonious argument

Now I, for one, think that AC and I have been having what we call over here a 'stimulating discussion' with few holds barred. Yet we are being civil to each other and, although there have been a few misunderstandings, I feel that we are now coming to appreciate each others point of view. Therfore I would say that were are not having a ding dong, more of a "to and fro" (a lot more gentle!). Sorry to be pedantic David!--Light current 22:13, 16 September 2005 (UTC)

All in good time David, all in good time ;-). AC and I are just preparing the ground at the moment. Its a lot easier to have these discussions before the event I find than to wrangle over little words in a semi complete article. What we are discussing also has bearing on the displacement current page, and the capacitor page and the transmission line page,(and probably others) so I would ask you to be patient a bit longer!

Does the 'Displacement Current Term' produce a magnetic field?

Without getting into the discussion of whether there is a physical 'thing' called electric displacement and an associated flow of this stuff, a much more interesting question (to me at least) is whether the 'displacement current term'

${\frac {d{\vec {D}}}{dt}}$

produces (generates, induces, whatever) a magnetic field or merely 'accompanies' a magnetic field. There are mathematical formulations that give the correct magnetic field without a displacement current term (these formulations take in to account the fact that instantaneous action at a distance is incompatible with Special Relativity). Additionally, it can be shown that if Coulombs Law is made compatible with the postulates of Special Relativity, magnetic effects are simply the electric field as observed from a relatively moving reference frame.

So, does the dispacement current term generate a magnetic field? Alfred Centauri 01:35, 16 September 2005 (UTC)

A magnetic field exists in EM waves -- no one knows what causes it, people can only guess. Is it just the relativistic effects of a moving electric field? BTW has anyone actually measured any of this flow of charge in EM waves? If so how did they do it?--Light current 01:47, 16 September 2005 (UTC)

What causes the electric field in an EM wave? Alfred Centauri 02:03, 16 September 2005 (UTC)

I dont actually know. Probably the magnetic field. I was led to believe that an EM wave propagates by the continuous interchange of energy between the electric and magnetic fields. As a result of this, each field 'causes' the other (further down the line of course). In this model, although you can postulate a so called current causing the magnetic field, I dont think its necessary to do so. The real question is, although this current is indicated by the equations, and a magnetic field exists, does this necessarily mean that this displacemnet current actually exists? Or does it really matter whether is it really exists or not since we can't measure it anyway? The argument about displacement current was originally to do with capacitors. I fear we have strayed slightly away from this, unless, of course, you are shortly going to make a new revelation based on the previous material on EM waves?--Light current 03:31, 16 September 2005 (UTC)

I've been doing some reading since you brought up the subject of displacement current and I plan to do a good bit more. From what I have read so far, there are some rigorous mathematical results (that I haven't examined yet) that show that a changing conservative electric field does not create a magnetic field. Further, I read that the magnetic field between the plates of a charging capacitor can be shown to be primarily due to the magnetic field of the charge moving in both the wires connected to the plates and in the plates themselves. Finally, I read that if you assume that the charge density on the plates of a capacitor is uniform and changing (the assumption used in most textbooks), the magnetic field due to the fringing E field cancels the contribution from the displacement current term.

Sorry to butt in here but I just noticed you said the charge density was assumed uniform on this parallel plate capacitor. But how does it become uniform initially? Answer: the energy has to travel somehow from the wires to the edge of the plates. So the charge density cannot be uniform on the plates at ac--Light current 16:02, 16 September 2005 (UTC)

<sigh> If I say assume the charge is uniform then assume that it is, please. I'm not asking you to believe that this is a realistic assumption. If you read carefully, you'll see that my point was that IF one assumes this is true, the result is different from what is taught or expected. Besides, I believe it is possible in principle to construct such a capacitor. Alfred Centauri 17:36, 16 September 2005 (UTC)

Yes I got your point OK and its interesting. I was just restating my belief thats all. BTW Im not sure about the existence of a real magnetic field between capacitor plates (other than that due to a EM wave)--Light current 17:52, 16 September 2005 (UTC)

Thus, even if you do assume that there is a displacement current betweent the plates of a capacitor and that the increasing charge is uniformly distributed on the plates (no TL effects), any measured magnetic field is not from the displacement current. Yet, while the notion of a TL model for a physical capacitor seems reasonable to me, I'm confused about something. It seems to me that the reason your are more comfortable with a TL capacitor model is because you believe TLs don't require a displacement current to explain their operation. If this is your belief, would it not be true that a capacitor that is not constructed as a TL would then be unexplainable according to your model? One last thing. According to what you and I have read, a changing magnetic flux density induces an electric field and this is the origin of the electric field in an EM wave. Doesn't this bother you? After all, a changing magnetic flux density is nothing other than a magnetic flux current density - in other words a magnetic displacement current completely analogous to the electric displacement current. Alfred Centauri 12:53, 16 September 2005 (UTC)

I confess a great deal of ignorance the area of Vector Field Theory so I shall defer to your superior knowledge in that subject. I have heard of an experiment (and the equipment is supplied for the demonstration of such an effect for the education of students!) which purports to demonstrate the passage of diplacement current in a parallel plate capacitor. It comprises 2 large discs (about 1ft in dia) separated by a distance of about 1ft. A sinusoidal voltage at ~ 15kHz is applied between the plates and a search coil is placed in the gap. THe search coil o/p is then displayed on a scope which shows-- well I'm not sure what it proves,-- but a sine wave at 15 kHz is diplayed. Obviously the search coil when properly oriented responds to a magnetic field, but the displacement current is so small in a capacitor of these dimensions that Im dubiuos whether that this is what's being seen. Its more likely to be coupling of the electric field to the (unbalanced) coil!

The reasons Im more comfortable with the TL representation of capacitors are numerous.

a)a pair of parallel plates fed from one end is an o/c TL

b)It is hard to think of a capacitor construction that does not conform to a transmission line structure, This is because practical capacitors always have 2 parallel plates (or paralleled combinations of these) that are usually rectangular. THe classical description of a capacitor with 2 parallel coaxial discs and fed from wires at the centre of the discs can easily be appreciated to be a number of wedge shaped parallel plate capacitors in parallel. Each wedge shape forms an end fed TL of decreasing Z0 towards the periphery. Each wedge is of course o/c at the end.

But nobody in his right mind would design a practical capacitor that way these days would he? Actually I had to design a HV capacitor of about 1pF to work at 20kV once using that design....But then Im not in my right mind!!--Light current 16:21, 16 September 2005 (UTC)

c)If all (or the practical majority of) capacitors can be considered as transmission lines, then there is no need to postulate displacement current in capacitors any more than it is necessary to explain it for transmission lines. I am not aware that dispalcement current is a necessary part of the explanation of ttransmission line theory but I could be wrong on that and I'm sure youll tell me if I am ;-)

Well, now that you mention it! You might be aware that a TL also support TE and TM waves. These modes turn out to be the superposition of TEM waves that are 'bouncing' between the conductors. That is, the direction of propagation of the TEM wave is oblique to the 'direction' of the TL. Now, it turns out that these TE and TM wave can also exist in a non-conductive TL such as, for example, a fiber optic cable. For these TLs, there is no conduction current! Further, you can't make a capacitor out of one these (as far as I know). Alfred Centauri 18:13, 16 September 2005 (UTC)

Well that is interesting. I have not yet found my book on fibre optical transmission. In the light (no pun intended) of this, I may have to modify my statement to restrict my argument to TEM waves only as per normal transmission lines with conductors. No conduction current in FO, so its all the other sort I assume, or just photons perhaps? Maybe FOs can still be considered a capacitor, but I was not originally intending to include them in this discussion. I would like to defer discussion on that particular angle until I have had time to revise/research the subject more fully. Then I will respond as to whether I think my argument will stretch that far.--Light current 18:28, 16 September 2005 (UTC)

Now it so happens, that you, whether by accident or design, have come up with the problem configuration of a contra fed pair of parallel plates/wires. This, as it happens, is exactly the way extended foil capacitors must be fed due to their construction. Extended foil capacitors are advertised to have extremely low inductance (in the single nanohenries). To achieve this low inductance, I can see no other possiblity than that these capacitors too act as transmission lines. BTW have you made any progress on the proposed experiment? I would be extremely puzzled/disappointed if the ContraFedLine (CFD) turned out not to behave as TL for then we would have to expalin how extended foil caps achieve near zero inductance!

In answer to your last part: Yeah, everything bothers me!. Thats why Im asking these fundamental questions: to try to understand things a bit better. BTW in reading a bit on classical EM theory last night, I came upon the brief mention of the photonic explanation of EM waves. THis sounds to me exactly like the old wave/ poarticle duality discussion-- or is there more to it than that?--Light current 15:28, 16 September 2005 (UTC)

Only a mathematical construct

Displacement current was an idea invented by Maxwell when he couldn't think of another way that current could flow beween the plates of a vacuum capacitor. Maxwell did not ever come across EM radiation (as it was Hertz who discovered it) and Maxwells concern was displacement current in capacitors. THis does not exist.

Some people today say that displacement current must exist for electromagnetic radiation to exist. This necessity has not been proven. What exists in EM waves are time varying electric and magnetic fields. Some people cannot concieve of a magnetic field without the presence of a current to cause it. This current in a EM wave has never been measured. This is because it doesnt exist and is just an imaginary concept to try to explain away EM radiation with no charge carriers. Discuss (10 marks for convincing replies)--Light current 23:00, 15 September 2005 (UTC)

The electric field and magnetic field are 'only' mathematical constructs. What is your point? Alfred Centauri 00:27, 16 September 2005 (UTC)

I thought my point was obvious displacement current is only a mathematical construct and does not really exist--Light current 00:34, 16 September 2005 (UTC)

If that's all there is to it then you made no point at all. There exists in the this universe phenomenon that are observable such as the electric force and the magnetic force. These forces can be mathematically modeled as force fields but does that mean that these force fields are physical? To say that something is an imaginary concept is saying nothing at all. Concepts are nothing other than imagination, my friend. The incredibly successful quantum theories we now have talk of probability currents - the flow of probability. I hope that you do agree that EM waves carry momentum thus, EM waves represent a momentum current. You seem to be hung up on the idea that a current must be the flow of something physical. Well, what is an electric current? It's not the flow of electrons or ions or protons or quarks. It is the flow of electric charge. Electric charge, what is that? - what a concept! Alfred Centauri 01:04, 16 September 2005 (UTC)

I was reading only a few hours ago about the pressure of sunlight on the earth, so yes, EM radiation must have momentum. But if current is the flow of electric charge, where does this charge come from in empty space.?If you are defining charge as little quanta of EM radiation - then I might agree!--Light current 01:24, 16 September 2005 (UTC)

Well, if space is empty, there is no charge right? Not so fast! It turns out that what we consider 'empty space' is chock full of ghostly charged particles. Look at the Casimir effect. The vacuum may even be full of something called the Higgs boson that give matter mass. For some additional 'light' reading, get a copy of "The Elegant Universe". In the superstring theory outlined in this popular book, electric charge is simply a particular vibrational mode of little bits on concentrated spacetime called strings (or superstrings) that live in 11 dimensions (give or take). If you think Displacement current is difficult or impossible to imagine, you ain't seen nothin' yet. Alfred Centauri 01:58, 16 September 2005 (UTC)

You said: "The human brain cannot concieve of a magnetic field without the presence of a current to cause it". Are you sure you want to go on record as having made this idiotic statement? Alfred Centauri 00:29, 16 September 2005 (UTC)

I dont believe the statement is idiotic. Again, for those who believe in displacement currents, their brains cannot concieve of a time varying magnetic field without them can they?--Light current 00:34, 16 September 2005 (UTC)

If you had said "My brain cannot conceive..." then, though I might disagree, I wouldn't consider the statement idiotic. Think about what you said - "The human brain cannot conceive...". I ask once again, do you wish to go on record as making such an idiotic statement? Alfred Centauri 01:04, 16 September 2005 (UTC)

I'm already on record. So rather than ask me again whether I want to go on record, it would be more helpful if you explained to me the errors of my ways. If I see the error, I will retract my statement. Im not trying to prove anything personal here :-)--Light current 01:20, 16 September 2005 (UTC)

Think about it - who are you to say what the human brain can or cannot conceive? First, that's highly presumptuous and second, such sweeping statements are likely to get you labeled as a 'crank' [1]. Take a look at the new section I added here and see what you think. Alfred Centauri 01:44, 16 September 2005 (UTC)

As my statement seems to have upset you so much, I am willing to modify it by saying that " Some people cannot concieve of a time varying magnetic field without a charge current to cause it". I really did not mean to cause offence to any one in my statement and I apologise for doing so. SORRY!!--Light current 01:57, 16 September 2005 (UTC)

Quantum Theory of EM radiation

That's correct - an EM wave is composed of discrete 'wavicles' of energy called photons. Further, the electromagnetic force is due to charged (whatever that means) particles such as electrons exchanging what are called virtual photons. These virtual photons cannot, in principle, be directly observed. This may cause some to wonder if this ghostly particles exist. However, it turns out that if calculate the magnetic moment of an electron without considering the interaction of an electron with its own virtual photons, you don't get the right answer. However, when you do take these guys into account, you get an agreement between theory and experiment to some 6 or 7 digits. That's pretty darn impressive to me. Alfred Centauri 17:58, 16 September 2005 (UTC)

Yes, I like this theory, I have few probelms with it (probably cos I dont fully understand it!). I also like the idea of particles & antiparticles suddenly appearing and disappearing for no apparent reason. As I remember saying to myself only the other day : "the sum of everything is probably nothing at all-- so why worry?!"--Light current 20:58, 16 September 2005 (UTC)

After all, isn't zero just (1 - 1)? Alfred Centauri 01:51, 17 September 2005 (UTC)

Exactly!--Light current 09:48, 17 September 2005 (UTC)

Million errors in this page

I'll come back and fix them when i have time:

1. displacement current is not a real current. it is a mathematical construct. it does not correspond to any flow of charge, which is what current is. Source: Marion and Heald, "Classical Electromagnetic Radiation"; Jackson, Classical Electrodynamics; Sears, Zemansky and Young, "University Physics".

2. It shouldn't say "'some' people say that displacement current does not in reality exist"; nobody who understands what it is believes it is a real current.

3. the first formula is totally wrong, or irrelevant, not sure which. the one on the bottom is correct.

4. Response of a dielectric to a changing field? It has nothing to do with a dielectric. Displacement current "exists" even in the vacuum. I think someone's confusing it with polarization.

5. it's not the flux of the electric field, it's the rate of change (time derivative).

6. Ampere's law only works for steady-state current distributions. Has nothing to do with the surfaces.

7. the epsilon form at the bottom assumes that the medium is linear and isotropic. It may assume it's not dispersive too, I'm not sure.

Pfalstad 04:30, 5 October 2005 (UTC)

I agree that there are some problems with this article but I'm somewhat perplexed by the examples you have given. Here are my thoughts on the points that you brought up:

1) A current is a flow. An electric current is a flow of electric charge. A displacement current is not a flow of electric charge by its modern definition so I'm not sure what you point is. Just as there are probability currents in QM, there are flux currents in EM. These currents are real in the sense that they represent the flow of some quantity. Whether that quantity is physical or not is a different question altogether.

the article, before I changed it, referred to displacement current as "a form of current" in the first sentence. this is not accurate, or at least is misleading. Pfalstad 16:18, 5 October 2005 (UTC)

2) I suppose what you mean is that nobody believes that displacement current is a flow of electric charge. However, I don't think that is the claim of the quote from the article. It is my opinion that the quote from the article refers to the question of whether electric displacement is physical or not.

Well, it should be clarified or removed. Pfalstad 16:18, 5 October 2005 (UTC)

3) Why? (I see a problem with it too but I'd like to know what precisely you see wrong with it).

No problem actually, I just forgot about the integral forms of maxwell's equations! Oops. Pfalstad 16:18, 5 October 2005 (UTC)

4) I think that Maxwell orginally pictured the displacement current as an actual electric current due to the displacement of charge within a dielectric. The vacuum does pose a problem for that view. However, according to QED, the vacuum isn't actually empty and can in fact be polarized. This effect is real and measurable.

The view of Maxwell is of historical interest only. Your comment about QED is well taken but the original article wasn't talking about QED (it was talking about dielectrics), and I think that is out of place in an article on classical electromagnetism (will confuse people), except perhaps for a section at the end.

5) Agreed. Further, it is the rate of change of the electric flux (Coulombs per second) which is not the same as the rate of change of the flux of the electric field (Volt-meter per second).

6) I assume that by steady state, you mean not changing with time (as opposed to the notion of AC steady state where the amplitude doesn't change with time). Ampere's law has nothing to do with surfaces? Maybe I missed something along the way but I was under the impression that Ampere's law equates the mmf around a closed path to the current through the oriented surface enclosed by the path.

Forget what I said about the surfaces, my point is that Ampere's law only works for time-invariant currents in its original form. Pfalstad 16:18, 5 October 2005 (UTC)

7) This is true if you intepret $\epsilon$ as a scalar rather than a rank 2 tensor.

Fair enough. Pfalstad 16:18, 5 October 2005 (UTC)

Since LC and I are exchanging ideas about displacement current amoung other things, I do not plan to edit this article in the near future. Alfred Centauri 16:09, 5 October 2005 (UTC)

Not totally happy with the first sentence. I want to dumb it down to start off the article as simply as possible, without calling it a current. "psuedocurrent" is close but isn't a word, and people complained about it; "fictitious current" sounds like I am debunking it. As far as I can tell, "displacement current" is defined by its mathematical form, or by calling it "a term in maxwell's equations". But I would rather not open with an equation if I can avoid it. Pfalstad 16:53, 5 October 2005 (UTC)

Troubling sentence

Im worried about this sentence:

The present day concept of displacement current therefore simply refers to the fact that a changing electric field produces a magnetic field.

Are we sure that everyone in the world understands Maxwell's displacement current to be NOT a current?? Im not!

--Light current 01:46, 30 December 2005 (UTC)

Well I don't care about what "everyone in the world" thinks; what do the standard texts say? Marion and Heald, talking about the capacitor: "There is a displacement current even though no charge moves across the space." It also makes a clear distinction between conduction current and displacement current. Smythe: "Maxwell apparently thought of the magnetic field as being caused by an actual displacement of electric charge, but such a picture is not needed to justify [Maxwell's equations]." Jackson: "Maxwell called the added term the displacement current. Its presence means that a changing electric field causes a magnetic field, even without a current...." If you can find a standard textbook which gives a different picture, let me know. Pfalstad 02:23, 30 December 2005 (UTC)

Note that the quote from Jackson indicates that displacement current (changing electric field) causes a magnetic field. Or at least it shows that standard textbooks say it does. Pfalstad 05:21, 30 December 2005 (UTC)

Well I think this confusion over terminology is probably more than half the problem we have with Catt et al. People are using different definitions of displacement current and Im not sure your definition, (dD/dt) has percolated all the way down thro the electrical engineering community. You can have disp current in a dielectric of course, but were talking about free space here, yes? In dielectrics, you can get a real measurable disp current. In vacuo, you cant. What was Maxwell talking about? dielectrics or vacuum?--Light current 02:34, 30 December 2005 (UTC)

I don't know what Maxwell was talking about, but nowadays, displacement current has nothing to do with dielectrics. It occurs in a vacuum or anywhere else. Can you find any standard electrical engineering textbook which says otherwise? Pfalstad 03:20, 30 December 2005 (UTC)

I refer you to the Electronics Engineers Handbook, Fink. pub McGraw Hill First Ed. 1975. page 1-18 Displacement current.

Electric fields of elementary cahrges extend considerably beyond the dimensions of charge carriers and may be represented in terms of electric flux. The expression for current, I=rho s v (where rho = vol density of charges,v = velocity, s= area) may be applied to show that a time changing electric flux in a dielectric produces a displacement current. The transfer dQ of free charges to conducting surfaces on opposite sides of a dielecric sets up a flux d(psi) in the dielectric and the charge density is :

rho = dQ/dV (V is volume)

= d(psi)/dV.

Since volume = s.l, and since dV = sdl, the displacement current is:

I (dis) = rho s v = d(psi)/dt.

Since psi = Ds and D= epsilonE, the displacement current in the dielectric may be written interms of electric field strength as:

I dis= dpsi/dt = s epsilon dE/dt.

How now , brown cow?? Would you mind replacing what you took out? Thanks!--Light current 03:28, 30 December 2005 (UTC)

Displacement current has 2 terms

Another ref to disp current. Fundamentals of Electromagnetic Field Theory, Zaky & Hawley, pub Harrap, London.1974 page 194.

Displacement 'D = epsilon0 E + P'

disp current density is:

jd = epsilon0 dE/dt + dP/dt

The second term on the rhs expresses the variation of polarisation of trhe medium and is called the polarisation curent density. It represents an actual displacement of elastically bound charges, and as such it is confined to dielectric media where the polarisation varies with time....

So displacement current consists of 2 terms, polarisation curent (only present in dielectrics) and the vacuum displacement current to which you refer.--Light current 03:54, 30 December 2005 (UTC)

Aha! You are right. But, is "vacuum displacement current" a term you saw somewhere, or did you just make it up? Anyway, displacement current in dielectrics does include an actual movement of charge, if not an actual conduction current.

Its quoted in the last reference as being what you call dispancement current density ie epsilon0 dE/dt--Light current 04:45, 30 December 2005 (UTC)

You said:

Well I think this confusion over terminology is probably more than half the problem we have with Catt et al. People are using different definitions of displacement current and Im not sure your definition, (dD/dt) has percolated all the way down thro the electrical engineering community. You can have disp current in a dielectric of course, but were talking about free space here, yes? In dielectrics, you can get a real measurable disp current. In vacuo, you cant. What was Maxwell talking about? dielectrics or vacuum?--Light current 02:34, 30 December 2005 (UTC)

Well I think you have shown that the dD/dt definition is agreed upon, yes? And that you can have displacement current in the vacuum, yes? Pfalstad 04:39, 30 December 2005 (UTC)

No.(sigh) I dont believe in displacement current in a vacuum as I've said many times.

dD/dt =jd (BTW diff operator is partial- but I cant show curlies)

D = epsilon0 E + P

1. dE/dt is not a real current.

As the book says " its really a ficticious current in the sense that it does not arise from the motion or displacement of any charge, either free or bound".

Fine, I agree. Everybody does. But it can be nonzero in the vacuum, and it is called "displacement current", yes? Even though it's not actually current.

Notin my book-- Sorry!--Light current 05:06, 30 December 2005 (UTC)

I don't understand. Not in your book, what? You just quoted me a section of your book giving displacement current as the sum of epsilon0 dE/dt and dP/dt. So in the vacuum that reduces to epsilon0 dE/dt. That's displacement current! Pfalstad 05:09, 30 December 2005 (UTC)

Sorry I meant not in my opinion!--Light current 05:17, 30 December 2005 (UTC)

In your opinion what.. It shouldn't be called that, or it's not really called that, or ...?  :) I agree it shouldn't be called that! Pfalstad 05:20, 30 December 2005 (UTC)

No.(sigh) I dont believe in displacement current in a vacuum as I've said many times.(here it is again)--Light current 05:23, 30 December 2005 (UTC)

You keep saying it, but what does that statement even mean!?!? Do you agree with the equations you quoted?

A.It means I dont believe anything can flow (except em energy) in a vacuum. THe equations are OK, its how you interpret them that's the question here!

Sorry to have to split your post.

Do you agree that at least some textbooks say that displacement current is equal to dD/dt? A Yes they should all say that!--Light current 05:37, 30 December 2005 (UTC).

Do you agree that dD/dt is nonzero in a vacuum? Pfalstad 05:27, 30 December 2005 (UTC)

A.Well its given by epsilon0 dE/dt. So it could be non zero yes!

HOWEVER, I personally disagree with the books as interpreting this as a flow of anything!

BTW Your definition is properly called vacuum displacement current ( which I dont belive in) --Light current 05:38, 30 December 2005 (UTC)

They don't interpret it as a "flow"; that's what I was trying to show by quoting the books above. At least I don't interpret it as a "flow" or "current". They call it "displacement current" for historical reasons and because it has the units of current. Same reason they use the word "electric flux" or "magnetic flux", even though there's no "flux" (flow); it has the same units and obeys some of the same equations as flow vectors in fluid dynamics. Pfalstad 05:46, 30 December 2005 (UTC)

What the hell is a current if its not a flow of something?? THe term is so redolent of things flowing that its caused all this damn trouble!!--Light current 05:51, 30 December 2005 (UTC)

2. dP/dt is a real current. I belive in this one!

--Light current 04:54, 30 December 2005 (UTC)

Since we do have 2 terms for disp current, we should alter the lead para to show this. At the moment its as it was when we were just talking about vacuum disp current. ie polarisation current is a displacement current, but its a real current!--Light current 00:21, 2 January 2006 (UTC)

Vacuum polarisation

Does this effect exist and if so, does it account for displacement current in vacuo?--Light current 03:15, 13 December 2005 (UTC)

Reply from Nigel Cook

Yes it does: see my illustration here: http://photos1.blogger.com/blogger/1931/1487/1600/electron.gif based on experimental data:

‘All charges are surrounded by clouds of virtual photons, which spend part of their existence dissociated into fermion-antifermion pairs. The virtual fermions with charges opposite to the bare charge will be, on average, closer to the bare charge than those virtual particles of like sign. Thus, at large distances, we observe a reduced bare charge due to this screening effect.’ – I. Levine, D. Koltick, et al., Physical Review Letters, v.78, 1997, no.3, p.424.

I'd like to suggest that some background history be added to this "displacement current" article. Some material from my page follows, which may provide ideas. Feel free to use anything that is useful! http://feynman137.tripod.com/ :

Maxwells statements

In his (Maxwells?) final (1873) edition of his book A Treatise on Electricity and Magnetism, Article 110:

‘... we have made only one step in the theory of the action of the medium. We have supposed it to be in a state of stress, but we have not in any way accounted for this stress, or explained how it is maintained...’

In Article 111, he admits further confusion and ignorance:

‘I have not been able to make the next step, namely, to account by mechanical considerations for these stresses in the dielectric [spacetime fabric]... When induction is transmitted through a dielectric, there is in the first place a displacement of electricity in the direction of the induction...’

First, Maxwell admits he doesn’t know what he’s talking about in the context of ‘displacement current’. Second, he talks more! Now Feynman has something about this in his lectures about light and EM, where he says idler wheels and gear cogs are replaced by equations. So let’s check out Maxwell's equations.

One source is A.F. Chalmers’ article, ‘Maxwell and the Displacement Current’ (Physics Education, vol. 10, 1975, pp. 45-9). Chalmers states that Orwell’s novel 1984 helps to illustrate how the tale was fabricated:

‘… history was constantly rewritten in such a way that it invariably appeared consistent with the reigning ideology.’

Maxwell tried to fix his original calculation deliberately in order to obtain the anticipated value for the speed of light, proven by Part 3 of his paper, On Physical Lines of Force (January 1862), as Chalmers explains:

‘Maxwell’s derivation contains an error, due to a faulty application of elasticity theory. If this error is corrected, we find that Maxwell’s model in fact yields a velocity of propagation in the electromagnetic medium which is a factor of root 2 smaller than the velocity of light.’

It took three years for Maxwell to finally force-fit his ‘displacement current’ theory to take the form which allows it to give the already-known speed of light without the 41% error. Chalmers noted: ‘the change was not explicitly acknowledged by Maxwell.’ Weber, not Maxwell, was the first to notice that, by dimensional analysis (which Maxwell popularised), 1/(square root of product of magnetic force permeability and electric force permittivity) = light speed.

Maxwell’s innovation was: Total current = electric current + displacement current. But he didn’t understand what the terms were physically! Really atoms are capacitors themselves, not solids as Maxwell thought in 1873 (X-rays and radioactivity only confirmed the nuclear atom in 1912). So the light speed mechanism of electricity is associated with ‘displacement current’ and electric current results from the electric field induced by ‘displacement current’.

Do you mean flow of electric charges is induced by what you call displacement current? How is this displacement current measured? Can it exist without EM radiation? Is it not inextricably bound up with em radiation, and in that case, why does it need to be considered separately from em radiation. If it does not need to be considered separately, then of course its not worth considering a a separte entity. If its not a separete entity, it doesnt exist. Where is the flaw in the above logic?--Light current 01:12, 14 December 2005 (UTC)

In March 2005, Electronics World carried a longish letter from me pointing out that the error in the Heaviside/Catt model of electricity is the neglect of the energy flowing in the direction of displacement current. We know energy flows between the conductors from Feynman’s correct heuristic interpretation of Dirac’s quantum electrodynamics. Gauge bosons, photons, are exchanged to cause forces, and we know that energy flows ‘through’ a charging/discharging capacitor, appearing on the opposite side of the circuit. Catt/Heaviside proclaim, nothing (including energy) flows from one plate to the other, which is false, like their ignorance of electrons in the conductors.

Id just like clarification on your last point above. Are you saying that, a capacitor being charged from a voltage or current source connected to terminal A with terminal B as common (ground), will allow passage of energy from terminal A to terminal B? If so, where does this energy go? I thought the capacitor stored the energy in its electric field. Can you explain your statement please?--Light current 00:24, 14 December 2005 (UTC)

Innocent question on displacment current

Is the time derivative of a sinusoidally varying electric field always going to produce a current?? (or just a mag field)--Light current 19:16, 23 December 2005 (UTC)

I don't understand your question, but a changing electric field will always produce a mag field, and will also produce a current in any nearby conductors. Pfalstad 20:38, 23 December 2005 (UTC)

THe question is: can a varying electric field just produce a magnetic field without any associated apparent current?--Light current 22:32, 23 December 2005 (UTC)

You've changed the question. At first, you asked about a sinusoidal variation. Then, you asked about a varying electric field without specifying how it varies. This is not nitpicking. There is a difference. Alfred Centauri 03:49, 24 December 2005 (UTC)

Sine wave specified to get non zero 2nd diff of wave form, thats all.--Light current 13:07, 24 December 2005 (UTC)

I'm not sure I see the difference. Unless it's another one of those crazy step functions. Anyway, LC, yes, a varying electric field can produce a magnetic field without producing a current, in free space anyway. That's how waves propagate. Pfalstad 09:31, 24 December 2005 (UTC)

Ah Paul, so you agree no (dispalcement) current needed for em waves?--Light current 13:05, 24 December 2005 (UTC)

(bangs head on wall) No current needed for propagation. Displacement current is needed, of course. Because displacement current is not a current, but a varying E field. Is current needed to produce a wave in the first place? Well maybe not, since a rotating magnet produces a wave. Not sure if electrons spins count as current. Pfalstad 16:06, 24 December 2005 (UTC)

OK here we have the crux of the matter. I agree a varying E field is needed. But if displacement current is not actually a current then it should not be called a current (flow of something) but a varying E field that we all knew existed before. Also you have a varying H field. (BTW What sort of current does that produce?)

Well sure, but too bad, that's what it's called. The terms are defined by physicists, not by people on wikipedia. Pfalstad 22:26, 24 December 2005 (UTC)

Im not talking about how you launch an em wave in the first place. That probaly needs some current to flow in the antenna but a rotating magnet is an interesting case-- does that prodce Em?? I dont think electron spin is current but I could be wrong! So it seems you agree that displacement current as defined by Maxwell does not actually exist as a true current. Also you seem to be saying that its not needed for propagation of an em wave. Is so, we are in complete agreement! --Light current 19:01, 24 December 2005 (UTC)

No, we're not. Displacement current is varying E field. Varying E field is needed for propagation of a wave. Displacement current is not a true current, no. Maxwell may have thought it was, but this is an article about current terminology and usage in the physics community. Pfalstad 22:26, 24 December 2005 (UTC)

As long as people dont believe its an actual current, Im happy to let it be called a 'current' for the sake of historical accuracy in reporting Maxwells mistake. But we must take care that the article continues to include the more modern (30 yr old now) hypotheses offering the other explanation both for capacitors and for free space propagation and denying existence of diplacement current as an actual flow of anything . As regards radiation, only the varying magnetic field is essential for propagation. This field is caused by d2E/dt2 (ie the changes in the electric field) directly (no need for a current of any sort) .

If you are calling d2E/dt2 a current then propagation needs a current. But a current is a flow of something!. In your interpretation of this 'current', can you say what actually flows?

This is why I feel the term 'displacement current' is very misleasding to everyone. Im not saying it should be deleted or anything like that. Im just saying that we need to keep a big health warning(explanation) on the usage of this term on the page. --Light current 01:37, 25 December 2005 (UTC)

How's this for a health warning: "However, it is universally accepted that displacement current does not exist as a real current (movement of charge)" and right in the first sentence, " it is not a real current (movement of charge)". I put those there, and certainly don't want them removed. Pfalstad 03:11, 25 December 2005 (UTC)

I like your exclusion clauses and I think the page is generally OK . I certainly wont be removing them - after all they say what I think. --Light current 03:40, 25 December 2005 (UTC) Ive just noticed this: The present status of Maxwell's displacement current

John Roche 1998 Eur. J. Phys. 19 155-166 doi:10.1088/0143-0807/19/2/009

PDF (140 KB) | References | Articles citing this article

John Roche Linacre College, Oxford, OX1 3JA, UK

Abstract. Physics literature on the displacement current from Maxwell to the present day is reviewed with the intention of clarifying the concept. Two major traditions of interpretation are identified, one deriving from Maxwell which maintains that the displacement current is electromagnetically equivalent to an electric current and one deriving from Lorentz which denies that there is any displacement current. The article attempts to resolve various outstanding ambiguities and it concludes with an assessment of the present status of both traditions of interpretation. The appropriateness or otherwise of introducing the concept of a 'displacement current' to undergraduates is also discussed briefly.

Print publication: Issue 2 (March 1998) Received 4 July 1997, in final form 22 October 1997 So it appears Catt is not alone!--Light current 02:45, 25 December 2005 (UTC)

Well, do you want to go read that? Notice that it says "two major traditions of interpretation". So the dispute is over interpretation, not physics. That's what I want to make clear. Also, you'll notice that I made very clear changes to this article stating that displacement current is not a current, not a flow of anything. All I'm trying to avoid is the confusion created by saying "displacement current does not exist", because that isn't clear about what is being said: is it a dispute over physical law? over interpretation? Just try to phrase it less ambiguously, that's all I ask. Pfalstad 03:11, 25 December 2005 (UTC)

Unfortunately Im not member of the IOP so I cant get a copy, but I think its sufficient to note that some others in physics dont agree with Maxwell either! I think? this has been pointed out on the page to some extent.

It is a dispute over interpretation mainly, but my opinion is that this darned word 'current' implies to a lot of people a 'flow' of something. Even tho' they admit it cant be real current, some still say that something flows betweeen the plates of a capacitor. This can lead people to incorrect thinking about how capacitors actually work (charge with dc or pass ac signals). I say nothing at all flows or needs to flow ever under any circumstances a t all from one plate to the other plate.

A capacitor operates by energy entering sideways and being reflected off the open end of the efffective TL that exists in all capacitors, and thence back to the source., as I said in my earlier posts. In this process, counter propagating currents are induced longitudinally in each plate of the capacitor. In this manner the apparent conduction current entering one side of the capacitor seems to be transferred to the other side and appears as a conduction current coming out of the other plate.. But it isnt tranferred. The current on the other side is induced by the em wave in just the same manner as on the first side. --Light current 03:40, 25 December 2005 (UTC)

Kirchoff's laws

"Kirchhoff's current law also requires displacement current to be included in order to be valid for time-varying currents; for example, it is required when applying that law to one of the plates of a capacitor unless one uses the relatively recent transmission line equivalent capacitor interpretation of Catt".

The stuff about Catt is not correct. Kirchoff's law definitely needs a correction to be valid for time-varying currents. That correction is made by adding the displacement current term (whatever you want to call it); this must be done when dealing with any time-varying fields, including a transmission line. Catt's model doesn't use Kirchoff's law, but that doesn't mean Kirchoff's law doesn't need displacement current. So the Catt stuff should be taken out.

Catt doesn't talk about Kirchoff's law, does he? If he does, you could say, "Ivor Catt claims that displacement current does not need to be included in Kirchoff's law." Or you could say "According to Ivor Catt, Kirchoff's law is not necessary for an understanding of the capacitor," if this article were about Kirchoff's law, which it isn't.

Kirchhoff's current law also requires displacement current... Yes you are right! because Catts interpretation is all about energy flowing up and down the space between the plates and Kirchoff doesnt enter into it. But we all know that at high frequencies you dont use Kirchoffs laws because in the limit, Kirchoff is wrong- but lets not get into that!

So we need an imaginary current to prop up an erroneous law!. Thats physics for you!--Light current 02:21, 30 December 2005 (UTC)

Well everyone is wrong, aren't they? Newton's laws aren't relativistic, Maxwell's equations don't fit in with quantum electrodynamics and the weak force, Ohm's law doesn't work in general, Kirchoff's law doesn't work at high frequencies... Even transmission line equations don't work at high enough frequencies (atomic-scale wavelengths). Pfalstad 02:31, 30 December 2005 (UTC)

Now now no need for anger!! Stay calm and enjoy the discussion! I think its right to question these things and look at them afresh. As I think i said before somewhere-- open your mind! and let it all flow through!--Light current 05:57, 30 December 2005 (UTC)

Sorry I misinterpreted your last post as an angry sarcastic attack on my views. I now see that it was not. Apologies

Not angry, just trying to make a point. It doesn't really make sense to call laws in physics "wrong".. Unless you call all of them "wrong", since they're all just approximations. Pfalstad 06:03, 30 December 2005 (UTC)

We have to use our brains to interpret others findings and not take them on face value. otherwise, the human race would make no progress!--Light current 06:06, 30 December 2005 (UTC)

displacement current produces magnetic field

On what basis do you, Light Current, claim that displacement current does not produce a magnetic field in a vacuum? You saw the quote from J. D. Jackson above. That is the most widely used EM textbook. Do you have any reputable source which disputes this? Do you agree that a changing electric field produces a magnetic field? It follows directly from the Ampere-Maxwell equation. Pfalstad 05:33, 30 December 2005 (UTC)

"Maxwell called the added term the displacement current. Its presence means that a changing electric field causes a magnetic field, even without a current...."

Yeah big deal. How can dis current produce anything when it dont exist? Has he proved its the current that does it or the other way round? I doubt it, hes just trotting out the samer old claptrap.--Light current 06:01, 30 December 2005 (UTC)

Experts have been know to be wrong. It happens all the time. Look at Newton he was completely wrong and now everyone agrees that he was!

This is an encyclopedia, not your own personal physics journal. We're supposed to report the conventional wisdom--what the experts say. We're not supposed to argue with them. If you want to put in opposing viewpoints, that's great, but Jackson is a physics PhD, and his is the most widely used EM textbook at the graduate level. He has a lot more expertise on this subject.

So if Jackson said the moon is made from green cheese - youd belive that?--Light current 06:28, 30 December 2005 (UTC)

Sure he could be wrong! They all could be wrong! Let's go into the physics article and say, "But this could all be false; it could be that physicists are lying, or that laws of physics are illusions created by a giant computer simulation we're plugged into while our brains sit in a vat."

Thats a bit of a silly statement isnt it?--Light current 06:28, 30 December 2005 (UTC)

In the case of "associated magnetic field", it's probably fine, since britannica also says "associated magnetic field", and I'm not even sure what the difference is between that and causing the field. But in general you shouldn't be putting your own personal viewpoints into the articles. Pfalstad 06:15, 30 December 2005 (UTC)

Well look Paul, no one, not even Dr Jackson really know what goes on in an em field. If they did they would have published it by now. So in the presence of increasing doubt on this matter, i feel it is wiser not to come down so firmly on the side of the old school but to leave the interpretation slightly more open whilst not actually introducing any untruths. That way we please everyone! yes?--Light current 06:34, 30 December 2005 (UTC)

Ahh the NPOV argument. I was wondering when wed get to that. Look, Im not putting my own pov in the article im just making sure that what we put is not misleading. But lets get it right. I mean we had a whole term missing from displacement current (the polarisation component) and nobody noticed for months!(Partly my fault -I was getting too carried away with Catts ideas)

You must try to differentiate between my own personal view and what I want in the article. I thought I was making it quite clear by answering your questions about what I believe. What I believe is not necessarily what I think should go in the article. But, we must just be careful not to exclude the changes over the past 30 yrs or so, otherwise, erroeous ideas will be propagated ad infinitum courtesy WP.--Light current 06:28, 30 December 2005 (UTC)

derivation for LC

I'll go real slow here.

$D=\epsilon E$ (source: Marion and Heald, p.11; Jackson, p.154; but then what do they know)

now take the partial derivative with respect to t of both sides.

${\frac {\partial \mathbf {D} }{\partial t}}=\varepsilon {\frac {\partial \mathbf {E} }{\partial t}}$

Make sense? I'll leave it there since it's not important to the article and arguing with you is an huge waste of time and energy. Pfalstad 14:51, 30 December 2005 (UTC)

OK I think I see my confusion. Its not partial diff I dont understand, its the tacet assumptions early in the article that have confused me and the lack of emphasis on the different 'epsilons'. I now assume that the differences in Jd shown in the article are due to the fact that in one case we are using epsilon0 and in the other case we're using epsilon which takes into account the susceptibility of the dielectric. I had not spotted the distinction between the two epsilons! Many apologies for that. If that is so, we need to show the derivation of the new epsilon from epsilon0, epsilonr, and chi (susceptibility) to highlight the differences that I have obviously missed. If it has confused me, its bound to confuse others so I think it should be made clearer.

I would like to assure you that you have not 'wasted your time or energy' (nor indeed mine) in arguing this case, because it has brought out certain deficiencies in the clarity of the article that we can now attempt to rectify. Thanks for your time, patience and understanding! BTW Im not keen on the taste of crow/umble!--Light current 18:18, 30 December 2005 (UTC)

No indeed; the article is better. I have made mistakes too, and I actually learned something. BUT, I get too wrapped up in the arguing. I think I need a wikibreak! 65.29.47.153 19:35, 30 December 2005 (UTC)

--Light current 17:52, 30 December 2005 (UTC)

I have put in some explanatory notes about the epsilons and the derivation of P etc. ive yet to 'mathify' them but they can be understood. I feel these extra notes will minimise confusion for the unwary. Maybe Paul, you could look at them to give opinion.Thanks :-)--Light current 18:41, 30 December 2005 (UTC)

That is a good idea, I will take a look if I have time later. I don't know that stuff well enough to just look; I'll have to look it up. In the meantime, check against permittivity. 65.29.47.153 19:35, 30 December 2005 (UTC)

Yes I know things can get a bit intense sometimes. Its not good to take it too seriously. I pretend its a bit of a game sometimes. But it it very addictive and can take up a great deal of time- something of which I have a lot at the moment. Perhaps I will have Wikibreak soon as well! As soon as I reach 8k edits!.

BTW I have the full details on P etc in my book. So together, well get it right Im sure. I havent covered this stuff in over 30 years till now so Im a bit rusty on it. Hence my mistakes.--Light current 20:26, 30 December 2005 (UTC)

Motivation for Displacement Current Term

It is stated in this article that "Maxwell incorporated the displacement current term into Ampère's law, whose original form does not work for time-varying currents. A surface S1 chosen to include only one plate of a capacitor should have the same current as a surface S2 chosen to include both capacitor plates. However, because charge stops at the first plate, Ampère's Law concludes there is no charge enclosed by S1."

First, I don't think the opening statement is correct.

What's incorrect about it? The original form doesn't work for time-varying currents. Take a surface S1 that encloses a wire w/no current. If you start a current in the wire at time t, the surface integral will be nonzero but the line integral around the surface will be zero, since the magnetic field hasn't had time to reach the edge of the surface yet. (Whether that was Maxwell's motivation or not, I can't say. My guess would be no. The opening statement is confusingly worded in light of the example that follows, I'll give you that.) Pfalstad 23:13, 1 January 2006 (UTC)

The original form doesn't work for a discontinuous current since, in that case, the divergence of the electric current density is non-zero somewhere whilst the divergence of the magnetic field must be zero everywhere. The addition of the displacement current term to Ampere's Law solves this problem by exactly cancelling the non-zero divergence of the current density. In the example you give above, you seem to be describing the problem as a due to the finite speed with which information propagates in space. I don't see how adding the displacement current term solves the problem you have described. Will you enlighten me? Alfred Centauri 00:27, 2 January 2006 (UTC)

Well this shouldn't go in the article, but.. The current creates a little magnetic field infinitesimally close to the wire. The changing magnetic field creates an electric field in the opposite direction to the current. The electric field creates a magnetic field, which propagates the original magnetic field out into space. (It's easier to see if you use the wave equation in A (vector potential), which I can't find online at the moment but it's in the Feynman lectures.) If you do the surface integral I described above, the changing electric field cancels out the current, giving you a zero result. Pfalstad 17:57, 2 January 2006 (UTC)

OK, I probably won't get my point across on the first try so please bear with me. But first, I understand your response loud and clear. With the addition of the displacement current term, we have a mechanism with which to propagate the information of the change in current from the vicinity of the wire out into space all the while maintaining the validity of Ampere's Law. This mechanism is, of course, the electromagnetic wave. Now, here is the subtle point I'm trying to get across. Isn't it true that before Maxwell, it was thought that electric and magnetic forces were instantaneous forces at a distance in analogy with Newton's gravitational force? If so, why would there be any concern (at the time) about Ampere's Law and time varying currents? It would seem to me that scientists of the day would assume that the magnetic effects of the change in current travelled instantaneously from the wire out into all space. It was certainly assumed that gravitational effects propagated instantaneously. It aslo appears to me that Ampere's Law in its original form would apply to time varying currents as long as it is assumed that magnetic effects travel instantaneously. So here's my subtle point. Before the addition of the displacement current term which allowed traveling wave solutions for the electric and magnetic fields with a finite propagation speed, why would there be a conflict between Ampere's Law and time-varying currents that would require a displacement current term to fix? Alfred Centauri 22:45, 2 January 2006 (UTC)

Right, I'm saying that shouldn't go in the article. Maxwell apparently wasn't looking at that. He was looking at the conflict with the continuity equation, according to the two sources I checked. Pfalstad 04:57, 3 January 2006 (UTC)

I don't know if this will help, but.... I always thought that Maxwell's motivation for the displacement current was that he discovered an inconsistency between Ampere's Law and the principle of Conservation of Charge. If you are interested, there is a detailed description of the mathematics related to this issue in the section The origin of the electromagnetic wave equation. -- Metacomet 00:37, 2 January 2006 (UTC)

It's not that Ampere's Law and the principle of Conservation of Charge are contradictory. It is that Ampere's Law combined with conservation of charge (expressed mathematically via the continuity equation) yield the unphysical result that the electric charge density is everywhere constant. Whether this motivated Maxwell is unclear to me. See [2] - specifically, the paragraph beginning with "One finds in the literature three basic justifications for introducing the “displacement current” term to Ampere’s law." Alfred Centauri 02:04, 2 January 2006 (UTC)

I was just trying to help. And if you read the link that I suggested, you will see that it says exactly the same thing that you are arguing with regard to Ampere and Conservation. I don't know if it motivated Maxwell either, but perhaps there is something in the historical record that would indicate his motivation. In any event, with 20/20 hindsight, it is a pretty straightforward way to show that Ampere's law as originally formulated was certainly incomplete, and that the displacement current was the missing term. -- Metacomet 03:51, 2 January 2006 (UTC)

Second, the example application of Ampere's Law to a capacitor applies to a steady current too. In fact, the example given has nothing to do with time-varying currents but instead illustrates why the displacement current term is required for Ampere's Law and the continuity equation to be consistent with the observation that electric charge density can change with time. That is, without the displacement current term, Ampere's Law combined with the continuity equation require that the electric charge density is constant everywhere.

Third, the example is worded poorly. Specifically, Ampere's Law relates the closed contour integral of the magnetic field intensity to the current through the oriented surface enclosed by the contour. The statement that "Ampère's Law concludes there is no charge enclosed by S1" is wrong on two counts: (1) it is current and not charge that is of interest and (2) the surface S1 is not closed and so cannot enclose anything.

I agree on both counts. Pfalstad 23:13, 1 January 2006 (UTC)

Shall I make the edits? Alfred Centauri 06:24, 1 January 2006 (UTC)

Please be my guest! (as long as you keep it simple-- no vector calculus please!)

BTW are you enjoying your break from those students?--Light current 06:32, 1 January 2006 (UTC)

I'm still working on that confounded house I have for sale. I have moved the following material from the main article to this section pending an edit. Alfred Centauri 03:17, 2 January 2006 (UTC)

---

Maxwell incorporated the displacement current term into Ampère's law, whose original form does not work for time-varying currents. A surface S₁ chosen to include only one plate of a capacitor should have the same current as a surface S₂ chosen to include both capacitor plates. However, because charge stops at the first plate, Ampère's Law concludes there is no charge enclosed by S₁. To compensate for this difference, Maxwell reasoned that, to be consistent, Ampère's law needed an additional term, the displacement current term.

Kirchhoff's current law also requires displacement current to be included in order to be valid for time-varying currents; for example, it is required when applying that law to one of the plates of a capacitor.

---

The electromagnetic wave equation article does a good job on this; you could just copy from there. I read Jackson and he emphasizes the fact that continuity equation is inconsistent with Ampere's law, and that Maxwell noticed this and fixed it. He also says Ampere's law was derived for "steady-state current phenomena with div.J = 0". (I guess you can't have a steady-state current with charge building up somewhere.) Marion and Heald says Ampere's law was "valid only for steady-state conditions and is insufficient for the case of time-dependent fields". I like Marion and Heald's wording better. Pfalstad 17:46, 2 January 2006 (UTC)

The more I look at the section of the article where the two paragraphs were pulled from, the more I believe the paragraphs are out of place there. I believe that a new, short section should be added before the 'Explanation' section entitled 'Motivation' with a sentence or two and a link to the relevant section in the electromagnetic wave equation article. Alfred Centauri 22:55, 2 January 2006 (UTC)

Would you please consider calling the new section: 'Necessity for the displacement current (term)' ?--Light current 23:02, 2 January 2006 (UTC)

How does 'Mathematical Necessity of the displacement current (term)' sound? Alfred Centauri 00:00, 3 January 2006 (UTC)

Sounds good to me because it leaves open the question of the physical interpretation of the term which we are all still discussing. Yes Im happy with that.--Light current 00:37, 3 January 2006 (UTC)

It's a bit long for a section header. What about simply, "Mathematical necessity" or "Mathematical motivation"? Since the title of the article is "Displacement current" it is already implied. -- Metacomet 00:41, 3 January 2006 (UTC)

I dont think the word 'motivation' is good. 'Need' may be better--Light current 00:42, 3 January 2006 (UTC)

I think "motivation" is the correct word here, but something like "origin" might be less confusing for some. 65.29.47.153 04:50, 3 January 2006 (UTC)

I am wondering whether the section entitled "The origin of the electromagnetic wave equation" should be moved from Electromagnetic wave equation to either Ampere's law or Displacement current. Any thoughts? -- Metacomet 08:55, 3 January 2006 (UTC)