Talk:Ampère's circuital law

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This article should correctly be entitled 'Ampère's Circuital Law'.

Ampère's Law is a different law relating to the magnetic force that acts between two loops of electric current. ( 08:02, 18 February 2007 (UTC))Reply[reply]


First of all, it's time to put this article under its correct title Ampère's Circuital Law. Ampère's Law is a different law altogether concerning the force between elements of electric current. --unsigned

Ok, but somebody needs to make an article about Ampere's Law, instead of leaving it as a redirect to here. I'd do it myself, but I am not versed in the technology (I got here from clicking on "Random Article") -- trlkly 09:37, 27 July 2007 (UTC)Reply[reply]

Displacement Current[edit]

It is a common myth, circulated in the secondary literature, that Maxwell conceived of displacement current in connection with an electric capacitor circuit. This is quite simply not so. Anybody who has studied his papers of 1861, 1865, and 1873 will find absolutely no evidence of the capacitor circuit being in any way involved in his conception of displacement current. Displacement current first appears in his 1861 paper On Physical Lines of Forcein connection with linear stress and elasticity in the solid which he considered to be the luminiferous medium. ( 16:17, 13 April 2007 (UTC))Reply[reply]

Alternate form of Ampère's Circuital Law[edit]

Why is there no mention of on this page? -- 06:23, 5 December 2005 (UTC)Reply[reply]

Was here,but someone must have deleted it.-- 10:16, 19 January 2006 (UTC)Reply[reply]

I put it back, they're integrated now. This page needs *work* and the terminolgy is all messed up. Particularly confusing is the difference between B and H. Not to mention that H is magnetic field density on the Maxwell's equations page, and magnetic flux density on this page.. I'm too confused to fix more. Fresheneesz 22:51, 3 February 2006 (UTC)Reply[reply]

H is not magnetic flux density.....B is magnetic flux density..H is magnetic flux intensity..similar what electric field is in electrostatics...[vijin]

whats dA[edit]

What's da in the first formula?

I'd vote for an infintesimal part of the surface S. This is a surface itself. In French, the word "aire" is used for surface. I suggest to change da for ds.

I added the defintion from the page Maxwell's equations. This page needs to define ALL its variables - its in poor shape. Fresheneesz 22:59, 3 February 2006 (UTC)Reply[reply]

Bad Units for vector D[edit]

I noticed that the page defines

as having units of A/m2. The units should in fact be coulombs/m2. When you do:

the result of the integral is in coulombs. Taking the derivative with respect to time yields coulombs/sec or amperes. This is what we want, since

gives a current, as H has units of A/M and integrating that over length results in Amperes.

I mention this here so that someone else can change it. I am new to Wikipedia and don't want to screw up the original article. UPDATE: I HAVE CORRECTED THIS IN THE ARTICLE.

Ampère did not discover the so-called "Ampère circutal law"[edit]

Ampère did not discover any expression for magnectic field from a elementary current because the field concept was unknown in Ampère's time.

He only worked with distance-force between current elements and (cf. the Ampère's force law equation article):

PLASE SEE HISTORIC REFS. (and remember also that magnectic field was a new conception only applied after Maxwell's days).

See for ex. R.A.R. Tricker, "Early Electrodynamics - The First Law of Circulation", 1965.

Yes, I concur.--Geremia (talk) 04:30, 30 July 2016 (UTC)Reply[reply]

I have thought for a while that the electromagnetism template is too long. I feel it gives a better overview of the subject if all of the main topics can be seen together. I created a new template and gave an explanation on the old template talk page, however I don't think many people are watching that page.

I have modified this article to demonstrate the new template and I would appreciate people's thoughts on it: constructive criticism, arguments for or against the change, suggestions for different layouts, etc.

To see an example of a similar template style, check out Template:Thermodynamic_equations. This example expands the sublist associated with the main topic article currently being viewed, then has a separate template for each main topic once you are viewing articles within that topic. My personal preference (at least for electromagnetism) would be to remain with just one template and expand the main topic sublist for all articles associated with that topic.--DJIndica 16:40, 6 November 2007 (UTC)Reply[reply]

Ampere's force law[edit]

Hello! I don't think Ampere's force law belongs in an article on Ampere's circuital law. They're named after the same person, but they're not the same law, and the title of the article was chosen specifically for that reason.

What I propose doing is:

  • Putting the information here into Lorentz force, since Ampere's force law and the Lorentz force law are logically equivalent, and Ampere's force law is just as often referred to as a "form of the Lorentz force law".
  • Create a redirect page at Ampere's force law, redirecting to Lorentz force.
  • Put a disambiguating-type note at the top of this article.

Any thoughts? --Steve (talk) 04:16, 20 February 2008 (UTC)Reply[reply]

Done. I should amend what I said before: Ampere's force law (as defined here) is not equivalent to the Lorentz force law, but is the combination of that and the Biot-Savart law. I wasn't clear on the definition before, and in what I wrote above, I was confusing it with the Laplace force (which, by the way, I also added into the Lorentz force article). Regardless, the section is much more at home in Lorentz force than it was here, and I tried to explain there exactly how it fits in. But it would also be appropriate as a separate article, if someone feels strongly about it. --Steve (talk) 00:08, 21 February 2008 (UTC)Reply[reply]

I have taken up your suggestion for a separate article and put it under Ampere's force law. I believe that is good policy because this law underlies the definition of the ampere, and should be made easy to find. Also, as the references indicate, the term "Ampere's law" often refers to this force law. Links are added to Ampere's circuital law and Lorentz force and Biot-Savart law.

Brews ohare (talk) 17:34, 21 February 2008 (UTC)Reply[reply]

Conservation of Charge and Ampère's circuital law[edit]

Ampère's circuital law is solenoidal by nature. In the versions seen in Maxwell's 1861 paper, there is no question of any build up of charge, since charge is not even involved in the equation. The only relevant factor is the velocity of the current. The modern day justification for displacement current, using the vacuum capacitor scenario, simply extends the concept of electric current to cater for the component of current that arises out of a change of charge density. It then instantly subtracts this component again in the form of adding the extra displacement current term. In this situation, the E in the displacement current satisfies Gauss's law. However, in the EM wave equation, the E vector satisfies one of the other components of the Lorentz force ie. E = -(partial)dA/dt. So in some respects, the modern day justification for adding displacement current is a tautology which produces a displacement current that is not even compatible with the EM wave equation. David Tombe (talk) 03:41, 26 November 2008 (UTC)Reply[reply]

Original Ampere's Law can be false even with steady currents and no charge accumulation[edit]

For example, for an electromagnetic wave in free space. --Steve (talk) 16:41, 26 November 2008 (UTC)Reply[reply]

Steve, are you saying that Ampere's original circuital law implied that curl B = 0 in free space? We'd need to see it written down. I don't think that the fact that curl B is non-zero in EM radiation, in any way contradicts Ampere's original circuital law. David Tombe (talk) 01:53, 27 November 2008 (UTC)Reply[reply]

I thought the problem with Ampere's law was that div J is not zero. Hence curl B is not J. I see that you have a different violation here, that J=0 but curl B isn't. Brews ohare (talk) 23:20, 26 November 2008 (UTC)Reply[reply]

This is going to be a difficult one to sort out because there are many strands to the argument. I did say on the displacement current talk page that this is perhpas one of the most confusing topics in all of physics.
Steve is correct when he states that curl B is non-zero in EM radiation. But the displacement current term which occurs in that situation satisfies the relationship. It has got nothing to do with the issue of conservation of charge or variation in charge density.
Before this discussion can be satisfactorily completed, somebody will need to get a hold of the original version of Ampere's circuital law, as per Ampere. I was responding to the statement in the main article that the original Ampere's circuital law is not always correct. I maintain that it is always correct. But I'd need to see it to be sure. In Maxwell's original papers, Ampere's circuital law only concerns the velocity of the current. That suggests that it was never intended to apply to issues concerning variation of charge density.
The modern justification for displacement current assumes that Ampere's law applies to situations involving variation in charge density, and then promptly subtracts that aspect. In other words, it is a tautology which simply reverts Ampere's law to its original form.
All this needs to be sorted out or else we will be arguing at cross purposes. David Tombe (talk) 01:30, 27 November 2008 (UTC)Reply[reply]

Brews, it's correct to neglect displacement current if and only if the displacement current equals zero (obviously). So the condition is that the displacement current is zero. "No changing electric fields" would seem to me to be an equivalent condition.

If charges are moving around (a.k.a. J isn't solenoidal), the electric field has to change (e.g. by Gauss's law) and therefore the displacement current therefore has to be nonzero. But the converse isn't true. --Steve (talk) 02:16, 27 November 2008 (UTC)Reply[reply]

Steve, there are two kinds of displacement current for each of two of the E components in the Lorentz force. The kind that occurs around the charging plates of a capacitor is the Gauss's law kind. The kind that ocurs in EM radiation is the E = -(partial)dA/dt kind. They are not the same. You were able to distinguish between the latter and the vXB component in the Lorentz force in relation to Faraday's law. Now you need to distinguish between the latter and the former in relation to displacement current and Ampere's circuital law. David Tombe (talk) 03:01, 27 November 2008 (UTC)Reply[reply]
There also are two definitions of displacement current in use in the literature: the Jackson-Maxwell definition based on ∂D/∂t, and the Griffiths definition based on only ε0 ∂E/∂t. It may be Steve uses the later. Brews ohare (talk) 22:45, 27 November 2008 (UTC)Reply[reply]

Original form of Ampere's law[edit]

I have changed the presentation of the original form of Ampere's law to refer to free current only. That agrees with Jackson and with Slater who use a formulation of Ampere's original law in terms of H, not B. Griffiths uses B, but isn't clear whether he means to include magnetization current in his J or not. It never comes up.

It's pretty clear that Ampere himself didn't include anything other than conduction currents, as he discussed forces between wires.

I think the logical flow is now clearer and more reasonable. Brews ohare (talk) 01:24, 27 November 2008 (UTC)Reply[reply]

Brews, see my edit in the section above. I strongly suspect that Ampere didn't concern himself with charge accumulation, but I don't know for sure. I suspect that whovever had written this wiki article was assuming that Ampere's original form was as is presented in some modern textbooks prior to the Maxwell addition. They were basing their arguments on a 'current density' based definition of Ampere's law which may not have been what Ampere had in mind at all.
I'll have a look through the main article now and see how it all looks. David Tombe (talk) 01:35, 27 November 2008 (UTC)Reply[reply]

EM Radiation and Conservation of Charge[edit]

The displacement current term as occurs in EM radiation bears no relationship to the arguments about conservation of charge. Until that fact is realized, then total confusion is going to reign here. We're going to see Ampere's circuital law being amended on the basis of conservation of charge around a capacitor, and then the result applied to the EM wave equation. The displacement current as is used in EM radiation requires a different justification because the E field is not determined by Gauss's law in this case. Gauss's law and E = -(partial)dA/dt are two distinct components in the Lorentz Force law. Once this fact is realized, the article can then be written in a more factually correct manner which clearly segregates these issues. David Tombe (talk) 03:13, 27 November 2008 (UTC)Reply[reply]

I think these issues are presently segregated in the article. Two reasons for failure of Ampere's original law are provided. Two components of displacement current are emphasized. Brews ohare (talk) 07:16, 27 November 2008 (UTC)Reply[reply]

Brews, yes, the segretaion is now becoming clearer. But do you see how we are still at a loss to account for the displacement current term for EM radiation? And I don't even think that Maxwell's linear polarization solution is the answer. The original Ampere's law doesn't contemplate the concept of a magnetic field without an associated electric current. This is where Steve's point becomes interesting. Steve correctly pointed out that the curl of B is non-zero in EM radiation. But from this he concluded that Ampere's original law must be wrong. I assume he was basing this on the assumption that Ampere's original law takes the modern day form of curl B = J, in which case it follows that in free space, J = 0, and so he sees a dilemma regarding EM radiation where curl B is non-zero. But curl B = J is not Ampere's original law. It is a mathematical extrapolation of Ampere's original law which would only hold if there actually is a current present at that point in space. We're back again to this issue of maths being extrapolated beyond its physical remit. When you realize this, then you will be more careful about the wording in the main article. It was far too oversimplistic to state that Ampere's original law was not correct in general. The original 1826 law which you can find here [1] is pretty correct. But there are issues with the modern formats regarding charge variation. I personally don't think that Ampere was concerned with charge variation. If Maxwell is anything to go by, Ampere was only concerned with the velocity of the current. In terms of Bernoulli's principle, Ampere's law was only originally concerned with the velocity aspect. The pressure (charge density variation) aspect only crept into it with the more modern vector formats that used J. Displacement current, as justified by conservation of charge, simply subtracts that aspect by providing an equal and opposite term to the pressure component in the J term. As for EM radiation, we are still no further on as regards explaining how the extra displacement current term creeps into Ampere's law. David Tombe (talk) 08:12, 27 November 2008 (UTC)Reply[reply]

How does it creep in? That could be an historical question, and I haven't been able to sort out for myself what Maxwell actually did. His vortices, rods, and squeezing balls are a hellish invention. Secondary historical sources suggest he did introduce the ε0∂E/∂t term, but I don't find any direct quotes from Maxwell - it's their opinion. It also seems to be the consensus of later physicists, whether valid or not. Brews ohare (talk) 22:54, 27 November 2008 (UTC)Reply[reply]
How does it creep in? That could be a physics question about intuitive feel for occurrence of the term. I strike out here too. The best I can say is it's necessary to predict the wave propagation. Can you improve on that? Brews ohare (talk) 22:54, 27 November 2008(UTC)

Brews, I think that the article is now as good as it's going to get within the context of modern sources. I would tend to leave it for a while. Ultimately, Ampere's original 1826 circuital law was a loop integral in a time frozen situation. This time frozen aspect corresponds to the partial spatial derivatives in the modern curl version. Hence the law doesn't distinguish between time varying currents and steady currents. It is therefore wrong to add the displacement current term on the argument that it is a necessary addition for time varying situations. The justification for adding the displacement current for the purposes of EM radiation is clearly not in the textbooks. It rides in on the back of the conservation of charge argument which is actually about a different effect. I maintain that when Stokes theorem produced the curl B = J version, that this resulted in a potential mathematical over-extrapolation. In other words, I would say that curl B can never actually be zero. There has to be an electric current for Ampere's law to make any sense. If we write curl B = dE/dt for EM radiation purposes then we need to actually justify the dE/dt expression from within the J term. This could be done if -(partial)dA/dt is taken to be he angular acceleration of Maxwell's vortices. But Maxwell himself didn't even appear to go fully down that road. He did however talk about the transmission of rotations due to tangential action in the preamble to part III (1861), but then he seemed to get sidetracked into linear polarization. I would say that the displacement current in EM radiation involves the Euler force, whereas the displacement current in charge accumulation and linear polarization involves radial Gauss's law. Maxwell himself is partly to blame for the EM radiation displacement current getting mixed up with Gauss's law. He adds displacement current to Ampere's circuital law at equation (112) after having derived it elastically. Then he immediately takes it down the road into Gauss's law and the equation of continuity. However, he does this for the purpose of leading to Coulomb's law and getting a formula for the ratio of electrostatic units to electromagneic units. He does this because he wants to apply the 1856 Weber/Kohlrausch results which link this ratio to the speed of light. Having done that, he then wants to apply the result to Newton's equation for the speed of sound at equation (132) and conclude that light is transverse undulations in the same medium that is the cause of electric and magnetic phenomena. David Tombe (talk) 02:26, 28 November 2008 (UTC)Reply[reply]

The Section on Magnetization Current[edit]

Do we actually need all this stuff about magnetization current? Ampere's circuital law is simply about doing a loop integral of a magnetic field around its source current. Once this has been explained then all we need to do is discuss the displacement current issue. Why all the extra complications about magnetization current? David Tombe (talk) 13:36, 27 November 2008 (UTC)Reply[reply]

The mess with magnetization current is necessary because the B-field formulation is introduced which drags along with it the explicit magnetization current. If only the H-field were used, it would not be necessary. Brews ohare (talk) 22:40, 27 November 2008 (UTC)Reply[reply]

In my opinion, the magnetization current as descibed here is an effect rather than a cause. I wouldn't bother with it at all. I don't think it makes any difference whether you use B or H. David Tombe (talk) 03:27, 28 November 2008 (UTC)Reply[reply]

The Magnetic Analogue to Gauss's law[edit]

It says in the introduction that Ampère's Circuital Law is the magnetic analogue to Gauss's law. In what respect? I would have thought that the magnetic analogue to Gauss's law would have been curl A = B.

I can see the analogy with Gauss' law in the sense that Gauss's law gives the source of the E field, whereas Ampère's Circuital Law gives the source of the B field. But Gauss's law only does so in respect of the zero-curl components of the E field. Faraday's law which looks exactly like Ampère's Circuital Law gives us the source of the curled components of the E field. So we have different reasons for saying that any of (1) curl A = B, (2) Gauss's law, or (3) Faraday's law, represent analogies to Ampère's Circuital Law. Shall we remove that clause from the introduction? David Tombe (talk) 08:55, 1 December 2008 (UTC)Reply[reply]

Continuity /Style[edit]

I noticed that there is a sentence that starts "Again this only applies in the case where field is constant in time...." Unfortunately this is not mentioned anywhere above. Presumably someone has edited this out before? Could edit the Again out, but then that would not really solve the problem - so maybe this needs to be dealt with at the beginning of the section (and then it probably would not need to be mentioned again?).

Also a thought about the style of the mathematics in the article. Maybe I am coming at this from the wrong - since i have some mathematical background - but could the descriptions of the mathematical symbols be boiled down a bit - or put in a hidden box. It does make the reading of the article a bit difficult. I guess maybe this is something that wiki style has something to say about - but I do think that having such a large section simply explaining the terms in an equation is a bit of an extravagance. (?)

-- (talk) 11:24, 11 April 2009 (UTC)Reply[reply]

I'm inclined to agree but remember everyone doesn't have the exposure that you do. And I personally support anything that helps the newbies to the subject.Dave 2346 (talk) 19:31, 11 July 2009 (UTC)Reply[reply]

right hand rule[edit]

(This has been dealt with)

The below statement only makes reference to the index finger and the thumb, therefor it can not be complete.

These ambiguities are resolved by the right-hand rule: When the index-finger of the right-hand points along the direction of line-integration, the outstretched thumb points in the direction that must be chosen for the vector area \mathrm{d}\mathbf{S}, and current passing in that same direction must be counted as positive.

Dave 2346 (talk) 19:51, 11 July 2009 (UTC)Reply[reply]

Might be clearer to say "When the index-finger of the right-hand curves along the direction of line-integration", or to make some reference to the palm pointing towards the inside of the loop... --Steve (talk) 19:22, 11 July 2009 (UTC)Reply[reply]

I made the change, I just needed a little push. :)Dave 2346 (talk) 19:51, 11 July 2009 (UTC)Reply[reply]

The article Ampere model of magnetization was created recently. I know nothing about electromagnetics, so I can't tell if it's basically the same thing as what's written here. If it is, it should just be redirected here. Thoughts? ... discospinster talk 22:42, 20 April 2010 (UTC)Reply[reply]

Mix of LaTeX and HTML[edit]

In the shortcomings section, for consistency with the rest of the article and clarity the html equations inline and buried in the text will be transformed to LaTeX. Also some clumsy words such as "warrant elaboration" are simplified. The long list of symbols at the start will be made more compact, not by re-writing the text or changing symbols, but grouping simalar quantities/operations together. In that list I also removed the over-repetetive "see below" statements for the curve C and surface S into a single statement after the list.-- F = q(E + v × B) 01:46, 21 December 2011 (UTC)Reply[reply]

FIX sign in maxwell's equation in free space curl(B) = (+) (1/c^2) dE/dt[edit]

How is Ampere's law different from Oersted's law?[edit]

Should they be merged?--ChetvornoTALK 17:03, 11 March 2014 (UTC)Reply[reply]

The figure "An electric current produces a magnetic field." is wrong[edit]

I do believe the figure has mixed-up the Left Hand and Right Hand rules with their respective current directions. I do believe the RH rule is used when considering positive current flow (according to my Serway text) while the LH rule is used for negative (the direction of electron flow) current flow. So, either the polarity on of the wire should be swapped to be in keeping with the RH rule, or, better, reverse the direction of B for the LH rule. I will be "bold" and remove it. (talk) 05:06, 3 June 2014 (UTC)Reply[reply]

See "It is conventional to choose the direction of the current to be in the direction of flow of positive charge." - Serway, 3rd Ed.. Thereafter, all examples use the RH rule in the rest of the text. So, use the LH rule when working with "actual" electrons as the current which flow from positive to negative. (talk) 05:17, 3 June 2014 (UTC)Reply[reply]


Surely in general (i.e including inside permeable materials) B=μ*H where μ=total permeability=μr*μ0. As this excellent article explains, H is governed by the free current whereas B is governed by the total current. μ accounts for the bound current induced in the permeable material by H. <Lorrain and Corson eqn 9-44> Jkeevil (talk) 15:05, 10 November 2014 (UTC)Reply[reply]