Talk:Displacement current

Earlier talk

moved to archives:

• Talk:displacement current/archive #1
• Talk:displacement current/archive2
• Talk:displacement current/archive3

copied from earlier talk for ref--Light current 01:40, 10 March 2006 (UTC)

Origins of Displacement Current

The web link for Maxwell's 1861 paper 'On Phyiscal Lines of Force' was provided. You can clearly see that displacement current was first introduced at equation (111), and you can clearly read about the context. The original Wikipedia article claimed that displacement current first appeared in the 1865 paper 'A Dynamical theory of the Electromagnetic Field'. This is not true. That's why the amendment was made. 11/2/07 (124.217.34.54 07:50, 11 February 2007 (UTC))

I fixed the date, thanks. But I'm not clear on the reasons for your other changes. You removed the introduction, replacing it with some history of displacement current, so I reverted that and some other changes, like removing the mathematical necessity section. Pfalstad 17:36, 11 February 2007 (UTC)

The second diagram in the Article shows electric current entering the capacitor. It should also show the electric current spreading out across the capacitor plate. http://www.ivorcatt.org/icrwiworld78dec1.htm ; http://www.ivorcatt.co.uk/x18j41.pdf . This current should be discussed in the article. Ivor Catt, February 2014 — Preceding unsigned comment added by 86.164.171.64 (talk) 23:20, 21 February 2014 (UTC) The second diagram in the Article wrongly shows the electric field as uniform. It is not. http://www.ivorcatt.org/icrwiworld78dec1.htm . Ivor Catt, 1 March 2014 — Preceding unsigned comment added by 86.164.171.64 (talk) 21:54, 1 March 2014 (UTC) It is not important. http://www.ivorcatt.co.uk/x436.htm , Ivor Catt 5 March 2014

It is not important for the demonstration how the charge is distributed on the capacitor plate. The only relevant point is that current is passing through integration surface S₁ but not through S₂. Without the displacement current term in the Ampere-Maxwell equation, the equation would be inconsistent; the result of the surface integral would depend on which surface you chose spanning the contour δS. And (disregarding fringing fields) the electric field between the plates will be substantially uniform as long as the capacitor is not charged so quickly that the voltage changes appreciably during the light travel time between the center and the periphery of the plate. --Chetvorno^TALK 01:21, 2 March 2014 (UTC)

Definitions of displacement current

I see your still at it LC. Why do you still equate displacement current with electric current in the sense of charge movement? Displacement current is not the transport of electric charge, right? Haven't we agreed on this in the past? No one will be able to measure the movement of (real) electric charge between the plates of a vacuum capacitor. But, this has nothing to do with detecting displacement current. As I've said before, displacement current is the change in electric displacement. Before one could measure displacement current directly, one must define and then measure electric displacement directly, right? Besides, displacement current can be transformed out of Maxwell's equations. Alfred Centauri 03:52, 9 March 2006 (UTC)

Nice to see you are still with us Alfred. When you say 'at it' , Im merely responding to a challenge I posted a few months ago. Yes you and I have agreed on: Displacement current is not the transport of electric charge, right? What Im not sure about agreeing with you on is that nothing 'flows' from one plate to the other. Here we have a User who has performed an experiment that indicates the conduction current in the wires equals the so called dispacement current in the capacitor. In that sense, it appears that User:Mak17f believes these currents to be the same thing and satisfying Kirchoffs law. As you correctly told me some time ago, one must be very careful in applying KL in electric field problems. In fact the field solution will always be correct, wherreas KL may lead you up the garden path (as in this case)! However, the expt does not prove that something is flowing between the plates because I believe that my alternative explanation above for what happens is equally vaild. BTW a lively discussion on all aspects of this subject is in progress at Talk:Ivor Catt.--Light current 14:48, 9 March 2006 (UTC)

I feel that I was extremely accommodating as to your experiment. You stated bluntly “The conduction current in the leads (if there is any) is certainly not equal to the displacement current (if there is any).” I showed there WAS conduction current in the leads as I said I would. I illustrated that this current (through calculations using the geometry of my setup) is equal to what we expected the displacement current to be. What is your explanation as to what happened? Or, are we just argueing to argue? Certainly if you have an alternative explanation, please explain it in detail and support it with calculations.Mak17f 15:24, 9 March 2006 (UTC)

You have indeed been extremely accomodating in your willingness to perform the experiment and in completing it so quickly!. I fear however that you may not have full grasped the purpose of the experiment which was to find out if anything physical flows from one plate of the capacitor to the other. I should perhaps have phrased my assertion slightly differently:

The measured value of displacement current (if there is any) is certainly not equal to the conduction current in the leads.

You have:

• measured the conduction current in the leads (I agreed that you would- aproximately anyway)
• illustrated that this current (through calculations using the geometry of my setup) is equal to what we expected the displacement current to be.

You have not:

• proved that anything physical flows from one plate to the other. You have assumed it by false application of KL.

Im not arguing for the sake of it although it may look like it sometimes.

There has been intense discussion on this subject over the past few months. I feel a lot of the misunderstanding has been about the definition of displacement curent. Is is a current (ie something that flows), or is it something that comes out of Maxwells equations?--Light current 15:47, 9 March 2006 (UTC)

This is the reason why I thought it was necessary to define exactly what I was planning to do before I conducted the experiment. Let me ask you a couple questions on your position:

1. Can capacitors be charged? Hold charge? What is the fastest they can be charged?
2. Can the charge polarity be reversed? How quickly?
3. Do you believe that I=dq/dt? Is there a time varying charge magnitude on the plates?
4. What current was I measuring? Where did the charge come from?Mak17f 16:05, 9 March 2006 (UTC)

Q1. Yes. Yes. Fastest time is equal to the 2 way transmission time of the equivalent transmission line if the gen is matched to the Z0 of the capcitor. Other values of source Z will give a longer charging time.

Q2 Yes. See ans to Q1

Q3

a)That is one of the definitions of current, yes.

b)Depends what you mean here. There is a time varying electric field. Any apparent charge will be due to the em wave. There cannot be any charge carriers rushing around at these speeds!.

Q4 You seemed to be measuring the conduction current in the lead. Whether this is the total current in the circuit is, of course, not clear with your setup as stray capacitace exists all over the place (even across your CT). You dont need real charge to activate your CT. Its the mag field in and around the conductor that does that.

Sorry if these are not the replies you ewere expecting but these are the only logical answers that fit the facts especially as no one has measured any current flowing between plates (AFAIK). It is also a consequence of KL not being generally applicable in field theory!--Light current 16:31, 9 March 2006 (UTC)

I'll adress your points. But above I also asked that you would tell me exactly what current you propose I measured in the experiment. Also, support the claim with calculations using values from the experiment. Mak17f 17:26, 9 March 2006 (UTC)

Your statement is ambiguous. But if your are asking me what current I wanted you to measure, it is the current actually flowing between the plates. You will need a thin sheet of resistive material (like graphite foil or sheet) with a wire fixed on to each side and fed to a diff amp plugin on the scope. My opinion is that you will not be able to measure any pd across this current probe.--Light current 17:36, 9 March 2006 (UTC)

---

Alfred Centauri's Comments

I'm certain I'll be sorry for sticking my nose into LCs and Mak17fs conversation here but I just can't resist. LC, when you say "There cannot be any charge carriers rushing around at these speeds!", I say 'so what?'. The electric current density is the product of charge density and velocity. With the appropriate charge density (e.g., the density of mobile electrons in a conductor), the electron drift velocity can (and is) exceedingly small for any reasonable current. So, what is your point here? Alfred Centauri 16:48, 9 March 2006 (UTC)

Its not the amount of current. The problem is the effective frequency at which they can move around the circuit inside the conductors. In fact at a very few MHz the carriers start to move to the conductor surface. At even more MHz, are there any left at all in the conductor or is it all in the em field?

--Light current 17:12, 9 March 2006 (UTC)

First, it's difficult for me to understand what picture it is you have in your mind when you use phrases like 'the frequency at which they can move around the circuit'. For me, such a phrase conjures up a picture of electrons circulating along a closed path where the frequency refers to the number of round trips made per second. For an alternating electron current within a conductor, I picture the electrons executing a sinusoidal motion that is superposed with their normal random motion. In this, case no electron moves around the circuit. Is this your view, also?

Secondly, it is not my understanding that electrons move toward the conductor surface as the frequency of the current increases. Rather, it is my understanding that the deeper inside the conductor the mobile electrons are, the less they participate in the alternating current. The degree to which this is true depends on the frequency of the current. Is this your understanding, also?

Thirdly, what the heck does your last question mean? What is it that isn't left in the conductor - mobile electrons? What is it that is all in the em field?

Lastly, in the end, it is the amount of current that is at issue here. You said "Because charge carriers in the metal travel very slowly and cannot cause actual charge separtaion in your cct in the times involed (~2us).So any apparent charge (if there is any) on the plates must be due to some other phenomenon". Charge separation is current. To separate charge, charge must be moved. For a given amount of charge to be separated (moved) in a given time, there must be a certain amount of current. In the above, you are claiming there is not enough current to separate the charge in the amount of time given for the reason that the charge is moving very slowly in the metal. Did you mean to say something different? Alfred Centauri 20:29, 9 March 2006 (UTC)

1. The picture I have in my mind is that in the the conductors there are free charge carriers. Lets call them electrons. These poor little electrons can only move in the conductor at a few mph. So how the heck can they transmit anything at 2c/3?. I picture the electrons executing a almost no motion due to the applied fiele. THe motion that is of their normal random motion and no individual electron actually moves very far (or at all even) at rf. So we agree.

2 I should have said: the deeper inside the conductor the mobile electrons are, the less they participate in the alternating current and that this may alos be relevant to the argument about the wires not actually conducting anything

3 At even more MHz, there any very few charge carriers capable of rf conduction at all in the conductor due to skin effect. All the energy then has to be transfered by the em field.

4 You cant achieve full separation of charge just by shuffling a few electrons back an forth at the far end of a long wire. It would takes time (like charging a battery) for the slowly moving charges to have net effect of charge separation.

*There is a way of charging a capacitor v quickly-- but youre not going to like the explanation I have for that!

--Light current 23:17, 9 March 2006 (UTC)

The link I included above is a decent explanation of how current flows. Alfred is correct in how he stated it above. Your fourth point is not correct. We have to overcome this hurdle before moving forward. In the mean time, I will update the article with the accepted textbook definitions. I'll provide references, and I hope opposing views will have the same. Mak17f 00:37, 10 March 2006 (UTC)

Well I looked at that link -its crap! If this is your idea of a good reference, Im very disappointed. It is very simplistic and does not answer the real questions. Its for kids. The top voted answer (tapping your neighbors shoulder) is just nonsense. The 'tapping' velocity has to be about the same as the overall velocity- its obvious. Its the same with electrons nudging each other: they cant 'nudge' faster than they can move. This is so obvious that it defies further explanation. The writer seems to be confusing distance with speed!!!! --Light current 01:09, 10 March 2006 (UTC)

http://www.jimloy.com/physics/electric.htm

Thgis link indicates that its the wave that travels at about the speed of light. But the electrons dont. Also where is the wave?--Light current 00:43, 11 March 2006 (UTC)

http://www.discoverycentermuseum.org/experiments/272.htm

http://answers.google.com/answers/threadview?id=345010Mak17f 16:30, 10 March 2006 (UTC)

(Mak17f, I have indented your entry above to help us keep straight who posted what - LC is quite strict about this kind of stuff ;<))

OK, rather than dispute LCs 4th point, I'm will instead describe my 'picture' of how the separation of charge occurs at 2/3 c or whatever. A conductor, regardless of whether it is the wire connected to a capacitor plate or is the plate itself, has a certain negative charge density and positive charge density. For a charge neutral conductor, these densities are the same. We know that the positive charge density (the protons in the nucleus of the elemental atoms) must remain more or less constant. We also know that the majority of the electrons that constitute the negative charge density are tightly bound to atomic nuclei and this contribution to the negative charge density must remain more or less constant. However, there are a significant number of electrons that are not bound to any particular nuclei but are instead bound to the structure of the solid as a whole. The density of these mobile or conduction band electrons can be changed easily and quickly and without much movement of the actual electrons. To help see this, I like to use the following macroscopic toy model.

Consider a three dimensional regular lattice of identical billard balls connected together by identical springs. When all the springs are in their 'rest' position, the system is in its lowest energy state corresponding to a neutral charge density state in a conductor. Now, imagine that a force is applied to one side of this cube formed by the billard ball/spring lattice. This force accelerates the outside billard balls on one side thus compressing the springs connecting the outside billard balls to their immediate neighbors (in the direction of the force) thus imparting a force on the immediate neighbors thus compressing the springs connected to their immediate neighbors and so on. The result of this force is a positive density wave - a change in the density of the billard balls that propagates through the lattice at a much higher velocity than the velocity of the billard balls themselves. In front of the wave, the density is undisturbed. Behind the wavefront, the density has changed to new value. One can also picture a opposite force that would result in a negative density wave that causes the springs to be stretched rather than compressed.

It shouldn't be hard to see that in this picture, the springs are loosely analogous to the Coulomb force between mobile electrons in a conductor and the density of the billard balls represent the electric charge density. The force that disturbs the lattice represents an external electric field while the energy propagating along the springs represents the energy carried by the EM field. Hopefully, this simple mechanical analogy suggests how charge density (and thus total charge) can change much more rapidly than the actual motion of electric charge would suggest. Alfred Centauri 01:45, 10 March 2006 (UTC)

P.S. I wrote this up before I read LCs critique of the link Mak17f provided. I am now prepared to be ridiculed - go for it LC. Alfred Centauri 01:45, 10 March 2006 (UTC)

I wouldnt ridicule you even if I could because people in glass houses shouldnt throw stones:-)--Light current 01:57, 10 March 2006 (UTC)

How can a wave travel faster than the elements that actually cause the propagation?--Light current 02:24, 10 March 2006 (UTC) Silly question!!--Light current 02:57, 11 March 2006 (UTC)

What does 'elements that actually cause the propagation' mean? What are, in your view, the elements that cause the propagation of, say, a pressure wave in air (or water or rock)? What, in your view, are the elements that cause the propagation of a transverse displacement wave on a taunt string? Is it the matter particles that make up the medium or is it an interaction between the particles in the medium that propagate a disturbance (wave)? Alfred Centauri 04:54, 10 March 2006 (UTC)

In your model the elements are the billiard balls. In air we were taught that it was the molecules of the air undergoing a net non random motion (above and beyond their thermal motin etc) the propagates the pressure wave. On stetched string, again it must be movement of each molecule that drags its neighboring molecule along by molecular attraction.

I would say both elements are essential to the propagation: both the ability of the 'elements' to move at the required velocity of overall propagation, and the ability of the interaction forces to transmit the wave at that velocity. In your ex. the balls must move at the propagation velocity albeit for a short time ; the springs must transmit the forces at the required velocity.

Now in the case of electronic charge carriers, we are told that on average they only move at a few mph (I take this as true altho' I have not measured it). Now whilst interaction forces may be able to act much faster that this, from the above supposition it is plain to see that proper charge separation due to movement of charge carriers is only possible in the lowest frequency cases (inc z.f)--Light current 17:16, 10 March 2006 (UTC)

LC, the particle velocity is not the same as the propagation velocity. For example, the air particle peak velocity for a sinusoidal plane sound wave propagating at a speed of c is given by:

$u_{peak}={\frac {2{\sqrt {2}}\cdot 10^{{\frac {SPL}{20}}-5}}{\rho _{0}c}}$

where SPL is the sound pressure level and $\rho _{c}=1.18kg/m^{3}$ is the density of air at standard pressure and temperature.

As an example, the propagation speed of a sound (pressure) wave in the air at sea level is about 345 m/s. What is the peak particle velocity for a 90dB SPL sinusoidal plane wave? If I've done my calculation correctly, the answer is about 0.0022 m/s.

So, I must disagree with your view that the elements (particles) of the medium must move at the required velocity of overall propagation. Alfred Centauri 22:45, 10 March 2006 (UTC)

OK I'll look at this.--Light current 23:29, 10 March 2006 (UTC)

Having looked at my book on sound, I find that even in longitudinal plane sound waves, the particle velocity is equal to the product of the wave velocity and the slope of the displacement curve (related to amplitude and freuency I presume). Therefore, the particles may move faster than, slower than or at the same speed as, the wave velocity. It is interseting to note that the wave equations for sound waves in air are similar to those for em waves travelling down a TL>

Therefore a sound (or other machanically produced) wave can (counter to intuition) propagate faster than the individual particle velocities. My School course stopped short of the wave equations for sound unfortunately. OK I admit was wrong about sound waves (Ouch!).(lack of proper education!)

Are you saying the same thing happens with em waves where the velocities are much higher? If you are, you can quickly get into trouble when the slope of displacement curve approaches unity as the particle velocity then approches c. --Light current 00:32, 11 March 2006 (UTC)

Shock waves

When the air particle velocity exceeds the wave velocity, a 'shock wave' is formed - see Sonic boom. In a near perfect analogy, electrons can exceed the local speed of light within a medium and an EM (light) 'shock wave' is produced - see Cherenkov radiation. However, as you point out, such a shock wave cannot be produced in the vacuum as that would imply that the electron velocity is equal to or greater than the speed of light in the vacuum. Alfred Centauri 02:09, 11 March 2006 (UTC)

Yes I was aware of the sonic shock wave and have seen the effect of Cerenkov radiation on water cuased by spent nuclear fuel rods (an eerie blue glow as I remember).Now the problem is whether this knowledge has any bearing on the subject at hand. We have em waves. Particles (charge carriers) may travel locally at high speeds but their average velocity is low, I think you will agree. So this does still leave the question of how charge carriers can get around a macoscopic circuit in the time to move any real charge. The answer, of course, is that they can't and any effects seen at the capacitor plates must be due to the em field. If there is a problem with the source frequency, just increase it until you're sure the carriers cant travel the distance in the time allowed.

Let me ask you a couple of questions:

If the generator is switched off at the peak of a cycle at the capcitor, will the capacitor have any separated charge on its plates? If so how did it get there?--Light current 02:47, 11 March 2006 (UTC)

The answer, as far as I'm concerned, is that the mobile charges don't need to move around the circuit for the charge density on the plates of the capacitor to change. Instead, the mobile charges only need to move closer together or farther apart in order to change the charge density. I'm not sure I can put it any simpler than that. This is the point I attempted to make with the billiard ball analogy. So, let me try again.

The spacing of the billard balls can change very quickly even though the velocity of the billard balls themselves is relatively low. Likewise, in an acoustic wave, the density (or pressure) wave propagates at a much faster speed than the actual particle velocity. Likewise, an electron density wave propagates much faster than the drift speed of the electrons. Finally, do recall that the net electric charge on the plate of a capacitor is determined by the mobile electron charge density there. That is, to 'charge' a capacitor, it is not required to pump electrons from one plate to the other - instead, we simply need to increase the mobile electron density on one plate while decreasing the density on the other - we need to 'push' the electrons closer together on the negative plate and 'pull' the electrons farther apart on the positive plate. To do this requires very little actual movement of charge.

If 1 Coulomb of charge has been separated, then 1 extra Coulomb of electrons has been placed on the negative plate and 1 Coulomb of electrons has been removed from the positive plate. Are these the same electrons? As far as I'm concerned, the answer is no. Can I convince you of this? Apparently not.

For now, that is the best I can do to explain my view of this subject. Oh, and as to your final questions: By switching off the generator, I assume you mean the generator is a current source so that 'switching off' means 'open the circuit'. If your generator is a voltage source, you'd need to open the circuit with a switch, right? Anyhow, it is my opinion that opening the circuit would indeed reveal charge separated onto the plates. Hopefully, you'll accept my explanation above as the answer to the question of how. Alfred Centauri 03:41, 11 March 2006 (UTC)

OK Im happy to accept the idea of the electron density wave (even tho' I havent seen one). How is this different from an em wave? (you hear me ask) and can these EDWs travel at close to the speed of light in the conductors? I agree that to temporarily 'charge' a capacitor, it is not required to pump electrons from one plate to the other but only to increase the electron density on one plate whilst decreasing the density on the other. But this can only lead to a temporary separation of charge on the capacitor unless the charge travels completely round the cct back to a source/sink of carriers. If 1 extra Coulomb of electrons is placed on the negative plate and 1 Coulomb of electrons is removed from the positive plate they dont have to be the same electrons as long as they have somewhere permanent to go/come from (like a battery or dc source).?

Opening the switch to turn off the gen. is correct. We all know that charge can be captured (separated) this way as in a simple 1/2W rectifier and capacitor at the end of a TL, but my point is that this so called charge is not dependent on the charge carriers which only shuttle back and forth (esp at high frequencies), but on the em wave. BTW has the plasmon frequency I have heard of anything to do with this problem?--Light current 04:19, 11 March 2006 (UTC)

This term plasmon is new to me but when I began to read the article, it seemed familiar. Like the photon and phonon, the plasmon is a quantized mode of a field - in this case the field quantity of interest is the (mobile) charge density. As to whether the plasma frequency has anything to do with this problem, I would say that the objection you raise about the electrons not moving fast enough (or is it far enough?) to charge the capacitor would be related to this IF the plasma frequency were low enough. However, as the article on plasmons state, the plasma frequency for most metals is in the ultraviolet range which is why we can't see through metals (excepting of course, transparent aluminum). So, it seems unlikely that objections based on plasma frequency will be valid here - unless your generator is one of those new TeraHertz models (p.s. even higher - if my calculation is correct, the plasma frequency for copper is 2.18 GigaGigaHertz - 2.18E18 Hz!)

Regarding the difference between the charge density waves I keep refering to and an EM wave: the answer is that they go hand in hand. When an EM wave is guided by, e.g., a parallel plate TL, the charge density wave is in lock step with the the guided EM wave - the two cannot be separated. In fact, it is the presence of the charge density wave in the conducting plates that acts to bound the EM wave to the interior region between the plates. Further, it is the propagation speed of the charge density wave in the plates that sets the propagation speed of the EM wave between the plates.

Please explain in more detail why you feel that a charge density wave "can only lead to a temporary separation of charge on the capacitor unless the charge travels completely round the cct back to a source/sink of carriers." This makes no sense to me at all. The source of carriers are the plates of the capacitor and the conductors in the circuit. The mobile carriers of charge are all there just waiting to be redistributed. To "permanently" charge a capacitor we need only to 'pump' the required amount of electrons through the generator and then disconnect the generator or the cap. That's it. Unless you plan on pumping every last mobile electron off of the positive plate and the conductor connecting that plate to the generator (that would make an interesting calculation!), you will not need to move an electron all the way from one plate to the other. Alfred Centauri 22:05, 11 March 2006 (UTC)

New questions

• Is an electromagnetic wave capable of achieving steady state charge separation at a point remote from its generation.
• If so, can we say that the em wave 'carries charge' with it?--Light current 03:23, 11 March 2006 (UTC)

I don't even understand what your are asking in your first question. Can you be more specific by providing more details of your setup and your assumptions?

As far as I'm concerned, the answer to your last question is NO regardless of the answer to your first question, whatever that turns out to be. If an EM wave carried electric charge, EM waves would interact with each other via the Coulomb interaction. This does not happen in classical EM theory (however, in QED, there is a second order photon-photon interaction that occurs when two photons each create a pair of virtual charged particles which then interact before the virtual particles annihilate back into photons - I don't think this effect has been experimentally observed yet). Alfred Centauri 22:01, 11 March 2006 (UTC)

I was asking whether an electromagnetic wave when sent either down a TL or thro' space, can achieve real permanent charge separation at a remote capacitor (connected to the TL or as part of a radio Rx for example). But the main question is the second one. If the answer to the first is true, then how is this charge conveyed? (esp thro' vacuum)--Light current 22:07, 11 March 2006 (UTC)

Ah, now I see. I think I've answered your question to MY satisfaction with my recent comments in the 'Shock wave' section. Recall that we can send an EM wave down a dielectric wave guide (optical fiber) but we cannot charge a capacitor with this wave. However, we can send an EM wave down a two-wire wave guide (twin-lead) and charge a capacitor. The reason we can do this with the twin lead is that the EM wave between the conductors in the twin lead is accompanied by a charge density wave in the conductors. This charge density wave in the conductors is the reason the EM wave can be guided by the conductors in the first place. So, we charge the cap at the end with real electric charge, not the EM wave. Alfred Centauri 22:26, 11 March 2006 (UTC)

----

Having consumed a libation or three, I re-read this section and began to think of a scenario in which what you call permanent charge separation might occur through the action of an EM wave from a remote location. I'm thinking of a conducting rod of a length that matches the wavelength of an EM plane wave incident upon it. Assuming the orientation of the rod in space is correct, the EM wave causes a sinusoidal current in the rod at the same frequency as the EM wave. Of course, this current generates a wave that destructively interferes with the incident wave such that some of the energy carried in the wave is absorbed by the rod. Now, what if this rod is cut in the middle at such time that the E field of the incident wave is at a maximum? Without the benefit of a rigorous analysis, I would think that the charge distribution on the rod at the time of the cut would be such that after the cut, one rod will be net positively charged and the other will be net negatively charged. Of course, for this to work the cut would need to be made VERY quickly. Perhaps a laser pulse could do it.

However, even if the above is not pure BS, I don't see how such a result could be construed to imply that EM waves 'carry' electric charge. Alfred Centauri 01:15, 12 March 2006 (UTC)

Your suggested differentiation betweeen dielectric propagation and 'waveguide' (or TL) propagation of 'em' is very interesting. So we cant charge a capacitor by feeding em energy down an optical fibre, you say? But em energy is transferred from one place to another in both cases, is it not? This implies that you think a TL is charged by the CDW and not by the em wave between the conductors. Am I correct in assuming you believe this?--Light current 00:59, 12 March 2006 (UTC)

You would be correct in assuming that I believe that a TL is charged by charge and not by the EM wave alone. Do keep in mind what I said earlier though, the CDW and EM wave in a TL go hand in hand. We can't have one without the other. Also, please see the section I added before your latest comment but which got involved in an edit conflict. Alfred Centauri 01:15, 12 March 2006 (UTC)

Ah ha! So if we cant have one without the other, no em wave guided by, or in, a pair of conductors can go faster than the CDW. But has this very high velocity (2c/3 say) of CDWs been shown to be possible?--Light current 01:26, 12 March 2006 (UTC)

To quote from my post in the 'Shock wave' section: "Further, it is the propagation speed of the charge density wave in the plates that sets the propagation speed of the EM wave between the plates." BTW, when I speak of a charge density wave, I'm not refering to what are called CDWs in the literature. Instead, I'm speaking of a propagating disturbance in the electric charge density in a conductor, $\rho _{e}({\vec {r}},t)$. At what speed would you expect a change in mobile electron density to propagate in a conductor? Alfred Centauri 02:17, 12 March 2006 (UTC)

The speed I would expect a change in mobile electron density to propagate in a conductor would be faster than I first thought but I dont think as fast as the guided em wave can go. But Im sure you'll prove me wrong on that one. If what you say is true, then there is no Catt (Ivor Catt)anomaly and everything is fine! (apart from skin effect that is!)--Light current 02:24, 12 March 2006 (UTC)

What is electric displacement?

Also Alfred we never did find out what you meant by a 'flow of displacement' (your apparent defn of DC). How do you define displacement? Displacement of what? Are you referring to vacuum polarisation perhaps when you talk of displacement in vacuo?--Light current 15:22, 9 March 2006 (UTC)

It's not actually my definition, right? After all, an air current is a flow of air - a water current is a flow of water - a displacement current is, literally, a flow electric displacement. What is electric displacement?

It seems that Maxwell thought of electric displacement as a physical displacement of electric charge from equilibrium in a medium - a polarization of the medium. The displacement current, in this view, is the time rate of change of the displacement from equilibrium which amounts to an actual movement of real electric charge - an actual electric current. However, unlike free charge that would accelerate under the influence of an electric field, these bound charges can only remain displaced from equilibrium positions as long as there is an external electric field to counteract the internal electric field between the bound charges. To change the displacement from equilibrium requires a change in the external field. Thus, the displacement current is proportional to the rate of change of the external electric field.

Electric displacement and displacement current as defined above cannot exist in the classical vacuum. However, according to the Standard Model, the vacuum is not empty but actually contains a sea of virtual particles including electrically charged particles. Thus, according to this view, the vacuum can indeed be polarized. It would seem reasonable then that vacuum displacement current of this sort could be detected in the same way an electric current is detected. Alas, virtual particles cannot be directly detected (thus the adjective 'virtual'). However, the effects of virtual particles can and have been detected (see, for example, Casimir effect, and Lamb shift). So, perhaps a changing vacuum polarization is in fact a displacement current. Alfred Centauri 16:20, 9 March 2006 (UTC)

Thank you for outlining your position so succinctly. I actually understand what you are saying! So if we can measure vacuum displacement current perhaps by the exptl method I outlined above, we may have discovered or proved something. I dont think vacuum ploarisation has yet been measured/proved to exist -- or has it?--Light current 16:43, 9 March 2006 (UTC)

I suppose the answer to your question depends on what you are willing to accept as 'proof'. In fact, predicted detectable effects due to the existance of virtual particles and the resulting vacuum polarization have been confirmed experimentally (once again, see Casimir effect and Lamb shift for examples). Of course, if you doubt the principles upon which the Standard Model is constructed, you probably will not be convinced by these results. Alfred Centauri 17:01, 9 March 2006 (UTC)

Well as you know Alfred, I always try to have an open mind and am willing to be convinced! But the real test as always is the experiment.--Light current 17:14, 9 March 2006 (UTC)

Unless of course the experiment cannot be performed -then we have a problem!--Light current 03:25, 11 March 2006 (UTC)

Hi - Umm - the J_D quoted on this page is actually the displacement current DENSITY. the actual displacement current is INT (Jd. dA)

---

Removed section

I removed the section 'Displacement Current & Magnetism' as it has some significant problems that must be addressed. The most obvious problem is that the the capacitor equation is a scalar equation but Ampere's Law is a vector equation. The step of determining a vector field from the ratio of two scalars is highly suspect except in a one dimensional problem. However, Ampere's Law cannot be applied to a one dimensional problem (try to define 'curl' in 1-D). I might try to fix this but the author should get first crack. Alfred Centauri 19:16, 14 October 2006 (UTC)

'== Displacement Current & Magnetism == Over the years, many scientists and engineers have questioned whether or not displacement current "causes" magnetic fields. The following simple derivation shows how displacement current and charges interact to form magnetic fields.

The capacitance of a parallel plate capacitor with plates of area A and plate separation of d may be expressed as:

$C=\varepsilon _{R}\epsilon _{O}{\frac {A}{d}}$ (1)

Where $\epsilon _{R}$ and $\epsilon _{0}$ are dielectric and free space permittivity, respectively.

Another basic equation relates the uniform charge, Q stored in a capacitor, to the capacitance C, and the Voltage across the plates, V.

$Q=CV$ (2)

Divide both sides of equation (2) by the distance between the plates, d:

${\frac {Q}{d}}=C{\frac {V}{d}}$ (3)

Since ${\frac {V}{d}}=E$, where E is the electric field between the plates, we may rewrite equation (3) as follows:

${\frac {Q}{d}}=CE$ (4)

Substitute the value for C from equation 1 into equation (4):

${\frac {Q}{d}}=\varepsilon _{R}\epsilon _{O}{\frac {A}{d}}E$ (5)

Multiply both sides of equation 5 by d, and take the partial derivative of equation 5 with respect to time. The result is shown below:

${\frac {\partial Q}{\partial t}}=\varepsilon _{R}\epsilon _{O}A{\frac {\partial E}{\partial t}}$ (6)

Using the constituitive relation $\varepsilon _{R}\epsilon _{O}E=D$, equation (6) may be written as:

${\frac {\partial Q}{\partial t}}=A{\frac {\partial D}{\partial t}}$ (7)

Ampere’s law, as adapted by Maxwell to include the effects of Displacement Current is often written as:

$\nabla \times H=J+{\frac {\partial D}{\partial t}}$ (8)

If we substitute the appropriate values from equation (7), we are able to rewrite equation (8) as:

$\nabla \times H=J+A^{-1}{\frac {\partial Q}{\partial t}}$ (9)

But $A^{-1}{\frac {\partial Q}{\partial t}}$ is another way of expressing J. In this case, since the electrical field is Transverse to the plane of the conductor, we define a new term,

$J_{T}=A^{-1}{\frac {\partial Q}{\partial t}}$ (10)

The term “J” has traditionally been taken to mean “longitudinal conduction current.” To differentiate it from $J_{T}$, let us rename J as $J_{L}$ standing for longitudinal current flow. With these re-definitions, we can now rewrite equation (9) in a form that is consistent with the spirit of Ampere:

$\nabla \times H=J_{L}+J_{T}$ (11)

Conclusion Equations 8, 9 and 11 may be used interchangeably, but only if one understands that the source of the magnetic fields is the motion of charges, ${\frac {\partial Q}{\partial t}}$ .

Need Images of Equations

The equations in this article (and all Wikipedia articles) need to be GIF images -- with the equation markup as alt text.

Normal browsers just show the math markup code.

Wikipedia needs to be usable without any special plugins, etc. —The preceding unsigned comment was added by 75.6.243.176 (talk) 10:02, 23 December 2006 (UTC).

Not Billiard Balls

I am a newbie to Wikipedia but not to displacement current. It is clear that most of the difficulties with this concept arise from a misunderstanding of the nature of electric fields and electric charge. So often one reads that "charge has to flow to have current" or words to that effect, if "flow" is replaced by "move" then the statement could be correct. Before leaping to a conclusion, let us think what a charge is. A charge is an entity, perhaps an electron, that is defined by the electric field it produces around it (the charge in a volume is the integral of the electric field over the surface of the volume). This field is infinite in extent. A feature of charged particles is the existance of two kinds of charge, positive and negative, Pedantic? I don't think so, it is this concept of an electric field that lies at the heart of the confusion about displacement current, I first engaged with Ivor Catt in Wireless World on this subject more than twenty years ago.

One of the matters that was confusing about Ivor Catt's analysis of electric current and associated waves was his insistance on using a transmission line to illustrate the "failings" of Maxwell's equations. To my astonishment the problems arising from this approach are still not understood, namely that the flow of electric current requires, in some bizarre way, the transfer of an electron. This is not the case, current exists when a charge (of whatever sort) moves, it does not have to arrive anywhere! This is easily observed in an old fashioned goldleaf electroscope, the kind with a bell jar and metal hook passing through the cork, gold leaf is draped over the hook inside the jar and there is a metal ball fixed to the hook outside the jar. Usually a comb will do the necessary, put a charge on it (use your hair if it's dry), bring the comb close to the ball of the electroscope without touching it and the gold leaves will fly apart. If you now withdraw the comb the leaves fall back to their original position. If you touch the ball or better, wipe the comb over it the gold leaves will fly further apart. When you now withdraw the comb the gold leaves do not return to their original position.

In the first instance, when you moved the comb towards the electroscope you increased the electrical field in the region of the electroscope. Here we come to the difficult bit, the bit that gives Ivor Catt, Light Current and so many others such a hard time. The difficulty arises because conductors are extremely complicated entities, be they metals, semiconductors, plasmas, supercoductors or anything else. The key feature of (solid) metals is the atomic structure. In solids atoms are bound together by electrical forces, in metals the forces act in such a way that local (to the atom) charge neutrality is not preserved, this means that the electrons are not bound to a particular atom, any passing wave will move them, they also move because they have a temperature above absolute zero, however the number of electrons able to move about is exactly equal to the number of positive charges (protons) left behind on the atoms that are fixed in the metal structure. Because these electrons (charge carriers) are free to move, they quickly rearrange themselves when the comb approaches the ball, in particular the charge density on the surface of the metal changes, if the comb is charged with electrons then some of the electrons on the ball surface move towards the gold leaves where the force due to the excess charge on their surfaces pushes them apart; the total number of electrons in the metal remains the same; a charge flow meter placed halfway down the hook will tell you how many electrons have moved along it, a current meter (ammeter) will tell you the rate they were flowing. Thus the electrons on the comb, due to their electric field (which distinguishes them from very small billiard balls) influence the free electrons in the electroscope to cause a net charge flow from one part of it to another. The quicker you move the comb the higher the current. If you move the comb back and forward in a regular way the ammeter will record an alternating current. If you place a resistor in series with the ammeter while moving the comb the resistor will get warmer due to this current. Of course, when the comb is moved back to its original position the charges on the metal of the electroscope return to their original distribution.

If the charge on the comb becomes transfered to the electroscope by touching it or wiping, it will quickly spread over the metal surface and the presence of a net charge (with respect to the surroundings) is demonstrated by the separation of the gold leaves.

The difficulties recorded in the dicussion on displacement current often revolve round such circuit concepts as capacitors, inductors and transmission lines, these are all aproximations that allow local solutions for electrical wave problems, even the idea of a conductor is a similar approximation. The circuit concepts are mentioned are unuseful for a general electrical theory because they all have linear dimensions in their realisation, giving real implementations of them a frequency characteristic, Maxwell's equations are free of such restraint. Circuit concepts are essential to the realisation of most electromagnetic devices but history is littered with the wreckage of projects that took the approximations too literally.

Maxwell's equations do not explain all the interaction of charged particles, that is the preserve of Q E D (quantum electrodynamics).84.198.164.234 20:58, 14 June 2007 (UTC)

My view is this:

All electromagnetic phenomena is due to photons and their motion (e.g. qed, momentum exchange force). That is, “charge” is just a number describing the fact that a region of space has a distribution of photons with velocity and spin. Charge is not a separate object on its own. Hence why a photon has zero charge, it is already, charge in essence, that is, photon motion is what we mean by charge. Electric and magnetic field are one and the same, (photons in motion) and the apparent differences due solely to the relative motion of source and observer (e.g. special relativity). Displacement current is a virtual effect associated with the motion of photons illustrated by this analogy. Consider a flow of fluid in the horizontal direction, but with the magnitude of the velocity a function of the vertical direction. A test particle will experience a vertical force, (non zero Curl) despite their being no physical particle with momentum in the vertical direction to force the test particle. Displacement current is analogous. Its the name we give to the virtual force that moves the particle vertical. That is, displacement current is as real as any other current, in that all currents are just the effects of photon motion, and all EM forces are due to momentum exchance of those photons. So, different distributions of photon densities and velocities (vector) are manifested as magnetic and electric fields, displacement or otherwise.

So, was it worth 2 cents?

Kevin aylward 22:09, 11 September 2007 (UTC)

Maxwell and Displacement Current

One needs to be very careful when criticizing Maxwell's involvement with displacement current. Maxwell conceived of the idea in conjunction with an external electromotive force acting on his sea of molecular vortices and causing a tangential stress on these vortices. In doing so, he equated electromotive force with electrical displacement in what was essentially Hooke's law, or a simple harmonic motion equation. (105 in his 1861 paper). He then took the time derivative of this equation and conceived of the concept of displacement current, which he then added to the free current term in Ampère's circuital law.

A few years later in his 1865 paper, he used this extended version of Ampère's circuital law to derive the electromagnetic wave equation. The displacement current is an essential ingredient of electromagnetic radiation and as such it is criminal to ignore the origins of the concept when analyzing the physical nature of light.

It is not Maxwell that needs to be criticized in relation to displacement current. It's true that his explanation regarding tangential stress on his vortices needs a considerable amount of elaboration.

In all probablity, the mathematical form that Maxwell established can probably apply equally to two different varieties of displacement current. There will be a linear displacement current as occurs between the plates of a capacitor.

This is most unlikely to be the same physical effect as the angular (tangential) displacement current which occurs in magnetization and EM radiation.

However, many textbooks have analyzed Maxwell's displacement current in relation to the capacitor when in truth they should have been analyzing it in relation to the magnetic field surrounding an electric circuit.

That is not the fault of Maxwell. Maxwell was a pioneer in the field and he can hardly be blamed for not having had the picture entirely in focus. David Tombe (talk) 19:05, 20 July 2008 (UTC)

The Necessity for Displacement Current

The latest edits to the main article involve a new section regarding the necessity for displacement current. This new section could be summed up in prose, simply by stating that the existence of a magnetic field surrounding the space between the plates of a charging or discharging capacitor implies that an electric current must be flowing between the plates. This does not mean that an expression in the form of Maxwell's displacement current is needed to be added to Ampère's circuital law. Maxwell's justification for adding displacement current to Ampère's circuital law was quite different. David Tombe (talk) 06:45, 22 November 2008 (UTC)

As important as the historical record is, this example addresses a different issue: the present-day understanding of displacement current (the main topic of this article). This standard example appears in many books along with the definition of displacement current. It demonstrates concretely why the displacement current term is needed: in circuits with a capacitor or other break, Ampere's law gives the wrong answer without it. As for a prose explanation, Maxwell's equations are mathematical equations, and displacement current is defined here mathematically; this justifies a mathematical explanation. However your point that Maxwell's original justifiction was different is important, and should probably be added to the History section. --Chetvorno^TALK 08:36, 22 November 2008 (UTC)

Chetvorno, On reflection, I may not have explained my point very well. You have illustrated how Ampère's circuital law and the Biot-Savart law appear to break down in the space between the plates of a capacitor. If we have a magnetic field without there being an electric current, then we need to explain how, and you have advocated how the mathematical expression for 'displacement current', dE/dt, acts as a substitute for the electric current term, and that therefore in general, we can add this displacement current term to Ampère's circuital law (or the Biot-Savart law) in order to give Ampère's circuital law general application. But this explanation is not complete, because it fails to address the issue of how the displacement current term is able to act as a substitute for the ordinary electric current term. The link between J and dE/dt is based on the fact that the latter represents the polarization current in a dielectric. That's why dE/dt can fit into Ampère's circuital law or the Biot-Savart law in place of J. This aspect of the explanation is being ignored. That is where it becomes necessary to investigate how Maxwell produced the displacement current in the first instant. It's only when we've established that physical link between J and dE/dt that we can then substitute the latter into the former in Ampère's circuital law in order to account for the cause of the magnetic field between the plates of a capacitor. In other words we must deal with the issue of displacement current first, before we start looking at how it all fits into capacitor circuits. We cannot begin by looking at a capacitor circuit and assuming that no current flows, and then remedying the dilemma by introducing displacement current without explaining what displacement current is. The explanation in the section which you wrote merely states that when there is no electric current flowing, then the magnetic field is instead being caused by a changing electric field. You have ignored how this changing electric field is related to the current which causes the magnetic field. There is a gap in the logic. What has happened historically is that Maxwell has invented the concept of displacement current. Later this concept has been applied between the plates of a capacitor. Later still, displacement current has been justified in terms of a capacitor circuit without reference to its own justification. David Tombe (talk) 09:20, 22 November 2008 (UTC)

That was the part that Maxwell had wrong. (I'm not sure I'm addressing your point, but here goes) The polarization component of the displacement current, ${\frac {\partial \mathbf {P} }{\partial t}}\,$ represents charge movement, but in the other component, ${\frac {\partial \mathbf {E} }{\partial t}}\,$, there is no charge movement (current) at all. The term 'displacement current' is misleading, it doesn't necessarily consist of a physical current (movement of charge). In regions where there are no dielectrics (polarization $\mathbf {P} =0\,$), such as a capacitor with vacuum between the plates, the 'displacement current' consists of the changing electric field itself. So there is no current of any kind between the plates; the changing electric field itself acts as a source of the magnetic field. --Chetvorno^TALK 10:58, 22 November 2008 (UTC)

Maxwell's displacement current, as per Maxwell, still applies to the polarization current in a dielectric, so I wouldn't go as far as to say that Maxwell got it wrong. What we seem to be dealing with here is another imposter which uses the name of displacement current and which has weighed in alongside Maxwell's displacement current in the modern literature. The sole justification for this latter day quantity is to prevent the breakdown of Ampère's circuital law and the Biot-Savart law in capacitor circuits. To this end, the new latter day displacement current is simply the equal and opposite of the divergent component of the real current, where the real current exists. This in turn ensures that the divergences of the two concurrent currents are equal and opposite, such as to retain the solenoidal nature of Ampère's circuital law. You haven't explained this in the section which you added concerning the necessity of displacement current. If you are going to advocate that a changing electric field is in itself sufficient to induce a magnetic field, then you will need to add a bit to explain how this latter day displacement current can be legitimately added to Ampère's circuital law or the Biot-Savart law. The explanation which I have given you is the modern textbook explanation. You will need to try to weave it into your explanation. David Tombe (talk) 02:25, 23 November 2008 (UTC) http://www.ivorcatt.org/icrwiworld78dec1.htm 2A00:23C4:C0A:900:90A5:1E4E:11C:D64B (talk) 20:19, 3 August 2019 (UTC)

The Explanation section

Who first decided to split the displacement vector D into and E component and a D component? In Maxwell's original papers, there is no separate P component, because the explanation given in this wikipedia article for the P component is essentially the same explanation that is given for the E component in Maxwell's papers. What the wikipedia article here is saying, is that as well as Maxwell's displacement current, there is another displacement current that doesn't involve displacement. Somewhere along the lines, another concept that is different from Maxwell's displacement current, has emerged under the name of Maxwell's displacement current to sit alongside the actual Maxwell's displacement current. David Tombe (talk) 09:45, 22 November 2008 (UTC)

I didn't write what you're referring to, but that is how displacement current is defined today. --Chetvorno^TALK 11:30, 22 November 2008 (UTC)

Yes indeed. As I have said above, an imposter, that uses the name of Maxwell's displacement current, has weighed in alongside the real Maxwell's displacement current in the modern literature. Maxwell's original displacement current is now catered for using the P vector, while the original D vector focuses on the new imposter. The new displacement current uses a justification that is quite different from the justification that is used for Maxwell's original displacement current. The new displacement current uses a justification which is based on maintaining the solenoidal nature of Ampère's circuital law in capacitor circuits. David Tombe (talk) 02:31, 23 November 2008 (UTC)

Importance of displacement current to electromagnetic waves

It should probably be mentioned somewhere in the article that the displacement current term, particularly the dE/dt part, has importance beyond circuit theory; its addition to Maxwell's equations allowed electromagnetic waves to be derived from them. --Chetvorno^TALK 12:34, 23 November 2008 (UTC)

Chetvorno, You are absolutely right. The crucial importance of displacement current is in connection with electromagnetic waves. In fact, I have often heard electronic engineers complaining about the existence of displacement current in circuit theory.

That is exactly what I was trying to address in the history and interprtetaion section, but I'll go back and take a look and see if I can bring the issue more to the fore. David Tombe (talk) 01:20, 24 November 2008 (UTC)

Weber and Kohlrausch 1856

Is there anybody who knows the full details of what exactly Weber and Kohlraush discovered in 1856? I have read conflicting reports over the years. It's generally agreed that they discovered the link between the speed of light and the ratio of the electrostatic units of charge to the electromagnetic units of charge. If that was so, then surely that would have be the point in history when optics, magnetism, and electricity were unified. However, there are conflicting reports about whether or not Weber and Kohlrausch were overtly aware of it, because Weber's constant was tied up with a factor of root 2. Maxwell got the hold of Weber's data in late 1861, while in London. It was then that he inserted it into his calculations and saw the connection between the speed of light and the elasticity of the electromagnetic medium. That point in history, in 1861, would certainly have represented a total unity between electricity, magnetism, and optics. So what exactly is the full significance of the fact that Maxwell used displacement current in 1864 to derive the electromagnetic wave equation? Was it not already a certainty by that stage that light was an electromagnetic wave? Then there is the additional issue regarding what Kirchhoff did in 1857. He got the speed of light linked up to electricity and magnetism too. Here is a link which includes the original 1857 Kirchhoff paper in question.[1] There is nothing about this in the Weber article on wikipedia. David Tombe (talk) 02:50, 25 November 2008 (UTC)

Removal of the vector theorem from the main article

Brews, The main reason that I removed the vector theorem was because the symbol A was going to cause confusion with the magnetic vector potential A. I was going to change it to another symbol when it occurred to me that we don't really need to justify this standard vector identity in this article. You inserted two key points surrounding this topic, both of which are mutually exclusive but equally relevant to he topic. The conservation of charge issue doesn't arise in the EM wave equation because , as you pointed out, we need zero divergence for any field involved in the equation, be it, A, B, H, or E.

Since capacitor theory is connected with cable telegraphy and transmission lines, and since in capacitor theory, the divergence of E is not zero, this puts a question mark over the telegraphy equations of both Kirchhoff and Heaviside.

There are two theories going on side by side, which seem to have been wrongly blended together ino one. Wireless telegraphy and cable telegraphy don't share exactly the same maths. David Tombe (talk) 01:27, 26 November 2008 (UTC)

Conservation of Charge and Ampère's circuital law

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) 03:36, 26 November 2008 (UTC)

Introduction of vector potential A

Hi David: You added this paragraph, which I removed:

"An identical wave equation holds for the electric field providing that ${\boldsymbol {E}}=-{\frac {\partial }{\partial t}}{\boldsymbol {A}}\,$. Hence the $\mathbf {E} \,$ field involved in the displacement current comes from the time varying component of the Lorentz force when it occurs in electromagnetic radiation. In EM radiation, the $\mathbf {E} \,$ field is not therefore the $\mathbf {E} \,$ field of Gauss's law."

You may have a useful remark here, but it needs some elaboration. First, no basis is laid for introduction of A. Second, the appearance of the Lorentz force has not been introduced, so the reader sees a "deus ex machina". Maybe you can fix this up. It also would help if a reference could be provided to support the claim that E from its various sources is "different". Brews ohare (talk) 18:52, 26 November 2008 (UTC)

Brews, yes we need to think about how to weave this point more coherently into the article. The point is that the displacement current as is used in the EM wave equation is not the same as the displacement current that is used in the conservation of charge analysis. The latter is related to Gauss's law, whereas the former obeys the relationship ${\boldsymbol {E}}=-{\frac {\partial }{\partial t}}{\boldsymbol {A}}\,$.

As you know yourself, the Lorentz force has got three components. I would make it four, but that's not relevant here. Let's call the three components G1, G3, and G4 for (1) Gauss's law, (2) the Coriolis force and (4) the Euler force.

EM radiation is using a G4 (Euler force) form of displacement current, whereas the conservation of charge analysis is using a G1 form.

Whereby you have correctly pointed out that the divergence of E has to be zero in the EM wave equation, you have not clarified the fact that in order for it to be compatible with the E in Faraday's law, it must also satisfy ${\boldsymbol {E}}=-{\frac {\partial }{\partial t}}{\boldsymbol {A}}\,$.

The conclusion is that where we can have an EM wave equation for A, B, E and H, we can never have an EM wave equation for D. David Tombe (talk) 01:03, 27 November 2008 (UTC)

To obtain conservation of charge

This section is less clear than it seems on the surface because the current and charge in the continuity equation might mean all the charges and currents, in which case just what current is meant in curl B = μJ? If J includes all the currents, then we can't add to it the entire displacement current without double counting the polarization current.

On the other hand, if the continuity equation includes only "free current" and "free charge", then what is meant in curl B = μJ? If now J includes only free current, then adding the entire displacement current to J adds the polarization current due to bound charge, and the time derivative of E term, but J still lacks the magnetization current that should be in the curl B equation.

It appears a better way might be to use the H-field throughout instead of the B-field. Brews ohare (talk) 09:25, 27 November 2008 (UTC)

Brews, if you look at Ampere's original law you will see that it can only make sense when it applies to free current. It is about integrating a magnetic field around a loop that encloses the source electric current. A displacement current that is justified on the basis of conservation of charge, as per this section, merely subtracts the aspect of current that is related to charge accumulation, and which wasn't even a consideration in Ampere's original law in the first place.

I told you that this was not a straightforward topic. What you have now, is what is in the textbooks. But it hardly explains the link to EM radiation. Maxwell was closer, but even linear polarization does not solve the problem.

The point is that the conservation of charge argument has got nothing to do with EM radiation. In EM radiation, curl B = (partial)dE/dt. Based on Ampere's original law, curl B should never equal zero. The question, that is not being tackled by anybody, is how do we relate J to (partial)dE/dt in the context of EM radiation in free space? What is the physical nature and mechanism that upholds this relationship between J and (partial)dE/dt when E equals -(partial)dA/dt? The whole conservation of charge thing is a red herring, and it's not Maxwell's red herring. Sure you know fine well that EM radiation is not connected with charge variation.

Maxwell started us on the right tracks, but he got sidetracked to linear polarization. Look back to that quote which I gave you about propagated rotations and then link -(partial)dA/dt to the Euler force. Then you might be on the right tracks. David Tombe (talk) 09:42, 27 November 2008 (UTC)

I simply restricted this section to an example where J_M =0. Brews ohare (talk) 16:55, 27 November 2008 (UTC)

I see the relation of the "displacement current" issue to the "free charge vs total charge" as follows. What they have in common is that they are confusing (in a kind of similar way!), but actually the two issues are quite orthogonal. The issue of "displacement current" arises equally in both forms of Maxwell equation. In one, it is ε₀ ∂E/∂t, in the other one, it is ∂D/∂t (=ε₀ ∂E/∂t+∂P/∂t). One might even call the latter "free displacement current" (equalling "displacement current" minus "bound displacement current"). So in the most complicated case, you have free current, bound current (=magnetization current), free displacement current, and bound displacement current -- and it makes logical sense to sum all four of them, because they are nonoverlapping, with the caveat that the latter two are not charge movements.

Of course, the free space Maxwell equations are simpler to understand, so it's easier to understand "displacement current" by restricting one's attention to this case, as you did.

I know that you understand all this but I wanted to record it here to deepen my own understanding.

In any case I don't really like the attempt to interpret ε₀ ∂E/∂t or ∂D/∂t as a current. Whereas magnetization current is okay with me. 84.227.244.143 (talk) 17:38, 9 April 2014 (UTC)

Good idea. from what I can see, magnetization current is an effect. It is not the causative agent in Ampere's circuital law. I'd tend to forget about it. David Tombe (talk) 03:28, 28 November 2008 (UTC)

Definition of displacement current is ambiguous

Oh no! Not this again. There are two common usages for "displacement current".

According to Jackson, page 238, the displacement current is

${\boldsymbol {J_{D}}}={\frac {\partial {\boldsymbol {D}}}{\partial t}}\ .$

Sounds sensible because D=displacement field.

Jackson's definition is used by Slater & Frank (p. 84) and by Owen (p.286) Bonnet and Cloude (p. 17) use

${\boldsymbol {J_{D}}}=\varepsilon {\frac {\partial {\boldsymbol {E}}}{\partial t}}\ .$

which I'd say was a version of Jackson's definition. Looking at Maxwell's paper, I'd say this was his usage inasmuch as he spent pages describing polarization contributions to the displacement current.

However, according to Griffiths, page 323, the displacement current is

${\boldsymbol {J_{D}}}=\varepsilon _{0}{\frac {\partial {\boldsymbol {E}}}{\partial t}}\ .$

Feynman (vol II, p. 18-2) uses Griffith's math, but does not use the term "displacement current". Griffiths definition is also that of TL Chow, and of Billingham (p. 180). Brews ohare (talk) 15:46, 27 November 2008 (UTC)

Presently the articles appear to agree with the Jackson-Maxwell definition. It is the definition closest to historical development. Brews ohare (talk) 16:08, 27 November 2008 (UTC)

Brews, see my comments on this in the section below. David Tombe (talk) 02:53, 28 November 2008 (UTC)

Did Maxwell use ε₀ ∂E / ∂t ?

D Tombe suggests that Maxwell focused entirely upon ∂P / ∂t, and there is no doubt he did spend a lot of time on this. However, I find Maxwell's theory of vortices sufficiently obscure that I cannot say definitely that he did not consider ε₀ ∂E / ∂t. One of the problems I have is that Maxwell develops a mechanical model for the aether which seems to make it look like he assumes a medium is present, but he disclaims all this by saying the model is just a way to set up the math, and it is the math that is fundamental, not the mechanical model leading to it. The model is just to aid visualization.

I wish merely to direct the mind of the reader to mechanical phenomena which will assist him in understanding the electrical ones. All such phrases in the present paper are to be considered as illustrative, not as explanatory.

For example, the discussion in Whittaker (1910) suggests that Maxwell did consider "propagation in free aether" which is an "elastic solid" and seems to suggest the modern form of the equations is due to Maxwell. On page 179 he says:

"The motion of these charges is equivalent to an electric current; and it was from this precedent that Maxwell derived the principle, that variations of displacement are to be counted as currents. But in adopting the idea, he altogether transformed it; for Faraday's conception of displacement was applicable only to ponderable dielectrics, and was in fact introduced solely to explain why the specific inductive capacity of such dielectrics is different from that of free aether; whereas according to Maxwell there is displacement wherever there is electric force, whether material bodies are present or not.

Berkson says "The formula v = c/√μ holds not only in the vacuum but also in material dielectrics where c and μ can be determined relative to the vacuum." "Maxwell had shown before that k in vacuum is 4πc², where c is the ratio between es and em units. Thus in a vacuum, where μ is one, the velocity of the waves is c."

I tend to the opinion that in fact Maxwell did introduce the idea now denoted by ε₀ ∂E / ∂t. Brews ohare (talk) 17:58, 27 November 2008 (UTC)

Brews, Maxwell introduced displacement current in relation to tangential stress in his sea of vortices. His views are written in the preamble to part III of his 1861 paper. At first he toys with the idea that the tangential action transmits rotations. This in my view would have been the correct interpretation for EM radiation purposes. But then Maxwell seems to get sidetracked more and more towards linear polarization of a dielectric. In other words, he seems to stray from the 'far field' effect to the 'near field' effect. The near field effect is only good for transmission lines and cable telegraphy. It is not good for wireless telegraphy.

Maxwell produces the mathematical terms ε₀ ∂E / ∂t and ∂D / ∂t. It would appear that he is using them both for the 'near field' situation, even though the former could also apply to the 'far field' if E = -(partial)dA/dt.

In other words, Maxwell is somewhat ambiguous. When he derives the EM wave equation in 1864, he eliminates the E term and he derives the equation only for H. We all know that the divergence of H is zero. But he got off the hook as regards having to declare his hand on the issue of the divergence of E in relation to the EM wave equation. It seems that he had already committed himself to a linear polarization interpretation of displacement current which would have a non-zero divergence and which wouldn't therefore fit into the EM wave equation.

I believe that Maxwell was in error in this respect. We need a 'magnetization friendly' displacement current in which E = -(partial)dA/dt and in which div E = 0. I don't think that Maxwell had thought this through fully. With Maxwell's concept of 'density of free electricity' instead of charge, he was never going to get a div E = 0 with his linear polarization explanation for displacement current.

It is only the modern textbooks, post aether, that have explained displacement current in terms of conservation of charge. They use the exact same mathematical expressions that Maxwell used but the physical meaning is quite different. Maxwell's explanation however still applies for dielectric polarization. But no explanation exists for EM radiation. Maxwell was unto it but he got sidetracked. Tesla may well have followed up on the vortex transmission idea but I haven't got the details. David Tombe (talk) 03:11, 28 November 2008 (UTC)

The Recent Edits

Brews, the recent changes were simply made to make the point more clearly. It was a start to tidying up that whole section. It could be drastically simplified.

You have put alot of stuff in from Maxwell's 1861 paper which is not directly relevant to the displacement current issue. The relevant part in the 1861 paper is the preamble to part III. That explains Maxwell's views on displacement current.

So all I said was that there has been alot of confusion over displacement current and that this is partly due to the fact that Maxwell's derivation was completely different from the modern textbook derivation. The modern textbooks use a conservation of charge approach, whereas Maxwell used tangential displacement in a sea of molecular vortices which is no longer recognized to exist in modern physics.

That is all that needs to be said on the issue. There is no need for references to Larmor and the aether. Maxwell hardly mentions the aether in his paper, and certainly not in relation to displacement current.

All that other stuff that you have written about concerns Maxwell's views on electric current and more general aspects about electromagnetism, and it contains alot of your own opinions too.

I was planning on starting at the top, simplifying it to key points, and when enough had been said, I was going to wipe the rest out. David Tombe (talk) 06:54, 18 January 2009 (UTC)

In relation to another recent edit by an anonymous, I believe that it was correctly reverted. Any analogy between displacement current in a capacitor and induced current in an inductor is only partial, and needs to be explained clearly.

A changing magnetic field induces an electric field which induces an electric current. That is EM induction. An electric field causes an electric current. It doesn't have to be a changing electric field. An electric current causes a magnetic field.

I can't see the analogy that the anonymous was driving at, other than that he saw a changing electric field as causing an electric current. But it wasn't the changing aspect of the electric field that was causing the current. Displacement current between the plates of a capacitor is caused by an applied electric field and it is continually reduced by an opposing electric field that is on the rise.

That opposing electric field does however have a certain degree of analogy to the electromagnetically induced back EMF.

It was better to have removed that edit, because the point quite simply wasn't being made clearly enough. Perhaps he was driving at the capacitative equivalent of Lenz's law. David Tombe (talk) 07:21, 18 January 2009 (UTC)

David: I don't agree with your remarks about Maxwell's presentation, which to me seems clearly to discuss the aether, and moreover to discuss it as if it were a material medium, and therefore requiring a treatment no different from other media (apart from its particular material properties). That being so, there is no need to add any extra term in the displacement for the vacuum, nor to treat the vacuum as a different case. Everything gets swept into the dielectric permittivity. Brews ohare (talk) 10:17, 18 January 2009 (UTC)

Brews, if you go to page 345 in the 1861 paper (page 34 of the pdf file), you will be at the tail end of part II, in which he deals with the link between electric current and magnetic field. Go down to line 6. Many people are not aware of this, but Maxwell's sea of molecular vortices was not "the aether" as such. However, as you can see from that sentence, he speculated that it may be partly composed of ordinary matter and partly composed of an aether associated with ordinary matter.

Anyway, that is just a point which you ought to bear in mind when using the term "aether" in relation to displacement current, because displacement current was conceived in relation to the electric particles and not the aether itself. I always try to avoid the term aether in relation to this issue, and specifically refer to the 'sea of molecular vortices'.

Maxwell conceived of displacement current in relation to a tangential stress in this sea of molecular vortices, and the relevant text in the 1861 paper is at the beginning of part III. In my view, that is the only part of the paper from which quotes would be relevant for the purposes of this article.

You are partly right when you say that he was treating it just like any other elastic medium. But you are also partly wrong, because it is clear from reading the preamble to part III, that Maxwell was wavering between linear displacement and rotational displacement. He is clearly not quite sure.

Therefore, it is better not to make statements to the extent that Maxwell was treating his sea of molecular vortices just like any other elastic medium. It is better just to stick to the facts and the exact terminologies.

The next stage of the problem is that by 1864, Maxwell seemed to have eventually settled on a linear polarization vision within a dielectric medium. I personally think that he should have stuck with the rotational displacement vision. But nevertheless, that is how it went.

And in that respect, Maxwell's explanation for displacement current ties in more or less exactly with the explanation that is used today for dielectric media.

But when it comes to the vacuum, the situation is quite different. The vacuum removes the entire basis of Maxwell's displacement current. So the modern textbooks use a completely different derivation based on conservation of charge. Maxwell never used conservation of charge in relation to justifying displacement current. It didn't remotely enter into the analysis.

So there are two distinct ways of justifying displacement current according to whether we are dealing with a dielectric or a vacuum.

But in my opinion, neither of those ways produce the displacement current of EM radiation. Maxwell's initial hunches about rotational displacement in the preamble of part III would have been the hunches to follow up for the purposes of EM radiation.

But you will see that when he derived the EM wave equation in his 1865 paper, he carefully eliminated the Gauss term, and produced an EM wave equation in H only, hence avoiding the controversy. David Tombe (talk) 05:23, 19 January 2009 (UTC)

David Tombe, you say "The vacuum removes the entire basis of Maxwell's displacement current". If this were true it would mean that you would not be able to detect the field from electric charge in a vacuum, and the whole of the vacuum tube industry that has be working quite successfully the last hundred years would be a figment of the imagination. The current flowing in the electrodes that arises from the displacement of charge in a vacuum tube is an important part of its functioning. In the case of the klystron, to mention one of many, it is the fundamental principle of its working. --Damorbel (talk) 10:49, 19 January 2009 (UTC)

Damorbel, perhaps I ought to have said that the vacuum removes the entire basis for Maxwell's explanation for displacement current. I did not say that displacement current does not exist.

But having said that, I can see nothing from what you have said above that would suggest that displacement current has to exist. Why would we need to have displacement current in order to be able to detect the field from electric charge in a vacuum?

I believe that two kinds of displacement current exist. Linear polarization in a dielectric, as a reaction to electric field is one kind. There is also the kind that exists in EM radiation. But nothing that you have said above proves the existence of either of these two kinds of displacement current. And what you say doesn't even prove the existence of the kind of displacement current in the vacuum that is postulated from conservation of charge.

You would need to explain in more detail why you think that the vacuum tube industry is dependent on the existence of displacement current. David Tombe (talk) 12:15, 19 January 2009 (UTC)

Maxwell noted that the change in an electric field with time was not different from the passage of charge carriers, thus if the electric field between two accumulation of charge is changed, for example by physically moving the charge items relative to each other then a current flows eqal to the rate of diplacement (the movement i.e. velocity) of the charged bodies times the charge. This effect is put to good use in Vibrating reed electrometers Such a device generates an alternating electric current proportional to the voltage accross its (varying) capacitance without any charge carriers passing through it.

You seem to have some difficulty with the concept of charge. Is charge not detected by observing that charged bodies exert a force on other charged bodies? Electrons for example repel each other? That two sheets of gold leaf when charged, repel each other? I refer you to the main electrometer article.

Displacement current exists because change of distance between observer and a charged body, let us say electron, causes the observer to detect a change in the electric field due to the electron. You know this happens because the field due to the electronic charge declines according to the inverse square law of the distance. It is this change in the electric field that the observer sees as a current.

Not all electronic devices use displacement current so obviously as the klystron, but almost all microwave tubes do so. In the klystron the signal modulates the velocity of electrons in a beam. Differing from a low frequency valve the output signal is not collected by gathering electrons at an anode but by capacitively coupling the power into a resonator, the output being the displacement current flowing in the output resonator (circuit).--Damorbel (talk) 23:00, 19 January 2009 (UTC)

Damorbel, It would strike me from what you have said above, that you have absolutely no knowledge about what Maxwell said regarding displacement current, despite the fact that the link to his paper is available here. I suggest that you read the first few pages of part III of that paper.

And I don't know what I said that gave you the impression that I have problems with the concept of charge, such that you felt the need to lecture me on basic aspects of Coulomb's law.

What exactly is your point? We all know that displacement current exists in non-conducting media when an electric field is varying.

All that was being said here was that the textbook explanation for displacement current in a vacuum is quite different from Maxwell's explanation for displacement current. David Tombe (talk) 05:18, 20 January 2009 (UTC)

David Tombe, the precise words Maxwell used are of no relevance. If you have made a new discovery that modern physics is based on a fortuitously incorrect interpretation of Maxwell's work by, among others Oliver Heaviside who derived the vector notation, well and good. But your (unique) discovery scarcely eliminates displacement current from the corpus of established phenomena.

By introducing the red herring of Maxwell's precise wording you are escaping from explaining the examples I gave of the effects of moving charge (without net charge transfer) being seen as a current. It astonishes me that you do not understand that all instances of alternating current (with no DC component) take place without a net transfer of charge, as in a capacitor with or without dielectric material between the plates (you may not be familiar with vacuum capacitors used in high power applications). Transformers also transfer current without charge transfer. Just as inserting a dielectric between the plates of a capacitor changes the performance of a device, putting a magnetic core in an inductor or a transformer has a similar effect. Devices for transferring alternating current, with or without these additions, have their advantages in appropriate circumstances.--Damorbel (talk) 09:47, 21 January 2009 (UTC)

Sorry Damorbel, this is a bit of a waste of time. I have never said at any time that I am opposed to displacement current. Displacement current is an essential aspect of electromagnetic radiation. So the whole argument seems rather pointless to me if it is based on your belief that I intend to eliminate displacement current from the corpus of established phenomena. David Tombe (talk) 15:00, 21 January 2009 (UTC)

What??

Article says:However it is not an electric current of moving charges, but a time-varying electric field. How can an electric field equate to a current?--2.98.149.24 (talk) 21:43, 20 April 2011 (UTC)

Such nonsense

Much of the article is devoted to explaining how the quantity ∂D/∂t (or ε₀∂E/∂t) can be viewed as sort of a charge movement, though not really, but still, kind of, in a misty kind of way.

Why bother? Just to give some kind of folk etymology to the "current" in the locution "displacement current"?

Observe the equation that motivates the term "displacement current":

$\nabla \times \mathbf {B} =\mu _{0}\left(\mathbf {J} +\varepsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\right)$

The equation was first discovered without the third term. So at that time, current had two roles (like morning star and evening star), namely charge movement and causer-of-magnetic-field, but the equation asserted that these were the same (in whatever setting).

But as soon as the third term was introduced, these roles separated. Magnetic fields are "caused" by the sum of two things, charge movement and changing electric field (times ε₀). These have the same units. So they both have the units of charge movement. So far, so good; lots of things have the same units.

But why this constant effort to view the changing electric field as a kind of virtual charge movement?

Even with half-hearted "joke" signs and crossed fingers, this leads to constant confusion.

It seems to be a perfect example of the dictum that with correct use of language, all philosophical problems disappear. 84.227.244.143 (talk) 16:59, 9 April 2014 (UTC)

The electric field of a charge is due (in part) to the gradient of the scalar potential of that charge. The change of the gradient's direction and magnitude is what generates curl of the magnetic field outside the current itself. If the curl of the magnetic field were limited to the presence of current density, then a curl of magnetic field should not be observed near a capacitor plate, and yet it does. So something must contribute to this.

However, one mistake is to assume that the electric field is uniform in the capacitor. That assumption leads to the conclusion that a "virtual electric charge" flows from one end to the other, generating the magnetic field from an unbroken "current" that somehow travels across the capacitor. That is false. As soon as you note the lack of uniformity in the electric field, one should realize real quick that the current is not continuous, even if one takes the conservation of charge into account. The only way that the "continuity equation" would imply an unbroken current is if one insisted that current flow continuously in the same direction, yet that is not a real requirement, and the "continuity equation" for charge conservation does not imply a continuity of current.

There is also a contribution to the electric field of a charge from the spatially varying vector potential of the charge at some velocity. For a constant velocity of charge, both of these time variations of the electric field (due to the scalar electric potential gradient and the magnetic vector potential time derivative) of each charge vary inversely with the cube of the distance from each charge, and therefore these are both near field phenomena. Also, at high frequency, the term based on the vector potential will dominate, as the vector potential of a charge (location being equal) depends in proportion to the velocity of charge, which means that the second time derivative (and therefore its contribution to the curl of the magnetic field) depends on the jerk of the charge. In either case the "continuity equation" implies continuity of charge, not current.

In the article on Ampere's force law, it is stated that, "Integrating around s' eliminates k and the original expression given by Ampere and Gauss is obtained." But as we now know, the integral comprises of a broken current in many circuits, notably in those with large capacitor gaps, or even in those where uneven charge distribution is produced by electrical standing waves inside the conductors, and thus k is not eliminated in general. ^talk2siNkarma86—Expert Sectioneer of Wikipedia 16:28, 23 February 2015 (UTC)

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Notes on "Current in capacitors"

Hallo everyone!

I would like to point out that for all the efforts done by all the people contributing to this article, its still pretty hard to understand for someone with only high-school level knowledge of physics, but by now I am used to feel clueless trying to understand a great many number of articles in Wikipedia, so I won't complain.

However, although I am really new in these concepts I would like to make some notes on the subchapter about "Current in capacitors". Please excuse me if my comments seem naive- its the best I could do:

1)There is a phrase saying "The electric field at face L is zero because the field due to charge on the right-hand plate is terminated by the equal but opposite charge on the left-hand plate.". I think that part is true only when the entire circuit which includes the capacitor is in equilibrium, meaning the EMF that produces the current is exactly counterbalanced by the voltage across the capacitor due to charge concentration. Outside that condition, there is always a net electric field (corresponding to the difference between the EMF who acts as energy source and the capacitor's voltage), because without it, meaning without voltage driving the current, no current could exist (actual voltage is "${\begin{aligned}V(t)&=V_{0}\left(1-e^{\frac {-t}{RC}}\right)\\\end{aligned}}$" in DC, with R = Resistance, C = Capacitance). I think this is implied but should be clearly expressed with proper wording to avoid confusion.

2)In the equation:

$\oint _{\partial S}{\boldsymbol {B}}\cdot d{\boldsymbol {\ell }}=\mu _{0}\int _{S}\left({\boldsymbol {J}}+\epsilon _{0}{\frac {\partial {\boldsymbol {E}}}{\partial t}}\right)\cdot d{\boldsymbol {S}}\,$,

it should be clearly noted that the quantities "J" and "$\epsilon _{0}{\frac {\partial {\boldsymbol {E}}}{\partial t}}$" are essentially equal and not additive: The first concerns the current outside the capacitor and the second the (imaginary) current between its plates. The above do stem from the text but because the phrasing is a little difficult, they may go unnoticed to beginners and thus they should probably be clearly denoted.

I hope that someone more expert than me may read these comments and may make some edits that would facilitate the understanding of this tricky passage. I would be grateful for any answer. Thanks! 2A02:587:450A:5D00:82F:D0F2:A9A1:F529 (talk) 15:33, 9 July 2017 (UTC)

That part of the article could definitely be improved. Responding to your points in order:

• 1) That part is incorrect. The E field at surface L is not zero, it is just so much smaller than the E field between the plates of the capacitor that it is taken to be zero. Also surface L and surface R are not plates in that they are intentionally depicted to not coincide with either face of either plate of the capacitor.
• 2) The two terms are additive, it is just that one or the other is nearly zero depending on the surface of integration. We can consider two cases. Case A, the surface goes between the plates of the capacitor then the conduction current is zero and the displacement current is strong. Case B, the surface goes through the wire in this case the conduction current is large and the displacement current is small enough to be taken in zero, So, the displacement current in case A is about equal to the conduction current in case B. We can also imaging a wacky case C, where the surface of integration passes through the plate so that parts of the surface have conduction current and parts have displacement current. So, it is not necessary that either the conduction current or displacement current must be zero, although we tend to choose the surface of integration so that is true. Constant314 (talk) 16:54, 9 July 2017 (UTC)

There is also something not right with the minus signs scattered around the text. Given the reference directions defined in the figure, I = I_D rather than I = -I_D. Constant314 (talk) 19:09, 9 July 2017 (UTC)

I have that straightened out. When we apply Kirchhoff's current law, we say that the sum of current entering a node (the capacitor plate in this case) is zero. But the diagram defined the reference directions such that the conduction current is leaving the node and the displacement current is entering the node. In this case the difference between the current entering the node and the current leaving the node must be zero, or I – I_D = 0 and consequently I = I_D. The text was correct that the charge on the left-hand plate is decreasing. Constant314 (talk) 19:37, 9 July 2017 (UTC)

Constant, thanks for taking the time to answer. I really had not hoped for such a fast response!

1)The E field at surface L should be V/L, where V= the voltage drop across the plate L if I understood it correctly. So, yes it would be tiny compared to the field of the capacitor but not zero, otherwise there would be no current. But i get your point.

2)Thanks for clarifying that. I am sure you can agree however that that point would probably deserve some clarification in the text as its rather complicated to grasp without prior knowledge. Or at least a comment.

3)I couldn't agree more about the minus signs, but I didn't mention it in order not to become tiresome, but thanks for pointing that out. Maybe someone at some point makes a serious effort to improve these points or explain them clearer in the text. Anyway, thanks for answering.2A02:587:450A:5D00:82F:D0F2:A9A1:F529 (talk) 21:21, 9 July 2017 (UTC)

If you look carefully you will see that surface L is depicted well outside the capacitor. At that point, the E field is caused by the voltage drop in the wire. At the wire, the E field would be IR where R is the resistance of the wire in ohms per meter; it is on the order of millivolts/meter. Right at the left-hand face of the left-hand plate, you would be looking at a surface of nearly constant potential; the gradient of the voltage there is nearly zero, except at the edge of the plate, so the E-field normal to the face there would be very close to zero. There might be some radial field due to voltage drop as the conduction current spreads out into the plate. The field between the plates could easily exceed 10⁶ V/m.

As for your point number two, I'm thinking about it. I did slightly rearrange the text and figure to try to lead the reader's eyes to the second figure with its obvious two surfaces and then the equations below showing no displacement current in one case and no conduction current in the other case. Constant314 (talk) 22:31, 9 July 2017 (UTC)

OK! And again, thanks for the answer! 2A02:587:450A:5D00:82F:D0F2:A9A1:F529 (talk) 03:22, 10 July 2017 (UTC)

I have been looking carefully at the section and I find that it uses untrue assertions to derive correct results, so if you think you don't understand it, you have good reasons. I am looking to fix it, but I have to choose between an awkward explanation using the existing figures or create new figures. Either way it takes time and effort. I'll start a new talk topic about incorrect assertions in the section when I'm ready to address them. Constant314 (talk) 15:10, 10 July 2017 (UTC)

Untrue assumptions in the “Current in capacitors” sub section

The "Current in capacitors" subsection seems to have two parts which are mostly redundant. The second half starts at the sentence right before the equation

$\oint _{\partial S}{\boldsymbol {B}}\cdot d{\boldsymbol {\ell }}=\mu _{0}\int _{S}\left({\boldsymbol {J}}+\epsilon _{0}{\frac {\partial {\boldsymbol {E}}}{\partial t}}\right)\cdot d{\boldsymbol {S}}\,$.

The first half assumes the existence of displacement current between the plates of a capacitor, assumes that it works just like current and proceeds to derive the fact that the displacement current density is dD/dt. This doesn’t seem important, since it is derived rather directly in the “Explanation” sub-section and again in the second half of this section and the following section “Mathematical formulation” also provides a justification. It is redundant, but tells the story in a different way. The redundancy is not the issue. The issue is that two false assertions are used in the derivation. The false assertions are:

• 1) “a displacement current ID flows in the vacuum, and this current produces the magnetic field in the region between the plates according to Ampère's law”. It is true that the magnetic field within the plates obeys Ampère's law, but it is untrue that the displacement current between the plates produces the magnetic field. The magnetic field everywhere is produced by the currents everywhere. So the magnetic field between the plates is a result of all the conduction currents and displacement currents. The contribution that a current makes to the magnetic field is proportional to the strength of the current and its path length. The path of the displacement current in an ordinary capacitor is very short. It is so short that if you computed the magnetic field due to all the currents with the displacement current and without the displacement current, you would get almost exactly the same value, even between the plates. So, we don’t have to have a displacement current between the plates to account for the magnetic field there.
• 2) “The magnetic field between the plates is the same as that outside the plates.” This is nonsense since the magnetic field does not have a single value outside or between the plates. Instead, the value varies with radius from the axis. But consider the magnetic field outside the capacitor and tangent to the wire. It has a value proportional to I/r_wire where r_wire is the radius is the wire. The magnetic field inside the capacitor at the same radius is less, because a circle there with radius r_wire encircles only a fraction of the total displacement current. What is true is that the line integral of the magnetic field over a closed curve is the same whether the surface bounded by the curve goes between the plates or through the wire. This is the statement that starts off the second section.

So, the first half of the “Current in capacitors” section is triply redundant and includes false assertions. I propose to take it out, retaining only the symbol definitions as needed. The only problem with dropping the first section is that the figure discussed in the second section does not explicitly show I_D, the displacement current. It may be sufficient to simple define it as the surface integral of dD/dt. I’ll wait a couple of days for comments. Constant314 (talk) 17:04, 11 July 2017 (UTC)

Agree with both the above points. --Chetvorno^TALK 03:43, 22 January 2018 (UTC)

Expert Attention Necessary

I just added the flag:

to the top of the article. This is a really, really bad article in its current state. A brief skim of the commentary below tells me it has largely been authored by individuals who know little or nothing about the topic - a typical cut and paste from elsewhere wikipedia approach.

The phrase 'Displacement Current' is an unfortunate historical legacy. It really has nothing to do with capacitance - the displacement current is the only cross coupling mechanism in the homogeneous Maxwell equations, where there simply is no charge of any kind. Those are the equations governing radiation, which unequivocally empirically exists, and is now a foundational component of our technological infrastructure.

A good beginning would be to address units in the introduction or a first section. Currently, units are not addressed at all. Regarding units, the electric field E is related to the magnetic coercive force H just as the displacement current D is to the magnetic flux density B. When you get that clearly expressed, the rest of the garbage in the article will rapidly disappear. There is no magnetic charge whose SI unit is the Weber. There is electric charge, whose SI unit is the Coulomb. Just as the fact that the Weber appears as a unit in magnetic descriptions does not imply the existence of the charge, the appearance of the Coulomb in electric descriptions does not imply the necessity of electric charges. If anything, the presence of actual electric charges in some situations is the anomoly, not the displacement current.206.116.24.195

The article can certainly use some improvement, but on the issue of units, it is clear: displacement current has the same units as conduction current. In fact, that the reason displacement is called a current is because it has the same dimensions as current and simply adds its effects to the effects of conduction current.

Some things that I would like to see in the intro include the fact that the differential terms in Maxwell’s equation’s are displacement current densities (which have the same units as current densities). I would also like for it to be pointed out that there are two displacement current densities in Maxwell’s equations: the electric displacement current (dD/dt) and the magnetic displacement current (dB/dt). It is interesting that the electric displacement current is seen as something mysterious that requires a lot of explanation and analogies whereas the magnetic displacement current is simply accepted has a fact. Constant314 (talk) 00:42, 22 January 2018 (UTC)

@Constant314: I agree that it should be described as displacement current "density". On your other point, I feel that calling the analogous term ($d\mathbf {B} /dt$) in Faraday's equation "magnetic displacement current" (if that's what you were suggesting) would be very confusing for readers. This already has a name, electromagnetic induction. I wouldn't mind adding mention in the article that electromagnetic induction is the magnetic analogue (dual) of displacement current. BTW, I think the reason displacement current is seen as "mysterious" is due to the asymmetry of sources. The main source of $\mathbf {curl\,B}$ is the current density $\mathbf {J}$, and this overshadowed displacement current for a long time. In contrast, rate of change of flux $d\mathbf {B} /dt$ (electromagnetic induction) is the only source of $\mathbf {curl\,E}$, so it was discovered earlier, in 1831. If magnetic monopoles existed, a current of monopoles would create a solenoidal (circular) electric field around it, there would be a source term $\mathbf {J_{M}}$ on the righthand side of Ampere's equation, and electromagnetic induction would also be a minor effect; "something mysterious that requires a lot of explanation".

@206.116.24.195: I am not clear on what "garbage" you would like to remove from the article. I would like to see a little less description of displacement current as a "current", since it is not one, but Constant314 has already removed most of that amateur stuff from the article. --Chetvorno^TALK 02:53, 22 January 2018 (UTC)

@Chetvorno: Thanks for the kind words. There are good references referring to dB/dt as magnetic displacement current (Balanis, Harrington, Jordan & Balmain). In the interest of accuray, there are two terms called displacement current. It would be sufficient to note that this article is about the electric displacement current without dwelling on the other.Constant314 (talk) 03:20, 22 January 2018 (UTC)

On second thought, an about box would take care of it.Constant314 (talk) 03:58, 22 January 2018 (UTC)

I have addressed some of the issues and there have been no further comments for about 14 months, so I am going to remove the expert needed box. If anyone wants to restore the box, please add a new reason or start a new talk topic. Constant314 (talk) 23:30, 9 March 2019 (UTC)

One thing that is seriously wrong is the diagram with the text 'Example showing two surfaces S1 and S2 that share the same bounding contour ∂S.' In that diagram, S1 and S2 do not share the same bounding contour (thanks to Ivor Catt for pointing this out)! --Brian Josephson (talk) 20:59, 27 July 2020 (UTC)

What I pointed out was different; http://www.ivorcatt.org/icrwiworld78dec1.htm . The current entering the capacitor flows sideways along the capacitor plate. Maxwell and Heaviside failed to notice this. Ivor Catt. 30 July 2020 — Preceding unsigned comment added by 2.24.141.99 (talk) 20:24, 30 July 2020 (UTC)

I'm very aware that you think that, but I very much doubt if that is the case.--Brian Josephson (talk) 20:30, 30 July 2020 (UTC)

It looks to me like they do share the same bounding contour. Maybe I am missing something. Perhaps it is not obvious that S2 is closed underneath the capacitor plate. Constant314 (talk) 21:02, 27 July 2020 (UTC)

I see what you mean, it is more that it is unclear what S2 is. If the label S2 were put to the right of the picture (and then perhaps partial-S moved to the left for clarity) then that would improve things. I see that the person who drew the diagram (Chetvorno) is taking part in this discussion so perhaps he can adjust the diagram for us? --Brian Josephson (talk) 21:11, 27 July 2020 (UTC)

And maybe a closed ellipse for the base would help a bit also — I don't know. --Brian Josephson (talk) 21:16, 27 July 2020 (UTC)

I tweaked the caption. Constant314 (talk) 21:18, 27 July 2020 (UTC)

Good, I guess that helps. Though it might be argued that the whole explanation is far too lengthy!--Brian Josephson (talk) 10:46, 28 July 2020 (UTC)

Electric displacement field

Please see Talk:Electric_displacement_field#Delete,_and_change_to_a_redirect. fgnievinski (talk) 02:50, 27 August 2023 (UTC)