AC flowing through a cap. What actually happens?

[Mr RB]

I do believe the premise was to capture what was happening inside the capacitor. which is not going to be specific to measurable relied upon specificity of currently known standards of electronic terms.
...

Killivolt, my argument is not about the specifics of what happens inside the capacitor. I have been quite clear about that. My argument has been with Ratchit's sloppy misuse of the global terms CURRENT and THROUGH, given that this is an electronics forum.

Current as a global term is a greater concept than what might be happening to one electron. "Current" must also be given a high importance as a concept and as a flow in a series circuit. Something that can easily be measured, calculated, simulated.

"Through" as a global concept is greater than what may be happening INSIDE a component to a single electron. If a mystery component in a series circuit has 1 amp in and 1 amp out, it satisfies "current through" in enough ways to be respected as true. If it later is discovered that that mystery component was a capacitor it is foolish to then say "oh well, that current we just measured going through the component wasn't going "through" after all".

If you want to know if CURRENT is going THROUGH something, use an ammeter.

Now if Ratchit had used the term "current INSIDE the capacitor" or "electron behaviour inside the capacitor" then I may have let it drop. But to state "There is no current through a X" on an electronics forum, for any type of X, needed to be called out.

Mr Al-

But anyway, let me ask you a question now. What if someone asks you this:
"Mr RB, does current flow through a capacitor?", and you reply, "Yes",
and then they ask you this:
"Mr RB, what is displacement current?".
Are you going to tell them that displacement current is the same thing as conduction current?
They then ask:
"Mr RB, then why do they call it displacement current?".
What do you tell them?

'Does CURRENT flow THROUGH a capacitor?' Yes. 'What is displacement current?' It is a term used for current by people who are overly concerned with what is happening inside a capacitor. 'Are you going to tell them that displacement current is the same thing as conduction current?' No, I'm going to tell them that current THROUGH anything can be measured with an ammeter. Whether it is displaced or conducted is only of relevance in the rare case you might care what is happening to an electron inside a component and might be of interest in physics but has practically zero place in electronics.

I'll take you back to your quote of Prof Viken, here is a man that is intelligent, highly educated and an expert in this field. Note how his reluctance to use the terms CURRENT and THROUGH left him incapacitated, struggling deperately to grasp a word, or words, any words, to describe CURRENT THROUGH. A fundamental concept.

Current through a cap is true. Now current inside a cap? Electron behaviour inside a cap? Well they can be argued over by pedantic people and physicists.

 

[ericgibbs]

hi Roman,
You are echoing my feelings from an earlier post, I feel the same way as you regarding the well proven conventions for current flow.

The more I read Ratchit's pseudo techno babble, the more I become concerned that the newbies readings his comments may take what he his saying as a fact, so I feel I must speak out against what he his posting.

I would suggest that his posts should carry a warning to newbies/wannabes 'using this terminology will seriously damage your career prospects'.

I suspect he is being controversial just as an attention seeking ploy, look at some of the other threads he has turned into unresolved saga's.

 

[killivolt]

hi Roman,
You are echoing my feelings from an earlier post, I feel the same way as you regarding the well proven conventions for current flow.

The more I read Ratchit's pseudo techno babble, the more I become concerned that the newbies readings his comments may take what he his saying as a fact, so I feel I must speak out against what he his posting.

I would suggest that his posts should carry a warning to newbies/wannabes 'using this terminology will seriously damage your career prospects'.

I suspect he is being controversial just as an attention seeking ploy, look at some of the other threads he has turned into unresolved saga's.

Top of the afternoon eric, I could see how it might affect someone's thinking. Maybe it should carry a warning have your "warning" possibly. It just seems it goes more into theory or theory's.

I think I'm responsible for pushing this as far as it could go; with different intentions. This thread reminds my of the "Wave Propagation" crashsite started a while back. It was really cool though, 3v0 got involved as well as a bunch of other smart "people" on the site. I have really enjoyed MR,RB, Mr,Al, The Electrician, as well as others who put in contributions to the thread. Reloadron's simple "picture" was great. I'll never forget it. If you ever want to know about capacitors this thread will say it all........and more.

Really neat when people start hurling Math around like giant stones. I wonder where Papabravo is, he was pretty good with it too!

 

[Ratchit]

The Electrician,

Notice that the common D'Arsonval ammeter relies on the magnetic field to measure a current as does the clamp-on ammeter.

Yes, there is certainly energy in electromagnetic fields. Inductors and capacitors exploit that fact. And there are also fields involved with conduction carriers when they move and when they congregate. But don't you think there is some kinetic energy involved with the moving mass of the charge carriers that does not involve fields? For instance, a stream of neutrons will have some kinetic energy associated with it, but no field will be present.

The D'Arsonval meter first requires a current to generate the magnetic field it requires.

ljcox,

I don't find it a paradox.

As I said, I don't have a problem with conduction/displacement current, but some of the commenters do.

Most of the participants here don't have a problem with it either. They have a problem with other people's explanation of it.

Mr RB,

Killivolt, my argument is not about the specifics of what happens inside the capacitor. I have been quite clear about that. My argument has been with Ratchit's sloppy misuse of the global terms CURRENT and THROUGH, given that this is an electronics forum.

Sloppy? And here I thought of was being overly precise. Pedantic even.

Current as a global term is a greater concept than what might be happening to one electron. "Current" must also be given a high importance as a concept and as a flow in a series circuit. Something that can easily be measured, calculated, simulated.

Global or local, current is the movement of a particle/s, whether one or many. Current is a definition more than a concept.

If you want to know if CURRENT is going THROUGH something, use an ammeter.

Doesn't work. Charged particles don't go through the dielectric of a capacitor. Electromagnetic fields do. Measuring the current going into or out of the capacitor only gives the appearance of current passage through the capacitor.

Now if Ratchit had used the term "current INSIDE the capacitor" or "electron behaviour inside the capacitor" then I may have let it drop. But to state "There is no current through a X" on an electronics forum, for any type of X, needed to be called out.

I never said that there was no current inside "any type of X". In fact, I said specifically that there was current through resistors and inductors, but no charge flow through capacitors. I challenge you to find where I said what you aver.

'Does CURRENT flow THROUGH a capacitor?' Yes.

Again no. Only electromagnetic fields pass through. These fields can be calculated and interpreted mathematically as a virtual current, but they don't have a physical manifestation as a conduction current.

'What is displacement current?' It is a term used for current by people who are overly concerned with what is happening inside a capacitor.

People like Maxwell? Didn't he and others of his time use that term, too?

No, I'm going to tell them that current THROUGH anything can be measured with an ammeter. Whether it is displaced or conducted is only of relevance in the rare case you might care what is happening to an electron inside a component and might be of interest in physics but has practically zero place in electronics.

If I were a nubie, the first thing I would ask you is how charge can accumulate and deplete on the capacitor plates if current is passing through it.

I'll take you back to your quote of Prof Viken, here is a man that is intelligent, highly educated and an expert in this field. Note how his reluctance to use the terms CURRENT and THROUGH left him incapacitated, struggling deperately to grasp a word, or words, any words, to describe CURRENT THROUGH. A fundamental concept.

He should have been better prepared to describe what is happening. I already gave a description of what he should have said. It is the conundrum of conduction current passing through a capacitor that gave him pause. He should have said that in a string of series capactiors, the charges shift from one plate to another in equal amounts, but don't go through any of the capacitors.

Current through a cap is true. Now current inside a cap? Electron behaviour inside a cap? Well they can be argued over by pedantic people and physicists.

Virtual current through a capacitor yes, conduction current, no. I don't understand your inclination to ignore what is happening inside a capacitor. Electromagnetic texts give extensive coverage to this subject. Physics is one of the foundation sciences of all things electronic. If electronics does not agree with physics, then it must be wrong.

ericgibbs,

You are echoing my feelings from an earlier post, I feel the same way as you regarding the well proven conventions for current flow.

Then perhaps you can explain the inconsistencies in his viewpoint better than he has.

The more I read Ratchit's pseudo techno babble, the more I become concerned that the newbies readings his comments may take what he his saying as a fact, so I feel I must speak out against what he his posting.

So far, I have not seen anything from you that proves me wrong. An unconventional outlook perhaps, but not wrong.

I would suggest that his posts should carry a warning to newbies/wannabes 'using this terminology will seriously damage your career prospects'.

I suspect he is being controversial just as an attention seeking ploy, look at some of the other threads he has turned into unresolved saga's.

A common tactic is to disparage the messenger if you can't refute the message.

killivolt,

I think I'm responsible for pushing this as far as it could go; with different intentions.

I think you are imputing too much influence for your actions to influence this thread. For many of your posts, I had no idea what you were talking about, so I could not comment on it. I don't know if others felt the same way, but unless there is understanding, there can be no meaningful discussion.

Ratch

 

[killivolt]

The Electrician,



Yes, there is certainly energy in electromagnetic fields. Inductors and capacitors exploit that fact. And there are also fields involved with conduction carriers when they move and when they congregate.
But don't you think there is some kinetic energy involved with the moving mass of the charge carriers that does not involve fields? For instance, a stream of neutrons will have some kinetic energy associated with it, but no field will be present.
Ratch

And here I thought you were done. Golf Clap.

Do you think, I did say there must be a thermal component upon release of a Photon.

I was thinking a form of "kinetics" but, not necessarily just "kinetics" you were thinking Pedantic. Up until now I was thinking the same thing about you. Very good, care to extrapolate. If you do just remember, I'm not trying to steal your thunder. I think there is more to it as well.

 

[The Electrician]

The Electrician,



But don't you think there is some kinetic energy involved with the moving mass of the charge carriers that does not involve fields? For instance, a stream of neutrons will have some kinetic energy associated with it, but no field will be present.

The drift velocity of the electrons in a copper wire is so slow, typically in the neighborhood of a millimeter/second, that the kinetic energy associated with that movement is negligible. See:
Drift velocity - Wikipedia, the free encyclopedia

If the drift velocity of a stream of neutrons were much larger, then the kinetic energy could be larger also.

The D'Arsonval meter first requires a current to generate the magnetic field it requires.

Ratch

Of course. The meter is intended to measure current, so, yes, there must be a current if it is to measure anything.

 

[MrAl]

Killivolt, my argument is not about the specifics of what happens inside the capacitor. I have been quite clear about that. My argument has been with Ratchit's sloppy misuse of the global terms CURRENT and THROUGH, given that this is an electronics forum.

Current as a global term is a greater concept than what might be happening to one electron. "Current" must also be given a high importance as a concept and as a flow in a series circuit. Something that can easily be measured, calculated, simulated.

"Through" as a global concept is greater than what may be happening INSIDE a component to a single electron. If a mystery component in a series circuit has 1 amp in and 1 amp out, it satisfies "current through" in enough ways to be respected as true. If it later is discovered that that mystery component was a capacitor it is foolish to then say "oh well, that current we just measured going through the component wasn't going "through" after all".

If you want to know if CURRENT is going THROUGH something, use an ammeter.

Now if Ratchit had used the term "current INSIDE the capacitor" or "electron behaviour inside the capacitor" then I may have let it drop. But to state "There is no current through a X" on an electronics forum, for any type of X, needed to be called out.

Mr Al-

'Does CURRENT flow THROUGH a capacitor?' Yes. 'What is displacement current?' It is a term used for current by people who are overly concerned with what is happening inside a capacitor. 'Are you going to tell them that displacement current is the same thing as conduction current?' No, I'm going to tell them that current THROUGH anything can be measured with an ammeter. Whether it is displaced or conducted is only of relevance in the rare case you might care what is happening to an electron inside a component and might be of interest in physics but has practically zero place in electronics.

I'll take you back to your quote of Prof Viken, here is a man that is intelligent, highly educated and an expert in this field. Note how his reluctance to use the terms CURRENT and THROUGH left him incapacitated, struggling deperately to grasp a word, or words, any words, to describe CURRENT THROUGH. A fundamental concept.

Current through a cap is true. Now current inside a cap? Electron behaviour inside a cap? Well they can be argued over by pedantic people and physicists.

Mr RB:


Zero place in electronics? You have to realize what you just said. You just said that this thread says nothing more about a capacitor then the external view, which if you read back, i was debating with Ratchit about, and i took the side you are taking now. But also if you read back, you'll see that i digressed in order to get more in line with what the original poster asked. The original poster wants to know what "really" happens.
Now you want to define what "really" happens as what happens outside the cap, while the main reason most of the people are talking here is to figure out what happens inside the cap. We already know what happens outside the cap, it's time to move on to what happens inside the cap.
I agree with you in that it is simpler to look at this from outside the cap where the wires allow us to measure the current directly, but here we are looking for the physical reason why the cap works at all, not just why it conducts current in its two leads. Do you understand this?
I am saying that you are right, that we can look at the cap from the outside, and I ARGUED WITH Ratchit that very same point way back in this thread, but i am also saying that now we want to take a look at the inside the cap. I regret to have to say that one or two people dont need a third persons permission to do this, whether they succeed or not.
If God himself came down here tomorrow and said, "MrAL, current goes through a capacitor". I'd say, well thank you very much for clearing that up. But that would not mean that i would not want to also know why this is happening. In other words i'd have to also reply, "Ok thanks God, so while you are here, how does that happen inside the cap or in or at the plates?"

The professor was rendered incapacitated? He taught what he set out to teach so i dont see how he was incapacitated. He stumbled over his words a little but was very careful not to say that current flows through a capacitor. He avoided that for a reason, and stated outright that current does not flow through a capacitor.

On this site we talk about electronics, mathematics, and physics. We are now in the realm of physics, not strictly electronics, which is a lot different because physics asks more questions than electronics does, and thus wants more answers.
Another illustration here...
"The field of an air core inductor extends to infinity"
Now do we have to know that when we analyze a circuit? Not really, no. But in physics if we didnt know that we couldnt understand it fully, and find out that quantum mechanics would state it slightly different, but still would not ignore it as we can get away with in electronics.
So you see we really have two different fields of study here, the electronic view and the physics view. We know what the electronic view is, but now we want to look at the physics view.

Thanks.

PS
You said that if we want to know if current is going through something, use an ammeter. We want to know if current is flowing through the vacuum of space between the capacitor plates. How do you suggest we do this?
You might be interested to know that Professor Viken tried this already too and was unsuccessful.

 

[The Electrician]

I don't find it a paradox.

When you say, as you did in post #274:

"My point is that the Theory of everything MAY show that the flow of charge carriers is a consequence of something else that we don't surrently know about and it should hopefully resolve the paradox between conduction & displacement currents."

you leave your readers with the impression that you believe there is a paradox. One way to make it clear that you don't think so is to say:

"...resolve the alleged paradox..." rather than just "...resolve the paradox..."

 

[The Electrician]

You said that if we want to know if current is going through something, use an ammeter. We want to know if current is flowing through the vacuum of space between the capacitor plates. How do you suggest we do this?
You might be interested to know that Professor Viken tried this already too and was unsuccessful.

We could use a clamp-on ammeter surrounding the vacuum region where we want to know the current, as I suggested in an earlier post. It might have to be a custom job as the commercially available versions are probably too big.

 

[killivolt]

Sit down and stay awhile

Here is some more fun. For those who wish to play in the sand box with us.

I wonder how many Physics students have been following this off the web crawler.



kv

Edit: I don't think Prof Viken was actually stumbling. I think it was a planned yet well orchestrated :Breaks: he is most likely to intelligent to just offer pre-defined views without sounding as if he is postulating. You will often see this when some Physicist and Mathematicians reveal evidence to the public without doing harm to their positions. Most will jump at the chance just to see if they can shake them from their tree. Then Crawl up over them.

Here's another fun one. This is not for anyone currently studying Physics on a serious level.

Edit:Edit: Photons, Neutrinos, And Their Anti-Particles

Edit:Edit:Edit: For the serious students: **broken link removed** , **broken link removed** , Beautiful theory collides with smashing particle data

 

[The Electrician]

Here are some references describing how it is that when a current passes through a wire, even DC, the energy is not flowing in the wire, but in the fields surrounding the wire:

Poynting vector - Wikipedia, the free encyclopedia

See the paragraph with the title: "The Poynting vector in a coaxial cable" where it is said "...electric energy is flowing through the dielectric between the conductors." Note that the energy flow is not inside the copper.

Also see:

SCIENCE HOBBYIST: Flowing Electrical Energy

which has lots of further references.

The wires that "carry" energy at 60 Hz from the generator to your home are just there to guide the fields which are the actual carriers of the energy.

Fortunately, treating the wires as though they were the energy carriers works out in practice because most of the energy is carried by fields close to the wire, even though the fields actually extend to infinity. Once you get a short distance away from the wires, the fields are so weak that the energy carried there is negligible.

The point of this is to understand that the modern theory supposes that the electric and magnetic fields are all important. To understand the fine details we must resort to understanding the behavior of the fields.

But, if we don't care about the fine details, for everyday work we don't need to worry about whether the energy is carried in the fields or inside the wire. I don't myself. When I connect a line cord to the primary of a transformer, I act as though the wires themselves are carrying the energy and it works out ok.

 

[MrAl]

We could use a clamp-on ammeter surrounding the vacuum region where we want to know the current, as I suggested in an earlier post. It might have to be a custom job as the commercially available versions are probably too big.

Hello there Electrician,

That is an interesting idea, but as i am sure you already know, a clamp on ammeter is just a transformer where the primary is looped through the core (usually) one time. The core reacts to the time varying magnetic field and develops a current in the secondary. That secondary current is then scaled to some kind of current measuring meter or another to allow us to get a numerical result.
Im sure you know all this, so im just really drawing attention to the fact that we are again measuring the B field. We know that 'normally' when we have a B field we have an associated real current as a flow of charge carriers, but then we have to make the assumption that displacement current is a flow of charge carriers. If we make that assumption, then we havent proven that a displacement current is a flow of charger carriers or not.
If a B field is created without a flow of charge carriers, we would never be able to tell the difference.
Classically, a current and a B field are found together and are inseparable, but we have some doubts as to if this is also true in the vacuum capacitor for example and we would like some very direct proof of this.

All this makes me start to believe that the only way to approach this problem is through some other theoretical means.
When i look at this another way, i find that when we compare two static charges (such as on either side of the cap) we have conservation of charge, but is that enough? When we have the real life case, that charge does not get there all by itself. We have to put it there, and later remove it. This all requires not only the flow of charge, but the acceleration and deceleration of charge which we havent yet accounted for. i have a feeling this is where the key to understanding this better lies.

 

[ljcox]

When you say, as you did in post #274:

"My point is that the Theory of everything MAY show that the flow of charge carriers is a consequence of something else that we don't surrently know about and it should hopefully resolve the paradox between conduction & displacement currents."

you leave your readers with the impression that you believe there is a paradox. One way to make it clear that you don't think so is to say:

"...resolve the alleged paradox..." rather than just "...resolve the paradox..."

Agreed, I should have said "alleged" paradox. But, come to think of it, what did you say about semantics?

I certainly don't find it to be a paradox. But as I said before, others do.

 

[Ross Craney]

It's an interesting thread & I see arguments from both sides that I agree with. I don't want to add fuel to the fire but this scenario came to mind while reading this thread. If you have a series circuit of a battery , a capacitor , an ammeter , another capacitor then back to the battery , will the ammeter indicate a current "flow" when the battery is connected ? If it does then it cannot be showing displacement current since it is not connected to either side of the battery.

 

[killivolt]

Exactly why I'm following it. I think Mr.Al would agree as well as other's. There is more to the story than meets the eye.

Thank you Ross. Once again, I'm taken back by the amount of viewers. This thread will or could be epic, if someone is willing to step outside the comfort zone.

kv

 

[The Electrician]

Hello there Electrician,

That is an interesting idea, but as i am sure you already know, a clamp on ammeter is just a transformer where the primary is looped through the core (usually) one time. The core reacts to the time varying magnetic field and develops a current in the secondary. That secondary current is then scaled to some kind of current measuring meter or another to allow us to get a numerical result.
Im sure you know all this, so im just really drawing attention to the fact that we are again measuring the B field. We know that 'normally' when we have a B field we have an associated real current as a flow of charge carriers, but then we have to make the assumption that displacement current is a flow of charge carriers. If we make that assumption, then we havent proven that a displacement current is a flow of charger carriers or not.
If a B field is created without a flow of charge carriers, we would never be able to tell the difference.

We don't have to make any assumptions. Of course we wouldn't be able to tell the difference. That's the whole point. If a clamp-on meter gave a reading when surrounding the vacuum between the plates of a vacuum capacitor, we would take that as an indication that a "displacement current" existed there. We know that there are no charge carriers in the vacuum (that's what a vacuum is, right? An absence of matter, including charge carriers), so if our clamp meter gave a reading, then there is a "displacement current" there. We assume nothing; we're measuring something.

Classically, a current and a B field are found together and are inseparable, but we have some doubts as to if this is also true in the vacuum capacitor for example and we would like some very direct proof of this.

All this makes me start to believe that the only way to approach this problem is through some other theoretical means.
When i look at this another way, i find that when we compare two static charges (such as on either side of the cap) we have conservation of charge, but is that enough? When we have the real life case, that charge does not get there all by itself. We have to put it there, and later remove it. This all requires not only the flow of charge, but the acceleration and deceleration of charge which we havent yet accounted for. i have a feeling this is where the key to understanding this better lies.

You've used the word "current" 6 times in this post. Three of them are qualified. I know what you mean by "displacement current", but what do you mean by "real current"? Is that the same as "conduction current"? If so, I think it would help eliminate confusion if you would just say "conduction current" if what you mean by "real current" is a current consisting of a flow of charge carriers.

If the case of the 3 instances where you didn't qualify the word "current", I have to guess what you mean. I think it would be helpful if you would always qualify "current".

When you say "Classically, a current and a B field are found together and are inseparable, but we have some doubts as to if this is also true in the vacuum capacitor for example and we would like some very direct proof of this." your failure to qualify the word "current" makes if difficult to reply since I don't know for sure what you mean by "current".

If by the unqualified word "current", you mean that quantity represented by the left hand side of the equation:

[latex]\oint H \cdot dl = I + \frac{\partial \Phi_D}{\partial t}[/latex]

then I can say this:

When you say "we have some doubts as to if this is also true in the vacuum capacitor for example and we would like some very direct proof of this." you are saying in effect:

Is it true that the quantity [latex]\frac{\partial \Phi_D}{\partial t}[/latex] contributes to the current that would be measured by a clamp-on meter surrounding a region of space (the clamp-on measures: [latex]\oint H \cdot dl[/latex])?

And, apparently, between the plates of a vacuum capacitor, since there are no mobile charge carriers, that quantity [latex]\frac{\partial \Phi_D}{\partial t}[/latex] is the only thing that could contribute to an H field.

So, is there any proof that [latex]\frac{\partial \Phi_D}{\partial t}[/latex] has a B field associated with it? Yes. The very existence of electromagnetic waves is the proof. If it were not true that both terms on the right hand side of [latex]\oint H \cdot dl = I + \frac{\partial \Phi_D}{\partial t}[/latex] are needed then in a vacuum (a vacuum is a region where I=0) we would have
[latex]\oint H \cdot dl = 0[/latex] and there would be no electromagnetic waves in free space. But we know that there are electromagnetic waves in free space, and this is the proof that in a charge-free region, [latex]\oint H \cdot dl =\frac{\partial \Phi_D}{\partial t}[/latex]. This means that a clamp-on meter surrounding the vacuum between the plates of a vacuum capacitor would measure the "displacement current" in that region.

 

[ljcox]

It's an interesting thread & I see arguments from both sides that I agree with. I don't want to add fuel to the fire but this scenario came to mind while reading this thread. If you have a series circuit of a battery , a capacitor , an ammeter , another capacitor then back to the battery , will the ammeter indicate a current "flow" when the battery is connected ? If it does then it cannot be showing displacement current since it is not connected to either side of the battery.

The Ammeter is reading the conduction current, not the displacement current.

The displacement current is only in the dielectric.

 

[The Electrician]

It's an interesting thread & I see arguments from both sides that I agree with. I don't want to add fuel to the fire but this scenario came to mind while reading this thread. If you have a series circuit of a battery , a capacitor , an ammeter , another capacitor then back to the battery , will the ammeter indicate a current "flow" when the battery is connected ?

Yes, a "conduction current" will pass through the ammeter for a short while. As soon as equilibrium (the capacitors become "charged") is established, the current will cease.

If it does then it cannot be showing displacement current since it is not connected to either side of the battery.

Could you explain in more detail how you arrive at this conclusion, keeping in mind that an external ammeter wouldn't be expected to measure the "displacement current", which is internal to the capacitor? Are you suggesting that if the ammeter were connected to one side of the battery, it would show "displacement current"? If so, how could this be, since the "displacement current" is internal to the capacitor?

 

[ljcox]

If it does then it cannot be showing displacement current since it is not connected to either side of the battery.

Ross,
Did you make a typo? Do you mean that the Ammeter is reading the displacement current?

Your reasoning seems to be - since the Ammeter is not connected to either side of the battery, then it must be measuring the displacement current.

 

[ljcox]

When you say "Classically, a current and a B field are found together and are inseparable, but we have some doubts as to if this is also true in the vacuum capacitor for example and we would like some very direct proof of this." your failure to qualify the word "current" makes if difficult to reply since I don't know for sure what you mean by "current".

If by the unqualified word "current", you mean that quantity represented by the left hand side of the equation:

[latex]\oint H \cdot dl = I + \frac{\partial \Phi_D}{\partial t}[/latex]

then I can say this:

When you say "we have some doubts as to if this is also true in the vacuum capacitor for example and we would like some very direct proof of this." you are saying in effect:

Is it true that the quantity [latex]\frac{\partial \Phi_D}{\partial t}[/latex] contributes to the current that would be measured by a clamp-on meter surrounding a region of space (the clamp-on measures: [latex]\oint H \cdot dl[/latex])?

And, apparently, between the plates of a vacuum capacitor, since there are no mobile charge carriers, that quantity [latex]\frac{\partial \Phi_D}{\partial t}[/latex] is the only thing that could contribute to an H field.

So, is there any proof that [latex]\frac{\partial \Phi_D}{\partial t}[/latex] has a B field associated with it? Yes. The very existence of electromagnetic waves is the proof. If it were not true that both terms on the right hand side of [latex]\oint H \cdot dl = I + \frac{\partial \Phi_D}{\partial t}[/latex] are needed then in a vacuum (a vacuum is a region where I=0) we would have
[latex]\oint H \cdot dl = 0[/latex] and there would be no electromagnetic waves in free space. But we know that there are electromagnetic waves in free space, and this is the proof that in a charge-free region, [latex]\oint H \cdot dl =\frac{\partial \Phi_D}{\partial t}[/latex]. This means that a clamp-on meter surrounding the vacuum between the plates of a vacuum capacitor would measure the "displacement current" in that region.

Thank you, this is a good argument for displacement current.