Superconductivity at room temperature??

[Reality Check]

The fact is that the whole conductor is filled with charge-carriers and they are flowing through all the conductors in series with zero divergence:
...

Still wrong - this is a divergence of current which has nothing to do with Gauss's law.

I did not intend to convey the idea that Gauss' law is only valid within a vacuum. It seems. however, that I did and i apologise if this is how you understood me. But I hope that I am now more clear.

Thank you for clarifying this.
So Gauss's law can be applied to the situtaion we are considering, i.e. a snadach of 2 metals with different resistivity.

Could you please apply Gauss's law to this sandwich and show that it means that there is no accumulation of charge at the interfaces?
If you have done this before then just link to the post. I expect to see a statement of the electric field, the calculation of the divergence and the resulting charge density.

 

[Reality Check]

The divergence of the current is not irrelevant in this discussion.

The divergence of the current is irrelevent to Gauss's law which is what we are discussing.

 

[johanfprins]

You've just given an example where the charge density changes with time at an interface. When you push the plates against the metal, the accumulated charge dissipates - in other words, d(rho)/dt is non-zero for a while and therefore div.J is non-zero too. Once equilibrium is established, d(rho)/dt=div.J=0.

For a change you are correct. The carrier charge-density changes since when a current flows the charge-carriers cannot stay accumulated at the interface anymore.

That's exactly what happens in the copper-iron-copper sandwich.

Nope!

When the current is first switched on, d(rho)/dt is non-zero for a while.

In the case above, the electric-field was switched on first and this caused charge-accumulation before the plates were pushed onto the metal: This accumulation resulted exactly because a current could not flow through the interface. When you then push the plates onto the metal, the accumulated charge-carriers change precisely because charge-carriers cannot stay accumulated at the interface while a current is flowing through the interface.

In the iron-copper-iron sandwich, there is no charge-accumulation anywhere before the power is switched on. When switching on the power, the electric field spreads with light-speed through the sandwich and this is so fast that the charge-carriers start to to move instantaneously everywhere as if they form a single body: This does not require a change in charge density at any position with time; since just as many charge-carriers immedately flow into a volume as out of the same volume (divergence of current is ZERO). Thus, the charge-carriers do not first have to redistribute as in the case when pushing the plates onto the conductor ONLY AFTER the electric field has been switched on.

Once equilibrium is established, d(rho)/dt=div.J=0. In neither case does d(rho)/dt=0 imply zero charge accumulation, since rho=constant is a perfectly valid solution.

Correct rho=constant tells you that the density of the charge-carriers remains everywhere the same: This means that there cannot be an accumulation of excess charge-carriers at any interface whatsoever within the iron-copper-iron sandwich.

Thank you for proving what I have maintained all along in such an elegant manner. If I had thought of this proof right from the start, our discussion would have been far far shorter and more precise.

 

[johanfprins]

Gauss's Law says excess charge is the only source of divergence.

I have not denied this anywhere: All I have said consistently is that the excess charge required is not caused by the accumulation of the charge-carriers at the interfaces, since charge-carriers cannot accumulate at any interface while a current is flowing through the iron-copper-iron sandwich (see post directly above).

Bound charge is still charge (remember, polarization is just a small position change of ordinary electrons and nuclei) we include it in the charge-density. Why wouldn't we?

GOOD!!! You are slowly catching on. This does not invalidate the fact that charge-carriers flowing through your iron-copper-iron sandwich cannot accumulate at the interfaces; and that the divergence can thus not be generated by the accumulation of the charge-carriers to form the excess charge required.

 

[johanfprins]

What's the lake, if not an accumulation of water?

Correct! And what's the charge-carriers within the iron-copper-iron sandwich, if not an accumulation of charge filling the device: And just as the equal inflow into and outflow out of the lake does not allow excess water to accumulate anywhere, one has that the equal inflow of charge-carriers into the sandwich and out of the sandwich, also does not allow excess charge carriers to accumulate within the sandwich.

Bye for now

 

[sol invictus]

rho=constant tells you that the density of the charge-carriers remains everywhere the same:

Right - just like that huge lake over there, the one with equal amounts of water flowing in and out.

This means that there cannot be an accumulation of excess charge-carriers at any interface whatsoever within the iron-copper-iron sandwich.

I see. Lakes don't exist. Got it.

When switching on the power, the electric field spreads with light-speed through the sandwich and this is so fast that the charge-carriers start to to move instantaneously everywhere as if they form a single body: This does not require a change in charge density at any position with time; since just as many charge-carriers immedately flow into a volume as out of the same volume (divergence of current is ZERO).

Think about it, Johan, please: compare two lengths of wire, equal cross-sections, but one made of copper and one made of iron (with one end attached to a voltage source and the other grounded, say). Do you really, truly, honestly believe that when the same electric field (i.e. voltage) is switched on across each wire, the current builds up as exactly the same function of time? Of course it doesn't. It can't, because the current after a while asymptotes to two different values, since the two wires have different resistance and I=V/R.

In our Cu-Fe-Cu sandwich problem when you switch on the field the currents in the iron and copper sections aren't going to be the equal either for a time. Therefore there is a necessarily a divergence in the current at each interface, and therefore (by div.J=-d(rho)/dt) equal and opposite charge accumulates there. Those charge accumulations increase the electric field inside the iron section. Eventually, enough charge accumulates so that the fields are such that the current in the copper equals the current in the iron even though the resistivity differs. Then div.J=0, which means no more charge accumulates, so you've reached a steady state - and the steady state necessarily has an accumulation of charge at each interface that keeps the E-field in the iron at the level required.

Note that this whole picture is both intuitively crystal clear and consistent with all relevant equations (current continuity, Gauss' law, and Ohm's law), whereas yours is inconsistent with Gauss' law and/or Ohm's law.

 

[D'rok]

Correct! And what's the charge-carriers within the iron-copper-iron sandwich, if not an accumulation of charge filling the device: And just as the equal inflow into and outflow out of the lake does not allow excess water to accumulate anywhere, one has that the equal inflow of charge-carriers into the sandwich and out of the sandwich, also does not allow excess charge carriers to accumulate within the sandwich.

Bye for now

Perhaps it would help if you defined precisely what you mean by "excess". What are "excess" charge carriers?

Using the lake analogy, if you have a lake with a fixed volume of water, and you consider any increase to that volume to be "excess" water, then more water would have to flow in than flow out for "excess" water to be present.

Is that what you are saying about "excess" charge carriers - i.e., that there is a "lake" of accumulated charge, but that "lake" doesn't accumulate any "excess" charge carriers in the sense of the lake analogy above?

 

[johanfprins]

Well, that's your problem.

Would you at least agree with the following statement? "There is an electric field divergence at a current-carrying iron-copper interface, but I believe despite Gauss's Law that there is no charge there." Does that sum it up?

Nope! I have maintained that even if Gauss' law applies, excess charge at the interfaces cannot be the result of the charge-carriers themselves accumulating at an interface (when negative charge is required) or "de"-accumulating at an interface (when positive charge is required). Accumulation and "de"-accumulation of the charge-carriers at interfaces can only occur when there is an electric-field without a current flowing through the interfaces.

 

[sol invictus]

Well Johan, I think we've managed to teach you enough basic E&M that you may understand what's required for your faith to hold true.

First, as you said yourself, it must be the case that "the charge-carriers start to to move instantaneously everywhere as if they form a single body". So even though copper and iron have different resistivity and the electric field is the same in each, the charge carriers ignore the differences and accelerate as though they were all connected rigidly together. Quite magical, that.

Note that the slightest difference in the rate at which they accelerate automatically results in an accumulation of charge somewhere, since div.J would be non-zero in that case. So Johan requires that the "charge-carrier-rigid-body" be perfectly rigid for all times.

Second, after a while the current in the Cu-Fe-Cu sandwich wire reaches a steady state. In the steady state, div.J must be zero, meaning the current is the same everywhere. If Ohm's law applies within the wire, since the resistivity of iron isn't the same as copper's, this automatically means that the E-field is not the same everywhere. If the E-field is not the same everywhere, div.E is not zero (that follows at least when the field lines remain parallel, as they do here), and therefore by Gauss' law there is an accumulation of charge.

(Where did that charge come from? Obviously from the fact that the charge carriers are not a perfectly rigid body. Charge carriers are electrons and holes; they can accelerate independently of each other, scatter of the metal, etc. They are anything but rigid, they are more like a gas. And subjected to the same field, more charge carriers accelerate more quickly in copper than in iron - hence the charge accumulation.)

So the second thing required for Johan's picture to work is that Ohm's law is wrong, or Gauss' law.

To summarize, for Johan to be correct, one needs to believe at least two unphysical things before breakfast:

(1) Charge carriers in the Cu-Fe-Cu sandwich always behave like a perfectly rigid body with constant linear density - in other words, the current in each section is always exactly equal, despite the fact that Cu is a much better conductor than Fe.

(2) Either Ohm's law is wrong or Gauss' law is wrong (or both), because the two combined tell us there is a charge accumulation at the interfaces.

 

[johanfprins]

Perhaps it would help if you defined precisely what you mean by "excess". What are "excess" charge carriers?

Using the lake analogy, if you have a lake with a fixed volume of water, and you consider any increase to that volume to be "excess" water, then more water would have to flow in than flow out for "excess" water to be present.

Is that what you are saying about "excess" charge carriers - i.e., that there is a "lake" of accumulated charge, but that "lake" doesn't accumulate any "excess" charge carriers in the sense of the lake analogy above?

I decided to skip Sol's usual claptrap and first answer this post: The lake analogy is not really a good one: It was "invented" by Sol in his usual devious manner.

We are talking of accumulation of excess charge at an interface. Consider an interface within the copper and enclose it within a Guassian volume: Although you enclose the charge-carriers within this volume, the electric-field flux entering the volume is the same as the flux leaving the volume: If the same volume, containing the same charge, was surrounded by vacuum, and an electric flux entered it, the electric flux that leaves it will be less than what entered it: But within the copper the enclosed charge of the charge-carriers does not change the electric flux.

In the case of the iron-copper interface the Gaussian volume also contains the same density of charge-carriers while a current is flowing since the charge-carriers cannot accumulate at the interface: Thus, the density of the charge-carriers themselves cannot be responsible for changing the electric-field flux, as can be derived from Gauss' law for the electric-flux moving through the Gaussian volume. Thus the claim by BZS that it is the actual charge-carriers that accumulate and, in this way, cause this change in flux, is incorrect. It is just simple logic!

I have important things to do, and must now really say goodbye until later

 

[ben m]

We are talking of accumulation of excess charge at an interface. Consider an interface within the copper and enclose it within a Guassian volume: Although you enclose the charge-carriers within this volume, the electric-field flux entering the volume is the same as the flux leaving the volume: If the same volume, containing the same charge, was surrounded by vacuum, and an electric flux entered it, the electric flux that leaves it will be less than what entered it: But within the copper the enclosed charge of the charge-carriers does not change the electric flux.

Seriously, Johan, how can you not understand this?

In the middle of the copper, there are (+) and (-) charges. They are equal in density, so the net charge density is zero. That's why the flux divergence is zero---your Gaussian surface surrounds both electrons and nuclei in equal numbers.

The (-) charges are moving to the right, so the net current is nonzero. We measure current and charge-density separately. They're different things.

 

[sol invictus]

Seriously, Johan, how can you not understand this?

I think he really doesn't understand it. He regularly confuses electric flux with current, for example. No one that understands E&M even a little could possibly make such a mistake - it indicates a lack of understanding of even the most basic conceptual structures of the theory (charge, field, current, voltage - those are all different things).

I think what throws us off is that Johan has a vocabulary that makes it sound like he knows physics, and he claims to have a graduate degree and be the author of many papers in the field. But based on the evidence from his posts on this forum, which by now is very extensive, he lacks even freshman level knowledge.

In essence, he doesn't understand anything about the theory. He has some picture in his head (which doesn't even seem to remain the same or be self-consistent), and it's just completely wrong. On top, he refuses to think about anything that challenges his picture, and he can't do math.

I don't think we can help him.

 

[ben m]

I think what throws us off is that Johan has a vocabulary that makes it sound like he knows physics, and he claims to have a graduate degree and be the author of many papers in the field. But based on the evidence from his posts on this forum, which by now is very extensive, he lacks even freshman level knowledge.

Yep. Poking around the first 50 pages of the thread, I was reminded how bad it was ... on everything.

The first 20 pages revolve around keeping track of a voltage around a circuit, and Johan literally couldn't do it. Then were 5 or 10 pages where he failed to understand acceleration. Now we learn that he's easily confused about the most basic, 1st-day-of-E&M-class manipulation of charges and electric fields.

The bits in the middle---where he didn't understand the difference between the Larmor formula and other radiation processes, and where he didn't understand dielectrics and polarization---are less surprising now, aren't they?

 

[Ziggurat]

a snadach of 2 metals with different resistivity.

Mmmmm... a two-metal snadach... I could really go for one of those right now.

 

[ben m]

I'd also encourage Johan to start thinking about the capacitor version of this. Consider the following sequence of cases.

...

Johan, I want to remind you about this post and encourage you to go through it.

Remember how this works. Gauss's Law has done just fine with everything you've thrown at it---bulges, iron, vacuum, superconductors, interfaces---except for the intuitive insistence that current and charge-imbalance can't coexist. You have offered no evidence whatsoever for this assertion; your attempts to prove the assertion have all contained explicit intro-E&M mistakes, like confusing flux with current.

Since you get so badly tangled in the math, I will give up trying to use E&M laws to convince you of anything.

The goal of the above post---which again, please do read carefully and without making the usual mistakes again---is show you, nonmathematically, that one part of your intuition is actually incompatible with another part. Your belief that capacitors can store free charge (you do believe this, right?) is incompatible with your belief that charge-excesses go away in the presence of current.

 

[johanfprins]

I have skipped posts 2079 (Ben), 2080 ("Reality" C), 2081 ("Reality" C) to make some posts. In between these posts Sol posted his usual claptrap in posts 2086 and 2089, which I also skipped. Now we have the pinnacle of claptrap in posts 2091 (Ben), 2092 (Sol) and 2094 (Ziggurat).

Where must I start? Next time I will start from the top with post 2079 (what a messy non-sensical post!), and work my way down.

In the mean time I would like to AGAIN summarise what the argument is about: BZS claimed that charge-carriers can accumulate at one contact while leaving positive charges behind at the other contact WHILE A CURRENT IS FLOWING so that this accumulation can TOTALLY cancel the applied electric field WHILE A CURRENT IS FLOWING through a superconductor. I have consistently maintained that a similar accumulation of charge-carriers (as what one obtains when no current is flowing) cannot be possible at the interfaces while a current is flowing. It can only happen when there is an electric-field without a current flowing.

BZS then came with the argument that such an accumulation of actual charge-carriers must occur while a current is flowing; and this is supposedly proved by the non-zero value one obtains when calculating the divergence across the interfaces while a current is flowing. I am still arguing that charge-carriers cannot accumulate at the interfaces in the same manner as they accumulate when there is an electric-field without a current flowing, and that the divergence across the interfaces is thus not caused by such an accumulation of the charge-carriers across the interfaces while a current is flowing. In fact the total amount of charge-carriers stays the same as the total amount of positive charges past which they are flowing within any Gaussian volume; whether taken across a boundaery within the copper or across a boundary within the iron, or across the interface between them. That there can be dynamic polarisation between the positive and negative, moving charge-carriers within the Gaussian volume I have not denied anywhere: But this is not the same as the accumulation of charge-carriers at the actual boundary when there is an electric field but no current flowing.

 

[ben m]

In the mean time I would like to AGAIN summarise what the argument is about: BZS claimed that charge-carriers can accumulate at one contact while leaving positive charges behind at the other contact WHILE A CURRENT IS FLOWING so that this accumulation can TOTALLY cancel the applied electric field WHILE A CURRENT IS FLOWING through a superconductor. I have consistently maintained that a similar accumulation of charge-carriers (as what one obtains when no current is flowing) cannot be possible at the interfaces while a current is flowing. It can only happen when there is an electric-field without a current flowing.

Yep. Understood. This is the point you maintain, and this is the point you are wrong about.

BZS then came with the argument that such an accumulation of actual charge-carriers must occur while a current is flowing; and this is supposedly proved by the non-zero value one obtains when calculating the divergence across the interfaces while a current is flowing.

Yes. Because Gauss's Law does not admit anything except "actual charge" as a cause for divergence of an electric field.

Remember, Johan, that you spent several pages insisting that the divergence was zero or nonsense? What happened to that? You seem to have changed your mind---the divergence is not zero, after all? Any apologies for the five pages you spent insulting everyone who tried to tell you so?

http://www.internationalskeptics.com/forums/showpost.php?p=7447627&postcount=1843

I will do this for you: The divergence of an applied conservative electric field while a current is flowing is ALWAYS ZERO.

http://www.internationalskeptics.com/forums/showpost.php?p=7464009&postcount=1857

This is what I did: I constructed a Gaussian surface around the copper: And low and behold, there are just as many electric-field lines entering at the one interface to the left iron block than are leaving at the other interface to the next block of iron; Thus, there is no divergence and therefore no excess, internal charge-density within the copper or on its interfaces to the iron. My answer is thus perfectly correct.

http://www.internationalskeptics.com/forums/showpost.php?p=7464009&postcount=1857

Thus, you cannot use Sol’s so-called “correct formula” to derive a gradient by means of differentiation. Since both values of the resistivity is present within both interfaces, it implies that the gradient must be infinity in both cases. So according to Sol’s reasoning the divergence is infinite, which requires an infinite charge within the interface! This is obviously physics-nonsense.

and so on.

 

[Reality Check]

Perhaps it would help if you defined precisely what you mean by "excess". What are "excess" charge carriers?

Hi D'rok, I do not know if you have been following our attempt to educate johanfprins about electromagnetism.

However I will (try to!) summarize the current topic. The example we are talking about is a copper-iron-copper sandwich with a constant current running through it. The question is whether there are charges accumulated at the interfaces or not.
We know that copper and iron have different resistivity. Thus the resistance of the layers is different. In theory we could change the width of the layers until they had the same resistance but that is just a wire!

There is a constant current so the voltage across each layer is different. Thus the change in electric potential is different across each layer. Thus the electric field within each layer is different (the gradient of the potential).
That is as far as we can go without doing a 'spherical cow' approximation. This is

• Use a constant electric field within each layer.
• Use 1D so that divergences just become a simple differentation.

So we have E_CU in the first copper layer, E_FE in the iron layer and then E_CU in the second copper layer. This is a square wave (or inverse square wave if you want E_FE > E_CU).

What does Gauss's law say about this? It says that the divergence of the electric field is proportional to the charge density.
We have an electric field. We can calculate its divergence!

The constant sections of the square wave differentiate to zero (no charge density). That leaves the 2 step functions. The result of differentiating these is a Dirac delta function, i.e. a finite charge density at the interfaces.

This is a charge accumulation at the interfaces.

More realistically we can have the electric field change slowly through the interfaces and then we get a peak of charge density at each interface rather than the more theoretical delta function.

Swapping the Fe layer for a superconducting layer just makes the electric field zero in that layer. Once again there is a change in electric field at the interfaces and that means a different charge density at the interfaces from the rest of the layers (a charge accumulation at the interfaces).

 

[D'rok]

Hi D'rok, I do not know if you have been following our attempt to educate johanfprins about electromagnetism.

However I will (try to!) summarize the current topic. The example we are talking about is a copper-iron-copper sandwich with a constant current running through it. The question is whether there are charges accumulated at the interfaces or not.
We know that copper and iron have different resistivity. Thus the resistance of the layers is different. In theory we could change the width of the layers until they had the same resistance but that is just a wire!

There is a constant current so the voltage across each layer is different. Thus the change in electric potential is different across each layer. Thus the electric field within each layer is different (the gradient of the potential).
That is as far as we can go without doing a 'spherical cow' approximation. This is

• Use a constant electric field within each layer.
• Use 1D so that divergences just become a simple differentation.

So we have E_CU in the first copper layer, E_FE in the iron layer and then E_CU in the second copper layer. This is a square wave (or inverse square wave if you want E_FE > E_CU).

What does Gauss's law say about this? It says that the divergence of the electric field is proportional to the charge density.
We have an electric field. We can calculate its divergence!

The constant sections of the square wave differentiate to zero (no charge density). That leaves the 2 step functions. The result of differentiating these is a Dirac delta function, i.e. a finite charge density at the interfaces.

This is a charge accumulation at the interfaces.

More realistically we can have the electric field change slowly through the interfaces and then we get a peak of charge density at each interface rather than the more theoretical delta function.

Swapping the Fe layer for a superconducting layer just makes the electric field zero in that layer. Once again there is a change in electric field at the interfaces and that means a different charge density at the interfaces from the rest of the layers (a charge accumulation at the interfaces).

Thanks. I think I more or less understand that explanation.

As a lurker, it seems to me that you guys and Johan don't even speak the same language. I think when you say for instance this:

The question is whether there are charges accumulated at the interfaces or not.

...it means something completely different to Johan than to you.

Dunno. It's hard to separate the signal from the noise in this thread.

 

[johanfprins]

I'd also encourage Johan to start thinking about the capacitor version of this. Consider the following sequence of cases.

Let's get J = (1 microamp/m^2) flowing through this structure:

Cu --- Fe ---- Cu

I'd say there is charge density at each boundary, about 10^-13 C/m^2. Johan says there is none.

As usual you are deliberately distorting what I am saying: I am stating the obvious fact that the divergence you calculate at an interface while a current is flowing through the interface cannot be caused by static accumulation of charge-carriers at the interface: The latter is only possible when applying an electric-field without allowing a current to flow through the interface. The charges you calculate from Gauss' law can thus not be caused by an accumulation of stationary charge-carriers at the interface. I have never said that Gauss' law is invalid: Only that what you are deducing from it at an interface (i.e. that charge-carriers accumulate at the interface while a current is flowing) is wrong.