Superconductivity at room temperature??

[sol invictus]

How do you expect me to answer anything if you do not tell me why E_x = E₀/2 between x=0 and x=L.

You cannot compute the divergence of a given vector field until you know why the field is what is given? Can you also not compute 2+2 unless you know why it's 2+2 and not 3+3?

You see why I abhor your posts.

Indeed - they show over and over again how utterly incompetent you are.

 

[Reality Check]

Yes, but you must apply Gauss’ law correctly, and then you will find that at the iron-copper interfaces there CANNOT be any accumulation of the charge carriers at all.

Where did you post a correct application of Gauss's law that shows this?

You have still not posted your proof that ben m's application of Gauss's law is wrong.

You probably do not know it, but Gauss’ law has a far wider application than just for electric field-lines.

You would be wrong: I know this.

P.S. You have not answered johanfprins: Citations to Gauss's law applies only to free electrons?(asked on 5th September 2011) yet.

This post implies that your mention of free electrons was incorrect. You may have meant that as an axample (in that case say so!).

 

[johanfprins]

Yes. I calculated the divergence div.(E), taking into account the magnitude and the direction of E correctly, and it was nonzero.

I admit that I was not clear on this when I wrote that: "Are you sure that you calculated the "divergence", or just the change in E across the interface?" My dispute has all along been that the divergence at an interface cannot be caused by the accumulation of free charge-carriers at the interface while a current is flowing through the interface. I note that I have not always accentuated this aspect, and that some of my arguments that I have posted above are, for this reason confusing. I apologise to the readers of this thread.

Yes of course you have calculated a divergence across the boundary between the copper and the iron and I did not find an error. What I should have written to conform to my argument is: "Are you sure that you calculated the "divergence" that is caused by an accumulation of free charge-carriers at the interface, or did you calculate a change in E across the interface which is caused by another reason"

Yes. In this case I also calculated the divergence of E, taking into account the magnitude and the direction, and the divergence was zero. Again, this is absurdly simple, standard vector calculus.

Agree.

The fact remains that the divergence of the current that flows through the interface remains zero, and therefore just as many current-carriers are flowing into the interface as are flowing out of the interface: Therefore there can be no accumulation of free charge-carriers at the interface. Thus your argument that free charger-carriers, which can be accelerated, can accumulate at an interface while a current is flowing through the interface is wrong. And your argument that such an accumulation of free charge-carriers is responsible for the cancelling of an applied electric field within a superconductor is also wrong.

Free charges can only accumulate at an interface when they cannot flow through the interface: Thus the divergence of the electric fiekld when going from copper to iron is not caused by an accumulation of free charges at the interface while a current is flowing through the interface; but by something else.

 

[johanfprins]

Why do you need to know that? Divergence is just a certain sum of derivatives of vector components.
If I asked you for the derivative df/dx of f(x) = x^2, do you have to ask "why" f changes value? No, df/dx = 2x no matter whether f(x) represents a spring energy, a trajectory, a hill, a lens, etc.

Yes I have to know, since E₀/2 can be caused by an element of length L which has the same resistivity as the two flanking elements but twice the surface area. Then, although the electric-field strength changes, there is no divergence.

ETA: in spite of your insistence to the contrary, this IS SAYING THAT GAUSS'S LAW IS WRONG.

Not so! By saying that the charge causing the divergence is not accumulated charge-carriers at the interface IS NOT SAYING THAT GAUSS' LAW IS WRONG. You also have a change in electric field when going through an interface between two dielectrics which do not have free charges. The "charge" causing this is not accumulated free charges at the interface but polarisation right through the material.

 

[johanfprins]

So, charge cannot accumulate anywhere ever if a current is flowing. And if current is not flowing, then charge carriers are (by definition) not moving and therefore not accumulating anywhere. Does it follow that the charge of a piece of metal can never change?

Nope: You can apply an electric field to a metal by placing it between two plates which do not make contact with this metal. In this case the electric-field will drive the negative charge-carriers towards the positive plate where they will now accumulate since they cannot flow through the interface into the positive plate.

When you, now push the plates against the metal so that a current can flow through the interfaces, a current I flows and there is no divergence of this current: So there cannot be any accumulation of free charges at the positive contact anymore.

 

[johanfprins]

You cannot compute the divergence of a given vector field until you know why the field is what is given? Can you also not compute 2+2 unless you know why it's 2+2 and not 3+3?

I have already answered this just above.

 

[johanfprins]

Where did you post a correct application of Gauss's law that shows this?

The divergence of the current through the interface is zero. This means that the charge-carriers moving into the interface are the same as the charge-carriers moving out of the interface, so that there cannot be an accumulation of free charge-carriers at the interface; which then causes the divergence of the electric-field. The divergence must be caused by another mechanism than by free charge-carriers that accumulate at an interface.

You have still not posted your proof that ben m's application of Gauss's law is wrong.

Deriving that there is a divergence between the copper and iron is not wrong, but ascribing this to the accumulation of free charge carriers at the interface while a current is flowing, is wrong; since free charges can only accumulate at an interface, under the action of an applied electric field, when they cannot flow through such an interface.

P.S. You have not answered johanfprins: Citations to Gauss's law applies only to free electrons?(asked on 5th September 2011) yet.

I went back to the posts of the 5th September, but could not find what you refer to here. Maybe I am not seeing it or maybe it has been snipped?

This post implies that your mention of free electrons was incorrect. You may have meant that as an axample (in that case say so!).

Would you mind repeating this argument?

 

[Reality Check]

The divergence of the current through the interface is zero.

Who cares about your unsupported assertion about the divergence of the current?
You seem to have forgotten (again!) Gauss's law

Gauss's law can alternatively be written in the differential form:

where ∇ · E is the divergence of the electric field, and ρ is the charge density.

No current.
No divergence of the current.
No relationship between any divergence of the current and the divergence of the electric field..

I went back to the posts of the 5th September, but could not find what you refer to here. Maybe I am not seeing it or maybe it has been snipped?

Try clicking on the link that I included. Here it is again.

P.S. You have not answered johanfprins: Citations to Gauss's law applies only to free electrons?
(asked on 5th September 2011) yet.
​

 

[sol invictus]

The fact remains that the divergence of the current that flows through the interface remains zero, and therefore just as many current-carriers are flowing into the interface as are flowing out of the interface: Therefore there can be no accumulation of free charge-carriers at the interface. Thus your argument that free charger-carriers, which can be accelerated, can accumulate at an interface while a current is flowing through the interface is wrong. And your argument that such an accumulation of free charge-carriers is responsible for the cancelling of an applied electric field within a superconductor is also wrong.

us: Hey Johan, look at that huge lake over there!

Johan: I have measured the inflow and outflow of water, and they are equal. Therefore there is no lake.

us:

Not so! By saying that the charge causing the divergence is not accumulated charge-carriers at the interface IS NOT SAYING THAT GAUSS' LAW IS WRONG. You also have a change in electric field when going through an interface between two dielectrics which do not have free charges. The "charge" causing this is not accumulated free charges at the interface but polarisation right through the material.

For weeks you've insisted furiously that there cannot be any charge at an interface through which a current was flowing, even when Gauss' law proves there must be. Now, it sounds like you are admitting you were wrong, but somehow in your alternate universe these charges must be bound rather than free, as in a polarized dielectric.

Of course, in the universe the rest of us inhabit, dielectrics do not allow currents to flow through them (by definition - but definitions aren't a strong point for you), and iron is not a dielectric. But at least you might have stopped denying the validity of Gauss' law and moved on to your next gobbet of nonsense.

 

[Reality Check]

johanfprins: How do you stop your charge-carriers from scattering

Since you seem to be stuck on an irrelevant "divergence of current" (not in Gauss's law), we may as well go onto your model and this question:

When we do get back to your model, the first thing you can show us is how you stop your charge-carriers from scattering, i.e. have no resistivity.

If your charge-carriers are electrons or any fermion then this is impossible. Thermal excitation will always place electrons above the Fermi surface where they can scatter.

So your charge-carriers cannot be electrons or any fermion. That makes it hard to see what they could be. You need a charged boson to create an energy gap to prevent thermal excitation above the Fermi surface - maybe a W boson?

 

[sol invictus]

Nope: You can apply an electric field to a metal by placing it between two plates which do not make contact with this metal. In this case the electric-field will drive the negative charge-carriers towards the positive plate where they will now accumulate since they cannot flow through the interface into the positive plate.

When you, now push the plates against the metal so that a current can flow through the interfaces, a current I flows and there is no divergence of this current: So there cannot be any accumulation of free charges at the positive contact anymore.

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.

That's exactly what happens in the copper-iron-copper sandwich. When the current is first switched on, d(rho)/dt is non-zero for a while. 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.

 

[ben m]

Not so! By saying that the charge causing the divergence is not accumulated charge-carriers at the interface IS NOT SAYING THAT GAUSS' LAW IS WRONG. You also have a change in electric field when going through an interface between two dielectrics which do not have free charges. The "charge" causing this is not accumulated free charges at the interface but polarisation right through the material.

Gauss's Law says excess charge is the only source of divergence. If you think you have found another source of divergence, then Gauss's Law is wrong and should be Prin's Law: div.E = rho + (something).

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? Did you think we weren't? (There is an E&M formalism that allows you to sort of ignore bound charge, by defining the "electric displacement", but it's just a rearrangement of terms and adds no new physics.)

 

[johanfprins]

Who cares about your unsupported assertion about the divergence of the current?
You seem to have forgotten (again!) Gauss's law
No current.
No divergence of the current.
No relationship between any divergence of the current and the divergence of the electric field..

You are oversimplifying what I am trying to say: Most probably because my own statements were not clear enough.

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: Thus they are not accumulating anywhere at any cross-sectional surface-area whether witin a conductor, or at an interface between two conductors.Thus the change in electric field at an interface at which the resistivity changes, cannot be caused by the direct accumulation of the free charge-carriers which convey the current; since they cannot accumulate anywhere once an equilibrium current has been established.

What is really happening has not yet been clearly identified. Probably since nobody bothered until we started this discussion on this thread. I have never found any text book on superconduction that stated that the electric-field is cancelled within a superconductor by the accumulation of free charge carriers at the interfaces to the superconductor while a current is flowing. Not one editor or referee twho rejected my manuscripts on superconduction has raised this as a solution for the cancellation of the applied electric-field within a superconductor. This is why it is a brand new concept and this is why I call it a part of the BZS model.

As I have mentioned before, I believe that the change in electric-field at the boundaries between the iron and copper is caused by, what I will call, "dynamical polarisation" owing to the change in average drift speeds within the two materials. It is an interesting physics problem and I will look in more depth into it when I have the time to do so.

Try clicking on the link that I included. Here it is again.

P.S. You have not answered johanfprins: Citations to Gauss's law applies only to free electrons?
(asked on 5th September 2011) yet.
​

I have stated that Gauss' law is applied by BZS within the metals as if the charge-carriers are free electrons, while they are not. I agree that my statement on Gauss' law in vacuum and within a metal has been confusing. 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.

 

[ben m]

Yes I have to know, since E₀/2 can be caused by an element of length L which has the same resistivity as the two flanking elements but twice the surface area.

Why would you want to know that? Oh, because I pointed out that in your example the area change led to zero divergence, and you're concerned that you might be in a case like this.

How did I figure out the zero-divergence? I looked at the area-change that you specified, and I wrote down the fields. I then calculated the divergence of the fields. The divergence operator does not know or care how I got the fields---it just cares what they are.

Sol has given you the fields. You can calculate the divergence purely from the givens. I can do it, Sol can do it, any undergrad can do it. Can you do it?

(I might also ask: why should anyone listen to E&M theorizing from someone who can't use vectors at all?)

 

[johanfprins]

us: Hey Johan, look at that huge lake over there!

Johan: I have measured the inflow and outflow of water, and they are equal. Therefore there is no lake.

us:

I have not said that thre is no lake, but that there is no accumulation of extra water in the lake.

For weeks you've insisted furiously that there cannot be any charge at an interface through which a current was flowing,

I still maintain that the free charge-carriers conveying the current cannot accumulate at the interface.

Now, it sounds like you are admitting you were wrong,

Not wrong that it cannot be the charge-carriers themselves that accumulate at the interfcae.

but somehow in your alternate universe these charges must be bound rather than free, as in a polarized dielectric.

Well for charges to accumulate they must be bound and the charge-carriers are free; so the cannot become bound. Therefore they cannot accumulate.

Of course, in the universe the rest of us inhabit, dielectrics do not allow currents to flow through them (by definition

By definition they do not; but in reality they do: The way in which they do this is by thermal-hopping between localised states. Both Mott and Anderson (as well as many others) have studied these conduction mechanisms. And, of course, a superconductor is also a dielectric that conducts by hopping where this hopping is, in this case, not caused by thermal fluctuations, but by quantum fluctuations. The copper-oxides are in essence dielectrics; and the metals go through a metal-insulator transition in order to superconduct.

 

[johanfprins]

Since you seem to be stuck on an irrelevant "divergence of current"

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

we may as well go onto your model and this question:

I agree and hope we will soon be able to move our attention to this aspect. Your questions are based on the BCS model which I will discuss first, before showing where the BZS model differs from the BCS model. And then where my model differs from the BCS and BZS models.

 

[TjW]

I have not said that thre is no lake, but that there is no accumulation of extra water in the lake.

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

 

[ben m]

I still maintain that the free charge-carriers conveying the current cannot accumulate at the interface.

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?

 

[ben m]

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.

Now let's replace the iron with a quite-bad conductor, like mercury.

Cu --- Hg (mercury)---- Cu

I'd say there is charge density at each boundary, about 5x10^-13 C/m^2. Johan says there is none. Keep replacing:

Cu --- carbon---- Cu

Wow, carbon is a fairly high-resistivity material. It's taking more and more voltage to push that microamp through it. I'd say there is a lot of charge density at each boundary, about 5x10^-10 C/m^2. Johan says there is none. Keep going:

Cu --- glass---- Cu

Wow, glass is a much worse conductor than carbon. It takes a real high-voltage supply to keep that current moving along. And I say there is now a LOT of charge density at each boundary, about 5x10^4 C/m^2. But ... Johan says there is none, right? There's no charge accumulation when a current is going past.

No, never mind, I hope that Johan admits this is a capacitor---a leaky one, with 1uA/m^2 dribbling through the dielectric---and that I am now for the first time allowed to use Gauss's Law even in the presence of this current to figure out how much charge is on each interface. Is that right? A capacitor with a leaky dielectric can have charge on the interfaces?

Johan, what I want you to do is tell me exactly what resistivity makes this distinction work in your mind. When is the charge determined by Prins' Law, and when is the charge being determined by Gauss's Law? Did it happen between the carbon and the glass? If I start heating up the glass, it becomes more conductive---will the capacitance suddenly drop to zero? If I heat up the iron, it becomes less conductive---can I reach the threshhold that way, and suddenly "turn off" Prins's Law?

(And I'd like to remind Johan of the mainstream view that there is no Prins' Law, and that Gauss's Law works just fine in all of the above cases.)

 

[Reality Check]

Your questions are based on the BCS model which I will discuss first, before showing where the BZS model differs from the BCS model.

Wrong: johanfprins: How do you stop your charge-carriers from scattering?is based on the physical fact that resistivity is caused by charge-carriers scattering from the lattice. If you have scattering then you have resistivity.
So to have no resistivity you have to stop the charge-carriers from scattering. This is impossible with electrons since they are fermions. Cooper pairing allows electons to act as bosons.

ETA: You do not need to discuss the BSC model first or compare your model to it.
Many people here are familiar with the BCS model (me for example) and so you will be just wasting your time doing more than linking to a good description of it.