Superconductivity at room temperature??

[johanfprins]

No we didn't. First you were unable to differentiate a vector function correctly (wrong).

I only differentiate a function when I am sure that it can be differentiated. For a low resistance material with a limited length it is unlikely that you can have a continuous function representing the resistivity which can be diffrentiated to give a gradient of such a non-continuous function.

Then you claimed that mathematically you can't differentiate a step function,

You are playing with words again: We are not talking about the Fermi-Dirac distribution here, but about a scalar field which can only have a gradient when it changes its value continuously with position. In the latter case the gradient of a step must always be infinte.

You seemed unwilling to apply Gauss's Law to this situation in the standard intro-E&M way (wrong yet again).

I did apply Gauss' law and found no excess charge-carriers within the copper.

The difference between the perfect-step-function and the smooth-resistivity change is utterly irrelevant to the general E&M behavior. Either case shows a charge layer of the same sheet density;

Nope! The accumulation of charge at an interface is not determined by the gradient of a resistivity, since if a step in the function could be physics (which it is not in this case), it must give a physically impossible infinite charge-density.

the width of the transition zone sets the volume density but has no effect outside of the transition zone itself.

This the typical hand-waving claptrap that theoretical physicists talk. You now want to fudge the result by talking about an undefined "transition zone".

Yes, this is the work function. Please notice that it is not responsible for the E field difference between the iron and copper---that difference is proportional to j, the work function behavior is not.

Where did I say that the work-function alone is responsible for charge accumulation while a current is flowing? As usual when you are in a corner you put words in my mouth I have never uttered.

Nicely done Johan! You have drawn a picture of a positively charged sheet on one side and a negatively charged sheet on the other side. You've drawn an accumulation of free charge, in a conductor, that cancels an electric field. That's exactly what we said would happen and that you objected to violently.

I have NEVER denied that you can have opposite charges accumulating on opposite interfaces which can partially cancel an electric field while a current is flowing. I have said that such an accumulation can never be high enough to TOTALLY cancel an applied electric field while a current is flowing.

Wrong again. This is spectacularly bizarre.

What is bizarre? You have claimed that you have excess charge-carriers accumulating within the copper. You have not said that you have opposite charge-sheets on the surfaces having equal charge.

First, the "field lines" you have drawn represent different field magnitudes (in the same direction). You've seen the divergence equation already. Do you know what divergence means? For a vector { Ex , Ey, Ez } the divergence is dEx/dx + dEy/dy + dEz/dz. The "parallel field lines" in the picture above sets Ey=0 and Ez=0. The remaining term is dEx/dx, which Ohm's Law (which you evaluated correctly) tells us is NOT zero.

What has this to do with a resistivity field-function which at low resistances cannot be continuous and can thus not be used to derive a gradient by differentiation?

Secondly, the usual statement "the flux of field lines is conserved"---the usual justification for statements like "the number of field lines is the same, so the fields are the same"---is only true in a source-free region, which this is not.

Not at all!. When you have an even amount of positive and negative charge within a volume, the flux entering the volume will always be equal to the flux leaving the volume.

Third: how can you draw a picture showing excess charges and then deny that they are excess charges?

The charge sheets at the interfaces of the copper have an equal amount of opposite charges: Thus there is no excess charge of one type within the copper.

Good, good, good. Did you notice that you've just inserted current divergence? If the current is different at different ends of the copper, then charge is being depleted at one end and accumulating at the other. (Conservation of charge: d rho/dt = div J).

This is only a valid argument when there is an electric-field that accelerates the charge-carriers.

This depletion of charge is where the charge sheets come from, Johan.

And this only the case while there is an electric-field accelerating the charge-carriers. Thus these so-called charge "sheets"(?) of yours can NEVER cancel the applied electric field within the material; since they can only be there while there is an applied electric field.

You've now identified the out-of-equilibrium behavior that leads to the equilibrium behavior that you objected to above.

Nope! I have objected to the statement by you that charge can accumulate by enough while a current is flowing to totally cancel the applied electric-field. I have never objected to accumulation of charge when a current flows per se.

The end of your post has been reported to the mods.

Good! I am sure they have a sense of humour. I had to end it in that way since it clearly describes in a picturesque manner how you, Sol, and Ziggurat approach physics.

 

[johanfprins]

One additional note here: the work function difference will create a charge separation at the boundary (positive charges on one side, negative charges on the other). It DOES NOT lead to any net charge at the boundary. The field produced is thus confined to the boundary region.

Have I stated anything else?

The charge which accumulates at the boundary because of the current, however, WILL be a net charge, as it must be to change the field throughout the copper.

Nope! you must have equal and opposite charges at the two opposite boundaries for a polarisation field to form within the copper: Thus, there is no net accumulation of charge within the copper.

 

[Perpetual Student]

The end of your post has been reported to the mods.

Bush league!

 

[ben m]

I only differentiate a function when I am sure that it can be differentiated. For a low resistance material with a limited length it is unlikely that you can have a continuous function representing the resistivity which can be diffrentiated to give a gradient of such a non-continuous function.

There are two answers.

a) Obviously it is experimentally possible to bump iron into copper in this way. This results in some actual resistivity which is a continuous function. Whether or not I can write it down as a simple function, Nature obviously knows what this function is.

b) "it is unlikely"? I can write down functions with this property in my sleep.

Example 1 (continuous f, discontinuous f')
rho = 1 for x<=0
rho = 1-x/0.01 for 0 < x<=0.01
rho = 0 for 0.01 < x

Example 2: (continuous f and f', discontinuous f'')
rho = 1 for x<=0
rho = cos^2(pi*x/0.02) for 0 < x <= 0.01
rho = 0 for 0.01 < x

Example 3: (continuous f, f', f'')

rho = 1 for x<=1
rho = 1 - 10x^3 + 15x^4 - 6x^5 for 0 < x <= 1
rho = 0 for 1 < x

and so on. Once again, Johan, you have very poor judgement of what is "possible" or "likely".

You are playing with words again: We are not talking about the Fermi-Dirac distribution here, but about a scalar field which can only have a gradient when it changes its value continuously with position. In the latter case the gradient of a step must always be infinte. I did apply Gauss' law and found no excess charge-carriers within the copper.

You applied Gauss's Law and found no net charge in the entire copper block. Your choice of Gaussian surface was insensitive to equal and opposite charges on the injection and extraction contacts.

I have NEVER denied that you can have opposite charges accumulating on opposite interfaces which can partially cancel an electric field while a current is flowing.

Sure you did---it was your very first response to the iron-copper-iron problem, remember? That's where you got by dropping the gradient term from the divergence.

The charge sheets at the interfaces of the copper have an equal amount of opposite charges: Thus there is no excess charge of one type within the copper.

There's one charge at one interface, the opposite charge at the other interface. Do I need to start over?

This is only a valid argument when there is an electric-field that accelerates the charge-carriers. And this only the case while there is an electric-field accelerating the charge-carriers. Thus these so-called charge "sheets"(?) of yours can NEVER cancel the applied electric field within the material; since they can only be there while there is an applied electric field.

Nope, wrong.

You presented an out-of-equilibrium situation (i.e., before the charge had accumulated) in which there IS an electric field. Before the charge accumulates, when there is a field, that field WILL move charge in a way that reduces the field.

I presented an equilibrium situation, when the charge is there and there is no field in the center block. The charge is in its equilibrium location, and the field is zero.

The difference between these two situations seems to confuse you. Stick to one, the simplest one. Assume for a moment that we ARE in the equilibrium situation that I described to begin with: zero E field in the superconductor, nonzero E field in the iron, a - charge sheet at the injection contact (it doesn't matter how thick) and a + charge sheet at the extraction (it doesn't matter how thick), a uniform current flow. Do you have that in mind? All of it at once? (Don't jump on my charge sheets while ignoring the fact that E_copper = 0. Don't jump on E_copper=0 without ignoring that the charge sheets are there. We're talking about the whole situation I described.)

My claim is that this is a stable equilibrium. Do you know what that means?

Do you know how to test an equilibrium? Push one small charge out of position---say, take one electron out of the - sheet and move it partway into the superconductor. What is the force on THIS electron?

 

[Ziggurat]

Nope! you must have equal and opposite charges at the two opposite boundaries for a polarisation field to form within the copper: Thus, there is no net accumulation of charge within the copper.

The charge which accumulates at the boundary because of the current, however, WILL be a net charge, as it must be to change the field throughout the copper.

Note the difference between singular and plural. And note that johan didn't pick up on the difference.

Oh, and you can call the field a "polarisation field" if you want, but it's just an ordinary electric field.

 

[johanfprins]

There are two answers.

a) Obviously it is experimentally possible to bump iron into copper in this way. This results in some actual resistivity which is a continuous function. Whether or not I can write it down as a simple function, Nature obviously knows what this function is.

b) "it is unlikely"? I can write down functions with this property in my sleep.

Example 1 (continuous f, discontinuous f')
rho = 1 for x<=0
rho = 1-x/0.01 for 0 < x<=0.01
rho = 0 for 0.01 < x

Example 2: (continuous f and f', discontinuous f'')
rho = 1 for x<=0
rho = cos^2(pi*x/0.02) for 0 < x <= 0.01
rho = 0 for 0.01 < x

Example 3: (continuous f, f', f'')

rho = 1 for x<=1
rho = 1 - 10x^3 + 15x^4 - 6x^5 for 0 < x <= 1
rho = 0 for 1 < x

and so on. Once again, Johan, you have very poor judgement of what is "possible" or "likely".

I have explained it very well in my post 1878 that one can only approximate a continuous resistivity field when the free path length S_DC is <<<<<L_C. This makes all your remarks above simple nonsense. And it is even more nonsense when claiming zero resistivity by letting (tau)_C go to infinity; as all the physicists who did reseach on superconductors during the past 80 years, accepted is possible: Only a nincompoop can believe this.

You applied Gauss's Law and found no net charge in the entire copper block. Your choice of Gaussian surface was insensitive to equal and opposite charges on the injection and extraction contacts.

Then you should have specified the volume which you want me to use to apply Gauss' law. You specified a "surface at either interface". That is not specifying a volume as one should when asking somebody else to apply Gauss' law. Owing to your deviousness, which you have displayed time and again on this thread, I decided to choose the volume as I see the problem. So do not now cry about it!

Sure you did---it was your very first response to the iron-copper-iron problem, remember? That's where you got by dropping the gradient term from the divergence.

No! I was still talking about not having enough charge-accumulation to cancel the applied electric-field. I did choose the Gaussian volume as I saw fit since you only talked about Gaussian surfaces at the interfaces and not about a volume across an interface. Why did you not specify the latter? I will tell you: Since you were as usual playing a game and not arguing real physics. I am getting sick and tired of your games!

There's one charge at one interface, the opposite charge at the other interface. Do I need to start over?

No you do not: But as I pointed out above, this is not the question you asked. If you meant only charge at one interface, you would have specified the Gaussian volume not to include the other interface. You did not because you were again trying to be devious as you have been all along on this thread.

Nope, wrong.

Nope! YOU are wrong!

You presented an out-of-equilibrium situation (i.e., before the charge had accumulated) in which there IS an electric field. Before the charge accumulates, when there is a field, that field WILL move charge in a way that reduces the field.

I did not present an out of equilibrium position: When measuring the total current through the iron-copper-iron with an ammeter, you will get a constant current, even though you now have acceleration of charges through the copper all the way from the injection contact to the ejection contact. This will, at best, generate a charge-gradient between the injection contact and the ejection contact; definitely not two opposite charge-sheets at the injection contact and the ejection contact which cancels an applied electric-field that has the same value at every point between the injection contact and the ejection contact.

I presented an equilibrium situation, when the charge is there and there is no field in the center block. The charge is in its equilibrium location, and the field is zero.

This is not possible while a current flows through a material which has charge-carriers that can be accelerated. Your “equilibrium situation” is similar to lifting yourself into the air by pulling on your bootstraps.

The difference between these two situations seems to confuse you. Stick to one, the simplest one. Assume for a moment that we ARE in the equilibrium situation that I described to begin with: zero E field in the superconductor,

"Superconductor" or copper? We were talking about copper

nonzero E field in the iron

Why should I assume the impossible as a starting hypothesis to extrapolate? I am not mad!

, a - charge sheet at the injection contact (it doesn't matter how thick) and a + charge sheet at the extraction (it doesn't matter how thick), a uniform current flow. Do you have that in mind? All of it at once?

Yes.

(Don't jump on my charge sheets while ignoring the fact that E_copper = 0.

E-copper can NEVER be zero: It is impossible within any material which has free charge-carriers that can be accelerated to accumulate enough charge in such charge sheets to cancel an applied electric field between the two charge sheets.

Don't jump on E_copper=0 without ignoring that the charge sheets are there. We're talking about the whole situation I described.)

Exactly, and as I have proved clearly in my post 1878, the electric-field in the copper can never be cancelled to become zero when the charge-carriers can be accelerated by an electric field; even when the charge carriers experienece no resistance to their motion through the copper. .

My claim is that this is a stable equilibrium. Do you know what that means?

Far better than you do.

Do you know how to test an equilibrium? Push one small charge out of position---say, take one electron out of the - sheet and move it partway into the superconductor. What is the force on THIS electron?

This argument does not prove that there can be two charge-sheets which have enough charge in them to cancel an applied electric field while a current is flowing through a material which has charge-carriers which can be accelerated: And this is true for any material which has charge-carriers that can be accelerated. Such a material can only cancel an applied electric field between two contacts when there is NO current flowing between the contacts. My God man; this is primary school physics!

 

[johanfprins]

Originally Posted by johanfprins
Nope! you must have equal and opposite charges at the two opposite boundaries for a polarisation field to form within the copper: Thus, there is no net accumulation of charge within the copper.
Originally Posted by Ziggurat
The charge which accumulates at the boundary because of the current, however, WILL be a net charge, as it must be to change the field throughout the copper.

Nope! A net charge at a single surface cannot on its own cancel any electric-field: You must have opposite charges at two opposite surfaces.

Oh, and you can call the field a "polarisation field" if you want, but it's just an ordinary electric field.

Of course it is an ordinary electric field that forms in response to an applied electric field. Or do you think that there are "non-ordinary" electric fields? REALLY.

 

[ben m]

I have explained it very well in my post 1878 that one can only approximate a continuous resistivity field when the free path length S_DC is <<<<<L_C. This makes all your remarks above simple nonsense.

You confuse yourself so easily, I think you do it on purpose. We only used the resistivities to get the electric fields, remember?

The electric field in the iron is nonzero and proportional to J. Do you disagree?

The electric field in the superconductor is zero. Do you disagree? I can't imagine what else you could possibly do by harping on the Drude-model resistivity.

The change in E field, via Gauss's Law, gives you the nonzero charge density. What law, other than Gauss's, do you use to generate spatially-varying E fields?

 

[Ziggurat]

Of course it is an ordinary electric field that forms in response to an applied electric field. Or do you think that there are "non-ordinary" electric fields? REALLY.

You're the one who called it a "polarization field" and not just an electric field, not me.

 

[johanfprins]

You confuse yourself so easily, I think you do it on purpose.

There is no confusion on my side only deviousness on your side

We only used the resistivities to get the electric fields, remember?

Only in iron and copper for which the relaxation times are small enough so that one can write that J=(rho)*E

The electric field in the iron is nonzero and proportional to J. Do you disagree?

I do not disagree on this since the relaxation time is small enough and I assume that the iron is long enough so that the relaxation-time approximation is valid. If the length of the iron becomes commensurate with the free path length of the charge-carriers, you cannot write that J=(rho)*E anymore, since (rho) can then not be approximated as being a continuous function of position

The electric field in the superconductor is zero. Do you disagree?

No I do not disagree that this is the experimental case. What we are trying to do is to explain why it is zero in a superconductor. This has never been explained by any model to date; except by my model.

I can't imagine what else you could possibly do by harping on the Drude-model resistivity.

Quite clearly you do not know your physics: The London Bros. used the Drude model to claim that the resistivity can be made zero by allowing the relaxation time to go to infinity. This is still regularly quoted in text books, and all the other models after the London Bros. are built on this assumption that the resistivity in a superconductor is zero since the relaxation time is infintely long. This immediately violates the validity of the relaxation time approximation. Furthermore it also means that the charge-carriers must be accelerated through a superconductor in the same manner as electrons are accelerated through a vacuum diode. In the latter case an applied electric field can never be zero EVER!

The change in E field, via Gauss's Law, gives you the nonzero charge density. What law, other than Gauss's, do you use to generate spatially-varying E fields?

You cannot use Gauss' law as a single surface which does not enclose a volume, as you wanted me to do. Gauss' law must enclose a volume and in you original question you talked about a single flat surface at the interface of the copper and the iron. If you had talked about a cylindrical volume enclosing only one interface (assuming that the interface between the copper and the iron is circular) and that the length of the cylinder is much longer on both sides of the interface than the free path lengths within the copper and the iron of the charge-carriers, you would have made sense. But you did not; so as usual you made non-sense.

 

[johanfprins]

You confuse yourself so easily, I think you do it on purpose.

There is no confusion on my side only deviousness on your side

We only used the resistivities to get the electric fields, remember?

Only in iron and copper for which the relaxation times are small enough so that one can write that J=(rho)*E

The electric field in the iron is nonzero and proportional to J. Do you disagree?

I do not disagree on this since the relaxation time is small enough and I assume that the iron is long enough so that the relaxation-time approximation is valid. If the length of the iron becomes commensurate with the free path length of the charge-carriers, you cannot write that J=(rho)*E anymore, since (rho) can then not be approximated as being a continuous function of position

The electric field in the superconductor is zero. Do you disagree?

No I do not disagree that this is the experimental case. What we are trying to do is to explain why it is zero in a superconductor. This has never been explained by any model to date; except by my model.

I can't imagine what else you could possibly do by harping on the Drude-model resistivity.

Quite clearly you do not know your physics: The London Bros. used the Drude model to claim that the resistivity can be made zero by allowing the relaxation time to go to infinity. This is still regularly quoted in text books, and all the other models after the London Bros. are built on this assumption that the resistivity in a superconductor is zero since the relaxation time is infintely long. This immediately violates the validity of the relaxation time approximation. Furthermore it also means that the charge-carriers must be accelerated through a superconductor in the same manner as electrons are accelerated through a vacuum diode. In the latter case an applied electric field can never be zero EVER!

The change in E field, via Gauss's Law, gives you the nonzero charge density. What law, other than Gauss's, do you use to generate spatially-varying E fields?

You cannot use Gauss' law as a single surface which does not enclose a volume, as you wanted me to do. Gauss' law must enclose a volume and in you original question you talked about a single flat surface at the interface of the copper and the iron. If you talked about a cylindrical volume enclosing only one interface (assuming that the interface between the copper and the iron is circular) and the length of the cylinder is much longer on both sides of the interface than the free path lengths within the copper and the iron of the charge-carriers, you would have made sense. But you did not; so as usual you made non-sense.

 

[johanfprins]

You're the one who called it a "polarization field" and not just an electric field, not me.

When opposite charges are overapping and thus cancelling so that there is no electric field outside of these overlapping charges, and one applies a field to these charges so that they separate, a field opposite to the applied field will ensue which will partially cancel the applied electric field. The field in response to the applied electric-field is a real electric field and since it forms in response to an applied electric field it is called a polarisation field. I hope this helps.

 

[ben m]

You cannot use Gauss' law as a single surface which does not enclose a volume, as you wanted me to do.

Johan, the charge sheet is not your Gaussian surface. The charge sheet is your *charge density*, and you are asked to draw a closed surface around it. This has been a basic E&M problem set problem for every physics department sophomore for a century.

http://en.wikipedia.org/wiki/Gaussian_surface#Gaussian_pillbox

Draw a surface that encloses one of the flat sheets.

       _______
       |      | 
=======|==?:::|::::::
=======|==?:::|::::::
=======|==?:::|::::::
=======|==?:::|::::::
=======|==?:::|::::::
       |______|

ETA: so let's try it again. There is a current flowing left to right. You yourself agree that E > 0 in the iron (on the left.) You yourself agree that E=0 in the superconductor (on the right.) Since you could not do it yourself, I've drawn the Gaussian surface for you. Are you able to use Gauss's Law yet? Can you use it to tell me whether or not there is net charge inside the Gaussian surface?

 

[johanfprins]

Johan, the charge sheet is not your Gaussian surface. The charge sheet is your *charge density*, and you are asked to draw a closed surface around it. This has been a basic E&M problem set problem for every physics department sophomore for a century.

http://en.wikipedia.org/wiki/Gaussian_surface#Gaussian_pillbox

Draw a surface that encloses one of the flat sheets.

       _______
       |      | 
=======|==?:::|::::::
=======|==?:::|::::::
=======|==?:::|::::::
=======|==?:::|::::::
=======|==?:::|::::::
       |______|

ETA: so let's try it again. There is a current flowing left to right. You yourself agree that E > 0 in the iron (on the left.) You yourself agree that E=0 in the superconductor (on the right.) Since you could not do it yourself, I've drawn the Gaussian surface for you. Are you able to use Gauss's Law yet? Can you use it to tell me whether or not there is net charge inside the Gaussian surface?

Thanks! At last you have asked the question correctly. Of course, with this construction you can conclude that there is a net charge inside the Gaussian volume: And when doing this for the opposite interface one obtains an equal and opposite net charge-sheet at that surface.

This separation of charges causes an electric-field opposite to the applied electric-field (i.e. a polarisation field); which, however, can never totally cancel the applied electric-field while a constant current I is flowing through the copper: The applied electric field can only be cancelled within the copper, when the same electric-field is applied across the iron-copper-iron sandwich without any current flowing through the copper all.

 

[ben m]

This separation of charges causes an electric-field opposite to the applied electric-field (i.e. a polarisation field); which, however, can never totally cancel the applied electric-field while a constant current I is flowing through the copper: The applied electric field can only be cancelled within the copper, when the same electric-field is applied across the iron-copper-iron sandwich without any current flowing through the copper all.

This is bizarre, Johan. You've got the equation in front of you showing that the E field is totally cancelled when current is flowing.

The E field in the iron is J * rho because current is flowing (rho=resistivity of iron)
The E field in the superconductor (or "copper") is zero because it's a superconductor.
The integral of the electric flux out of the Gaussian surface (of area A) is (-A*J*rho).
Therefore, by Gauss's Law the charge inside the surface is q = -epsilon0*A*J*rho, i.e. it's a sheet charge of surface density lambda=-epsilon0*J*rho.

On the opposite side of the superconductor, we find a sheet of charge with surface density lambda = +epsilon0*J*rho.

What electric field do you expect from these surface charges, taken by themselves?

E=0   E=-J*rho   E=0
   -    <--   +      
   -    <--   +      
   -    <--   +      
   -    <--   +

Oh, look! The excess charges that Gauss's Law tell you are there are exactly the charges needed to cancel the field (+J*rho) that exists outside the superconductor while a current J is flowing.

I really don't understand your objection in the slightest. Do you think that lambda = epsilon0*J*rho is too much charge for some reason---do you think that some smaller charge accumulates and cancels only part of the field? (Why? How much, excactly? What cancels the rest of the field?)

More importantly---did you learn anything from the experience of making a dozen or so basic undergrad E&M mistakes (denying that any field was canceled, forgetting how to take derivatives, denying that step-functions existed, denying that step-functions could be differentiated, doubting that differentiable functions existed, invoking work functions, and confusing the charge-sheet itself with the Gaussian surface) in the process of trying to insult everyone else's knowledge of physics?

 

[johanfprins]

This is bizarre, Johan. You've got the equation in front of you showing that the E field is totally cancelled when current is flowing.

Which equation? Or are you trying to explain it as follows?

The E field in the iron is J * rho because current is flowing (rho=resistivity of iron)

So far OK.

The E field in the superconductor (or "copper") is zero because it's a superconductor.

This the experimental result which you have to explain in order to model superconduction. It is not being explained by saying that is what we measure, and therefore what we measure is what we use as our initial input to explain why the field is zero.

The integral of the electric flux out of the Gaussian surface (of area A) is (-A*J*rho). Therefore, by Gauss's Law the charge inside the surface is q = -epsilon0*A*J*rho, i.e. it's a sheet charge of surface density lambda=-epsilon0*J*rho.
On the opposite side of the superconductor, we find a sheet of charge with surface density lambda = +epsilon0*J*rho.

So far I am with you. This is so, as long as both the iron and copper have high enough resistivities so that their relaxation times are small enough to, on average, allow the use differential operators within them.

What electric field do you expect from these surface charges, taken by themselves?

A polarisation field which partially cancel the applied electric field while there is a current flowing through the copper.

E=0   E=-J*rho   E=0
   -    <--   +      
   -    <--   +      
   -    <--   +      
   -    <--   +

I do not understand your diagram here: Where is E supposed to be zero? E can NEVER be zero while a current flows through a material which has free charge-carriers that can be accelerated; even when these charger-carriers do not scatter while moving through the material from the injection contact to the target contact.

Why on earth will E become zero in any material which has charge carriers that can be accelerated? You say that one has charge-carriers within a superconductor that are free and can be accelerated. If this were so E would never be equal to zero as we experimentally measure that it is.

Before we proceed any further, please, will you be kind enough to answer the two following questions:

1. Can the accumulation of charge in the copper become high enough to cancel the
applied electric-field within the copper? Yes or no?

2. If yes: Why has it never been observed in copper?
If no: Why will it happen within a superconductor if a superconductor has, just
like copper, free charge-carriers that can be accelerated?

In the mean time I have to attend to a few urgent issues; but am looking forward to proceed further with this discussion after you have answered these questions

 

[ben m]

So far I am with you. This is so, as long as both the iron and copper have high enough resistivities so that their relaxation times are small enough to, on average, allow the use differential operators within them.

Nope. Go back. We're talking about Gauss's Law---look it up, do you see resistivity in there? No, just field. If you know that E=0 at some location, you know enough to calculate the flux through a Gaussian surface at that location. If you know E=J.rho at some other location, likewise. That's what we're talking about.

Why are you avoiding this? You claim to know the E fields, but you refuse to apply Gauss's Law because the long-relaxation-times problem prevents you from knowing the E field? What the heck?

(Let me double-check: Don't forget that we have replaced the copper with a hypothetical zero-resistivity material, like a superconductor.)

I do not understand your diagram here: Where is E supposed to be zero? E can NEVER be zero while a current flows through a material which has free charge-carriers that can be accelerated; even when these charger-carriers do not scatter while moving through the material from the injection contact to the target contact.

Sorry, Johan, you keep saying that no matter what Gauss's Law says.

E is zero inside this block of superconductor, we're trying to use E&M to figure out what laws of E&M cause it to be zero. Stay focused.

The point of this discussion is to show that zero-resistivity, with no other physics assumptions, is perfectly sufficient to get the zero-E-field "perfect cancellation" conditions from normal E&M, even when a current is flowing. Understand? Zero-E-field follows from zero-resistivity in ordinary E&M.

Why on earth will E become zero in any material which has charge carriers that can be accelerated? You say that one has charge-carriers within a superconductor that are free and can be accelerated. If this were so E would never be equal to zero as we experimentally measure that it is.

E becomes zero in a material in which excess charge density has accumulated at the boundaries in a way that cancels out the field.

This charge, at the boundaries, is perfectly happy coexisting with moving charges that carry a current.

This charge does not accelerate through the E=0 region. Why would it? E=0. Can you remember both of those facts at the same time? E=0 AND charge at the boundaries. E=0 AND charge at the boundaries. Don't tell me again "but the E field will accelerate the charge ..." as though you'd forgotten that E=0. Don't tell me "E cannot be zero" as though you'd forgotten that the charge at the boundaries make it zero.

If you ever get around to understanding the basics, we will be able to prove, again using the laws of E&M, that excess charge "sitting" at the boundaries is the equilibrium state and the charge indeed has no forces trying to make it run away.

1. Can the accumulation of charge in the copper become high enough to cancel the
applied electric-field within the copper? Yes or no?

We're back at ordinary copper, with ordinary copper resistivity? You've gotten the equations yourself, Johan. The boundary between iron and (ordinary) copper accumulates a sheet charge of density epsilon0*J*(rho_iron - rho_copper). This reduces the E field from the external field of J*rho_iron to the internal field of J*rho_copper. It does not reduce it to zero.

If you ever getting around to equilibria, it is easy to prove as usual that this is the stable equilibrium---if someone comes in and magically reduces the sheet charge below epsilon0*J*(rho_iron - rho_copper), the laws of E&M work to increase the sheet charge back up. If someone comes along and increases it above epsilon0*J*(rho_iron - rho_copper), the laws of E&M work to reduce it back to equilibrium.

If no: Why will it happen within a superconductor if a superconductor has, just
like copper, free charge-carriers that can be accelerated?

The superconductor does the same thing as the copper EXCEPT that the sheet charge is larger (epsilon0*J*(rho_iron - zero) instead of epsilon0*J*(rho_iron - rho_copper)) and that its fields cancel out ALL of the external field.

Again, the excess charge carriers are at a boundary. There is no force trying to accelerate them away. If they are displaced, they come back. Notice that the excess charge carriers are not all the charge carriers---there are plenty of other charges in the net-neutral bath of charge carriers which carry a current without stopping at the boundary.

 

[ben m]

CASE 1: iron/superconductor/iron

External applied field (from battery/power supply/etc alone)

   E = E0       E=E0       E=E0
 --->    ---->    ----->   ---->  ----> 
 --->    ---->    ----->   ---->  ----> 
 --->    ---->    ----->   ---->  ----> 
 --->    ---->    ----->   ---->  ----> 
 --->    ---->    ----->   ---->  ----> 


Field due to charge sheets alone
         
   E = 0         E = -E0     E=0
            -    <-----   +      
            -    <-----   +      
            -    <-----   +      
            -    <-----   +      
            -    <-----   +      

total field (both external supply AND charge sheets)

   E = E0       E=0       E=E0
 ---> --->  -             + ----->   ----> 
 ---> --->  -             + ----->   ----> 
 ---> --->  -             + ----->   ----> 
 ---> --->  -             + ----->   ----> 
 ---> --->  -             + ----->   ---->

CASE 2: iron/copper/iron. For concreteness let's say rho_copper = 1/2 rho_iron.

External field (from battery/power supply/etc alone)

   E = E0       E=E0       E=E0
 --->    ---->    ----->   ---->  ----> 
 --->    ---->    ----->   ---->  ----> 
 --->    ---->    ----->   ---->  ----> 
 --->    ---->    ----->   ---->  ----> 
 --->    ---->    ----->   ---->  ----> 


Field due to charge sheets alone
         
   E = 0         E = -E0/2     E=0
            -    <--    +      
                 <--         
            -    <--    +      
                 <--          
            -    <--    +      

total field (both external supply AND charge sheets)

   E = E0       E=E0/2       E=E0
 ---> --->  -     -->     + ----->   ----> 
 ---> --->        -->       ----->   ----> 
 ---> --->  -     -->     + ----->   ----> 
 ---> --->        -->       ----->   ----> 
 ---> --->  -     -->     + ----->   ---->

Both of these configurations (a) obey Maxwell's Equations and (b) have well-behaved, constant, equilibrium current densities.

 

[marplots]

Question from the cheap seats --

If you form a superconductor by attaching two different superconducting materials to each other (maybe the sandwich version mentioned earlier), are there effects at the junction (where the junction can be as intimate as possible in the "thought version").

Does the answer to this question help distinguish different models/modes for superconduction?

 

[johanfprins]

Ben’s post 1897

Nope. Go back. We're talking about Gauss's Law---look it up, do you see resistivity in there? No, just field.

This is exactly what I have been saying all along. It is you , Sol and Ziggurat who claimed that one can calculate the gradient of rho as if rho is really a continuous resistivity-function; even right up to the interface: This is of course physically impossible nonsense.

If you know that E=0 at some location, you know enough to calculate the flux through a Gaussian surface at that location.

We are arguing whether E=0 is possible when a current flows through a material which has free charge-carriers that can be accelerated. We are not arguing that we “know” E is actually equal to zero within such a material; since we do not know that this is possible at all. Before this question is settled, it is impossible to know that E is actually zero. So your argument is nonsensical: As usual! The incontrovertible physics-fact remains that when a material has free charge-carriers that can be accelerated by an electric-field, and a current is flowing through such a material, the flux through any accumulated charge at the interfaces can never be such that E=0 within the material while a current is flowing; no matter what the “resistivity” of the material is.

If you know E=J.rho at some other location, likewise. That's what we're talking about.

Let me try again: Assume that the iron blocks are large (long) enough so that you can use the approximation that within the iron blocks that E_I=J*(rho)_I; and you have a “superconductor” which according to your wrong assumption, supposedly can super-conduct even though it has free charge-carriers that can be accelerated. For what physical reason would you have that the electric field within such a hypothetical “superconductor” is zero? I have asked you this before: And I am asking you again to give a reason why!

Why are you avoiding this?

I am NOT avoiding anything when I point out to you that you cannot have that E=0 while a current is flowing through any conductor which has free charge-carriers that can be accelerated.

You claim to know the E fields, but you refuse to apply Gauss's Law because the long-relaxation-times problem prevents you from knowing the E field?

That is not what I have said. I am applying Gauss’ law correctly; and I am telling you that if a material has free charge-carriers that can be accelerated, the flux through an accumulated contact-charge can never cancel an applied electric field on any side of such a charged-interface while a current is flowing through it.

(Let me double-check: Don't forget that we have replaced the copper with a hypothetical zero-resistivity material, like a superconductor.)

I have not forgotten this; This is what you have claimed; but without telling anybody what you define as zero-resistivity: You have, in addition added that the superconductor has free charge-carriers that can be accelerated. I am telling you that this is a contradiction in terms; since a material which has free charge-carriers that can be a accelerated can never totally cancel an applied electric-field within it while a current is flowing through it: And since an applied electric-field is cancelled within a superconductor while a current is flowing through it, this means that a material which has free charge-carriers that can be accelerated can never be a superconductor ever. Get it?!

Sorry, Johan, you keep saying that no matter what Gauss's Law says.
E is zero inside this block of superconductor, we're trying to use E&M to figure out what laws of E&M cause it to be zero. Stay focused.

You are the one who is not focused on what I am telling you: An applied electric-field within any material (typically a metal) which has free charge-carriers that can be accelerated, can only be totally cancelled by charge accumulation at opposite surfaces when there is no current flowing through such a material: NEVER while a current is flowing through such a material; since when a current is flowing the charges cannot accumulate to a high enough density to totally cancel the applied electric field completely. Cancellation can only be partial when a current is flowing.

The point of this discussion is to show that zero-resistivity,

First define for me what is zero resistivity. Resistivity is given for a material with free charge-carriers that can be accelerated, by:

(rho)=m/(N*q²*(tau))

Since you claim that a superconductor has charge-carriers that can be accelerated, can you tell me which of these parameters change to cause (rho) to be zero within a superconductor? PLEASE!!!

with no other physics assumptions,

Not true. You have made the assumption that there are free charge-carriers within a superconductor that can be accelerated by an electric-field. So there is an assumption! But it is totally wrong!!

In fact, both my model (which you refuse to even read) and the BCS model (which you apparently (?) accept as valid) concur on the fact that there are no, or very few, “free” charge-carriers which can be accelerated when a material is in the superconducting state. Assuming that you will accept an argument based on the BCS model, let us look at your physically impossible claim that the charge-carriers transporting a super-current through a superconductor are “free” charge-carriers which can be accelerated when there is an electric-field present:

According to the BCS model, the material is superconducting when there is an energy gap 2*(DELTA) within the electron-energy spectrum. Above the gap there are “free-electron” states, and below the gap you have a band “filled to the brim” with electrons which all supposedly formed Cooper pairs. The Fermi-level is then supposedly “pinned” halfway between the higher-energy band of “free-electron” states and the filled band of electrons containing the Cooper pairs.

After the superconductor phase transition has occurred, the density of the "free electrons" within the higher energy band is negligible, and these charge-carriers can thus not convey much of a current, even if there could be an electric-field present. Since the lower energy band is filled to the brim with electrons it also has no, or very few, “free” charge-carriers, like for example holes, which can be accelerated. This means that there are essentially no “free” charge-carriers within a superconductor that can be accelerated by an electric field, as you have assumed is possible for all the charge-carriers that transport a super-current. In fact, the BCS energy gap with the Fermi-level at the centre of the gap, will act as a complete insulator if it is required to transport a current as if it has free charge-carriers that can be accelerated.

Something else is responsible for charge-transfer through a superconductor than “free” charge-carriers. In the BCS theory it is claimed that the current is supposedly driven by the gradient of the phase-angle of a “Cooper pair condensate”; which eventually leads to the conclusion that the gradient of a scalar field can be a circular vector field: The latter is obvious poppycock!! Nonetheless, in both my model, and the BCS model, a superconducting current does not, and cannot, relate to “free” charge carriers that can be accelerated by an electric-field.

is perfectly sufficient to get the zero-E-field "perfect cancellation" conditions from normal E&M, even when a current is flowing.

Not so! A zero E-field is impossible while a current is flowing through any material which has free charge-carriers that can be accelerated by an applied electric-field.

Understand? Zero-E-field follows from zero-resistivity in ordinary E&M.

From what does zero resistivity follow: From zero electric field? Which one determines which one: The classical chicken and egg problem: The chicken exists because there is an egg, and the egg exists because there is a chicken: Or, the wall is black because it is not white and it is non-white because it is black. Circular reasoning is clearly your special forte! I am willing to accept that zero electric field follows from “zero-resistivity” provided you can define (or model) zero resistivity for me in terms of the intrinsic form of Ohm's law [E=(rho)*E]; which you are invoking here to claim that zero electric-field follows from zero resistivity (or the other way around?): Unfortunately again reasoning in your usual clueless fashion.

E becomes zero in a material in which excess charge density has accumulated at the boundaries in a way that cancels out the field.

In a material which has free charge-carriers that can be accelerated, the applied electric-field cannot be totally cancelled by accumulated charges at the interfaces while a current is flowing through such a the material. This is simple kindergarten physics!

This charge, at the boundaries, is perfectly happy coexisting with moving charges that carry a current.

So what? Although this charge is happy coexisting with moving charges, the accumulation of charges at the interfaces can never be high enough to TOTALLY cancel the applied electric field when a current flows through a material which has free charge-carriers that can be accelerated.

This charge does not accelerate through the E=0 region. Why would it? E=0. Can you remember both of those facts at the same time? E=0 AND charge at the boundaries. E=0 AND charge at the boundaries.

I agree that charge at the boundaries is there whether a current is flowing or not flowing. BUT only when a current is not flowing can there be enough of this charge accumulation to totally cancel the applied electric field within a material which has free charge-carriers that can be accelerated: When a current is, however, flowing, the charge accumulation can never be large enough to totally cancel the applied electric field in such a material

Don't tell me again "but the E field will accelerate the charge ..."

When a current flows, a partially cancelled applied electric-field does always accelerate the charge-carriers within a material which has free charge carriers that can be accelerated.

as though you'd forgotten that E=0.

How can I forget something that has not been proved to be so? E can never be totally cancelled within a conductor (which has free charge-carriers that can be accelerated) while a current is flowing through the material: The applied electric-field can only be reduced while a current is flowing through such a material, but NEVER be totally cancelled, no matter whether the charge-carriers dissipate energy during their motion through the material or do not dissipate any energy during this motion.

Don't tell me "E cannot be zero" as though you'd forgotten that the charge at the boundaries make it zero.

E can only be made zero (by the charge-accumulation at the boundaries) within a material which has free charge-carriers that can be accelerated when there is no current flowing through such a material.

If you ever get around to understanding the basics, we will be able to prove, again using the laws of E&M, that excess charge "sitting" at the boundaries is the equilibrium state and the charge indeed has no forces trying to make it run away.

I have never stated that there are “forces trying to make it run away”. The charge-accumulation is there, even when an equilibrium-current is flowing through a material which has free charge-carriers that can be accelerated, but while this current is flowing, these charges can never accumulate to a high enough density so that they can totally cancel an applied electric-field within such a material. They can only partially cancel the applied electric-field while a current is flowing; no matter what the “resistivity” of the material is.

We're back at ordinary copper, with ordinary copper resistivity? You've gotten the equations yourself, Johan. The boundary between iron and (ordinary) copper accumulates a sheet charge of density epsilon0*J*(rho_iron - rho_copper). This reduces the E field from the external field of J*rho_iron to the internal field of J*rho_copper. It does not reduce it to zero.

I am in agreement with you here since I have never said anything else. Of course this is subject to the condition that the resistivity (rho) can be considered as a continuous function; which is not possible for a conductor of length L unless the scattering distance s_D is much, much smaller than L: When the average scattering interval increases to very large values, compared to the length L, this argument fails completely.

If you ever getting around to equilibria, it is easy to prove as usual that this is the stable equilibrium---if someone comes in and magically reduces the sheet charge below epsilon0*J*(rho_iron - rho_copper), the laws of E&M work to increase the sheet charge back up. If someone comes along and increases it above epsilon0*J*(rho_iron - rho_copper), the laws of E&M work to reduce it back to equilibrium.

Have I ever stated anything opposite to this statement anywhere? I have not: So why do make this statement?

The superconductor does the same thing as the copper EXCEPT that the sheet charge is larger (epsilon0*J*(rho_iron - zero instead of epsilon0*J*(rho_iron - rho_copper)) and that its fields cancel out ALL of the external field.

WRONG AS USUAL! If your supposed "superconductor" has free charge-carriers that can be accelerated, and a current flows through your supposed "superconductor" having such charge-carriers, there can never accumulate enough charges at the interfaces to totally cancel the electric field within your supposed "superconductor". This is not possible in any material which has free charge-carriers that can be accelerated, no matter whether these charge-carriers, which are transporting the current, experience resistance to their motion through the material or move through the material without dissipating any energy within the material.

Again, the excess charge carriers are at a boundary. There is no force trying to accelerate them away.

I have never stated that there is such a force after equilibrium has been reached

If they are displaced, they come back

Have I ever stated anything else somewhere?

Notice that the excess charge carriers are not all the charge carriers---there are plenty of other charges in the net-neutral bath of charge carriers which carry a current without stopping at the boundary.

Again, I have never stated that the accumulated charges are all the charges. Why are you bringing up arguments which I have never used? Just to confuse the issue as you have done all along on this thread?