I have never insulted you, johan. I have said you are wrong, because I believe you are wrong, but I have not once insulted you. And I will continue to not insult you.
Thanks. I probably confused some of Sol Invictus's comments with yours. Sol is so insulting that he even wrote that I must leave physics to the "real physicists". In this process he did not just insult me but also the universities at which I have studied as well as my professors. And he does this while hiding behind anonymity. I find such behavior despicable; but have had to become used to it during the past ten years from the main stream physicists. I note that you did not advise Sol that he owes me an apology; so you must be finding his behavior acceptable?
No. The limitations of R = V/I is not that it doesn't handle zero scattering cases, but that it doesn't handle non-linear current vs. voltage, or changing currents.
The latter also. But if there is no scattering of the charge-carriers within a normally conducting material, the current will not settle down having an average constant drift speed; and Ohm's law is only valid when you have a constant average drift speed.
Use Drude's equation in which resistivity is approximated by an average drift speed and a relaxation time. Do not be lazy like the London Brothers were, who put the resistivity term equal to zero without first integrating this equation; and thus developed gobblygoog physics.
First solve this equation (ignoring any contact resistances because they are not relevant as far as the material's resistivity is concerned). Any first year student should be able to do this. Now plot the current as a function of time for different resistivities, from very high to zero. You will find that for a high resistivity the current increases and then settles down at an equilibrium value:
Only within this region is Ohm's law valid. As the resistivity decreases one finds that it takes longer and longer times for the current to settle down to reach the conditions under which Ohm's law is valid. When you make the resistivity zero, the current keeps on increasing to infinity: It never settles down so that Ohm's law is not valid for this "zero resistivity".
But the zero scattering case works out perfectly as a zero resistance case, without any need for adjustment. It's exactly the behavior you would expect.
I have just demonstrated to you that Ohm's law is
not valid for zero scattering. The fact that it seems to be valid for superconduction,
does not explain superconduction, but presents the riddle that must be solved before one can understand superconduction. Why does it seem that Ohm's law apply for "zero resistivity"
in this case while it does not apply for "zero resistivity" when you have normal conduction; as I have just demonstrated by solving Drude's equation?
Indeed, it is not. You also need the Meissner effect, which cannot be explained by the absence of scattering alone. Without the Meissner effect, but just zero scattering, you would have an ideal conductor, not a superconductor.
Agree fully.
But no scattering would mean zero resistance.
This is why I asked you to define zero resistivity; since in an ideal conductor this cannot be defined by using Ohm's law; as I have just now argued by using Drude's famous equation.
In your scenario, not only are the charge carriers accelerating, the current is increasing. You have not established an equilibrium situation.
It cannot establish within an "ideal" conductor as I have just now deduced from Drude's equation: The only reason why it will establish is the effect of contact-resistances: Without them, no equilibrium state is possible.
If you let your system come to equilibrium, you would indeed find zero voltage and zero resistance across the scatterless region, as the current would have increased until the entire voltage drop occurred in the regions which still have scattering.
It is only the contact resistances that cause equilibrium in this case, and then you end up accelerating the charge-carriers from one contact to the other which requires a voltage drop, and demands energy dissipation within the target contact. Within a superconductor there is no acceleration and no energy dissipation within the target contact.
Ben described this in detail earlier as it applies to acceleration of charge carriers around a bent wire.
And I then pointed out that when you accelerate charges around a ring, you have a mini accelerator and
must then emit cyclotron, or synchrotron radiation.
You are correct that when charge carriers are accelerated, the resultant electromagnetic field creates back-action on the charge carrier, and the charge carrier exchanges energy with its surroundings. There's a simple name for the macroscopic effect this produces: inductance.
You keep on trying to use "inductance" for a DC current. It does not apply. Even Maxwell's equations are in accord with that.
But you are wrong that this means charge carriers in a superconductor cannot accelerate. They most certainly can and do. There is no other way to change the current in a superconductor except to accelerate charge carriers.
If they accelerate you must measure a voltage: It is, however, the defining discovery that there cannot be such a voltage which Onnes used to identify superconduction. So you must be wrong.
The only way in which a current through a superconductor between two contcats can be increased is to increase the rate at which charge-carriers are being injected. In the case of a circular current it increases to cancel the increase in applied magnetic field which otherwise would have been within the superconducting ring. In both cases acceleration of the charges cannot occur since an electric-field is cancelled by the polarization of the charge-carriers; thus preventing the electric-field from accelerating the charge-carriers
But there is. That's how you change the current in a superconductor. That's how you make the current bend.
If an electric field were present you would have measured a voltage. Onnes's discovery that a voltage does not manifest over two points to superconductor while a current is flowing is incontrovertible proof that the charge-carriers are not accelerated by an electric field within a superconductor. Please stop contradicting impeccable experimental evidence.
But we know from direct observation of superconductors that this is not true.
What you think is "direct observation of superconductors" is a misinterpretation of what you are seeing. If you cannot measure a voltage, there cannot be acceleration: If this could be true, Newton's lwas would be totally invalid.
Ben explained this one quite nicely.
Ben is wrong: If he were correct that acceleration of charges without scattering cannot generate EM we would not have had synchrotron radiation. And I can assure that we do have synchrotron radiation.
Nope. If the current through a circular wire has uniform current density, then the magnetic field inside the wire will vary linearly with radius from the center. So only the single point at the center will have B = 0, everywhere else within the wire will have nonzero field.
I agree I made a booboo on this one by not being very clear about what I was trying to say when it comes to a superconductor and the presence of a magnetic field under these conditions. What I was trying to say, is that
if there is any net magnetic field present within any region of such a material, that region cannot be superconducting. This can be seen as folows: Take a thinnish superconducting strip-layer and increase an applied magnetic field perpendicular to its surface. As soon as the magnetic field penetrates right through the material, superconduction
stops.
What the main stream scientists are arguing is that a superconducting current flows through a surface layer (at a penetration depth lambda) in which the magnetic field is not cancelled. Now if this is so, why does superconduction stop in its tracks when a magnetic field is present within the whole superconducting layer. It just does not make experimental sense.
For a superconductor, the current is a surface current, but that surface current is not infinitely thin, it has depth. And because of that depth, the magnetic field will also penetrate into the superconductor, to basically the same depth as the current does.
This can obviously not be so; since the presence of a net magnetic field
always totally quenches superconduction. So what happens when you increase an externally applied magnetic field, it penetrates the SC material, but is also absorbed so that it decays from a maximum at the surface to become zero at the end of a penetration depth lambda.
Since there
is a magnetic field energy within this layer, this region is not superconducting anymore; and the current must flow beneath it, within the region where there is no magnetic field. Once the magnetic field becomes high enough that it "punches through" the superconductor, there is
no more superconducting material left within which a current can flow; and superconduction becomes impossible; just as is experimentally observed.
According to Maxwell's equations the only possible way to exclude a magnetic field from the current-carrying region is to make the current carrying region have zero volume. Which is not possible in the real world.
This is probably one of the reasons why the mechanism responsible for absorbing an applied magnetic field has
nothing to do with Maxwell's equation at all.
