Originally Posted by johanfprins
It seems that we have been arguing past each other since my only argument was that the divergence cannot be caused by the static accumulation of the charge-carriers. If I have been misunderstood because I have been unclear on this, then I do apologise. I hope that my viewpoint is now clear.
Your "only argument"? You have been "misunderstood" and "unclear"?
We must go back to the history of this argument: You claimed that when one switches on a voltage across a circuit containing a superconducting element, there is an initial voltage across the superconductor which accelerates the charge-carriers within the superconductor; and that during this process of acceleration these charge-carriers are being trapped at the one interface, thus leaving positive charges behind at the other interface, so that eventually these accumulated, stationary, trapped charge-carriers totally cancel the voltage across the superconductor.
I have pointed out to you that it is
not possible for charge-carriers which can be accelerated to accumulate to a high enough density so that they can totally cancel the applied electric-field while a current keeps on flowing. And that such a cancellation of the applied electric-field is only possible when there is
no current flowing through the interfaces to a conductor.
You then came with your iron-copper-iron device and claimed that the change in electric field when passing from the iron into the copper or vice versa is a divergence that can
only be explained in terms of Gauss’ law, and which thus requires the accumulation of negative charge-carriers when they flow from the copper into the iron. Since I have not encountered this argument before, it means that you have placed me on a learning curve; and when on a learning curve it is more possible to make mistakes.
Nonetheless, I argued that even if such an accumulation were to be possible, this accumulation can never be high enough to totally cancel an applied electric field. After further thought I came to the conclusion that the charge-carriers cannot accumulate at the interface
at all since the increase in energy required for this to occur will be too high. I thus started arguing that the "divergence" you calculated by using a Gauss-volume across the interface cannot be caused by an accumulation of charge-carriers at the interface. The following statement must thus be seen within this context:
Originally Posted by johanfprins i.e:
http://www.internationalskeptics.com/forums/showpost.php...postcount=1843
The divergence of an applied conservative electric field while a current is flowing is ALWAYS ZERO.
I do not deny that the electric flux as calculated changes, but I do not believe that this "divergence" is caused by an accumulation of charge-carriers; and therefore it cannot be explained in terms of Gauss’ law. Thus, my post means that
in terms of Gauss’ law “the divergence of an applied conservative electric field while a current is flowing is ALWAYS ZERO”.
Clear as a bell. As of eight pages ago, you were perfectly clear about your belief that the divergence was itself zero. You have now changed this belief because Sol, Zig, and I were patient enough to ignore your insults and walk you five times through the derivation.
I decided to change my approach since it became clear that your thoughts were so ossified that you refused to even try to understand my argument. Thus, I decided to first convince you that the change in electric field is not caused by charge-carriers becoming immobile and being trapped at an interface: Leaving the possibility of “dynamic” accumulation as a dangling carrot in front of your noses.
It's incredibly annoying; you have now erased the memory of this walkthrough, and twisted it into "I knew all along that Gauss's Law applied to this interface accumulation of non-free charges."
This is proof that you went for the carrot. And I succeeded in getting you to acknowledge that the charge-carriers do not become immobile and trapped at the interface (see your post 2128 and posts following this post).
No you didn't, you made it up about two pages ago after one of your previous made-up objections collapsed. Again.
Correct, I deliberately created the impression that “I knew all along that Gauss’ law…..etc.”; and you took the bait.
I will now demonstrate to you that charge-carriers can also not “dynamically” accumulate at such an interface: Assume that one has a copper-element with length L and cross-sectional area A forming an interface with an iron element with length L and cross-sectional area A, and you switch on a voltage V across the copper-iron.
If for some reason the applied electric-field E were to be the same within the copper and the iron (i.e. the voltage across both of them equal to V/L) the currents through them will be different owing to the fact that
RCU is smaller than
RIR. Thus:
I
CU =(V/L)/
RCU>I
IR=(V/L)/
RIR
This means that more charge-carriers are now flowing into the interface than flowing out of the interface:
There will thus be a “dynamic” accumulation of charge-carriers; and this accumulation is actually caused by the fact that there is no “divergence” of the electric-field through the interface:
However, we know that the electric field does change when going through the barrier so that the voltage across the copper is V
CU and across the iron is V
IR where the total voltage V is the sum of these two voltages. In this case one has that:
I
CU =V
CU/
RCU=I
IR=V
IR/
RIR
This means that
the same amount of charge-carriers are flowing into the interface and out of the interface:
There will thus be NO “dynamic” accumulation of charge-carriers; and this absence of charge-carrier accumulation is responsible for the change in electric-field through the interface: The latter change in electric field can thus not be a divergence caused by Gauss’ law; which requires an accumulation of charge-carriers as you all have consistently claimed on this thread: It is caused by just the opposite; namely the requirement that there can be no accumulation of charge-carriers within the interface.