Interpretation and application of Poynting's theorem?

harrylin

OK another side issue (and certainly his definition happens to be the one that relates to your claim about electric field), but thanks for the link! I found and next explained why the "perfect conductor" conditions do not apply to conductors in a circulating E-field and you denied that - that's the status quo. So, grab a beer or go on a hike like I will now.

Q-reeus

I honestly have no idea what you mean here. What exactly am I denying? Provide some detailed example please. I see someone has stepped in with a nay line on KVL. Would like to see the logic behind it, and just how many seconds it takes me to refute any supposed counterexample to validity of KVL.

harrylin

Sorry, please take those matters out of this thread.

Q-reeus

I need to know, given you say I am denying something presumably true, just exactly what that thing is! So please - that has to be cleared up here and now. What have I denied that is true?

harrylin

I perceived several subtly wrong things (mostly yours IMHO) following my post #23, despite the inclusion of much literature and courses. Thus I stick to my conclusion in post #49 that we had to give up on it and I certainly won't come back to it here.
Note that -to my regret- I now found a video (no.19) with Lewin first inaccurately stating that "the emf generated must remain zero" in a superconductor, but next correctly stating that eddy currents are induced. Anyway, that's not my problem and neither does it matter for this thread - as long as everyone agrees that currents can be induced!

If you want, you could start a thread on application of conservative field theory results on non-conservative electric fields or force-less changing electron speed (but don't count on me!).

Q-reeus

Harald - no sweat. What I will be interested to follow is your view that Poynting theorem is wrong. You may be surprised to know I have certain misgivings also, but I doubt they coincide with your own. Anyway, serve it up please!
Pass!

harrylin

Hehe I was going to (it's ready) - but now I got second thoughts. Regretfully for this thread, I contemplate to first do something more useful with my write-up.

harrylin

That may be so, but I found that such textbooks simply cite Poynting on this:
https://en.wikisource.org/wiki/On_th...magnetic_Field

He did however add the precision that it "expresses the energy transformed by the conductor into heat, chemical energy, and so on".

Darwin123

I think the writer is technically correct the way he said it. However, the thought expressed is a incomplete.
When the electric current satisfies the original Ohm's Law, where conductivity is always a real quantity, then in some sense E.j is the rate at which internal energy is changing. "Internal energy" is often referred to as "heat", although this is inconsistent with the way the word "heat" is used in the laws of thermodynamics.
A reason that this thought is incomplete is that not all electric currents satisfy Ohms Law. Here is an example. Suppose one had an object which was an insulator. and the center of the insulator was electrically charged. The object is immersed in salt water. When I say insulator, I mean that it is an insulator both electrically an thermally. Therefore, electrical current can't pass through the object. The object can't contain its own internal energy.
A potential difference is applied across the tank which contains the charged object. A constant electric field is applied both to the salt water and the object. The electric field is applied to both the ions in the water and the insulating object.
The electric current passing through the salt water may satisfy Ohm's Law. I don't think it does precisely due to electrolytic chemistry. However, I hypothesize the the current passing through the salt water satisfies Ohm's Law where the salt water has a constant conductivity.
The electric field applies a force to the insulated object. Therefore, the insulated object moves through the water. I hypothesize that the object was initially stationary. The velocity of the object is small enough that viscosity doesn't play a role. The object accelerates in response to the electric field.
There are two different types of electric current here. The current that passes through the salt water and the current caused by the moving charge density in the center of the object.
E.j in the salt water probably does turn into internal energy of the water. However, the insulated object is acting like any electrically charge body. The movement of the object doesn't immediately turn into internal energy. Some of E.j goes into the kinetic energy of the insulating object.
So the part of the current that satisfies the original Ohm's law really does heat the water, in the sense of internal energy. Part of the current that doesn't satisfy Ohm's Law turns into kinetic energy. So what happened?
Poynting's theorem includes kinetic energy. However, it does not discriminate between the part of the kinetic energy that is in the internal energy, and the part of the kinetic energy that is macroscopic. So the decision on how to partition the kinetic energy has to be made by the constitutive equations and the force laws.
Conductivity includes information on the microscopic states of the salt water. Conductivity is a macroscopic property that is merely an ensemble average of microscopic properties. So in a sense, conductivity is defined in terms of the internal energy. So any time you use a conductivity as a parameter, you are deciding what part of the kinetic energy is internal energy. The assignment of conductivity is part of the definition of internal energy.
The insulated object has no internal energy. The most important parameter with regards to the insulating object is the center of mass. So the kinetic energy of the insulating object is primarily a macroscopic quantity. So the kinetic energy of the insulating object can not be part of the internal energy.
The rate at which the insulated object is gaining kinetic energy is determined by the Lorentz force law. Applying the Lorentz force law to the insulating object implies a length scale. Large objects are not part of the conductivity. Large objects by definition can be characterized by the Lorentz force law. So Ohm's Law and the Lorentz force law are basically constitutive equations that imply a length scale.
There has to be a length scale that determines how the kinetic energy is partitioned. The constitutive parameters implicitly contain the length scale.
Maybe in our discussion we should discriminate between macroscopic kinetic energy and microscopic kinetic energy. Conductivity tells us how fast the microscopic kinetic energy is changing. However, the Lorentz force law tells us how the macroscopic kinetic energy is changing.
Poynting's theorem has no length scale. It has no thermodynamics. In a sense, it has no "heat". Extra hypotheses have to be thrown in if you want a meaningful analysis of "heat".