Interpretation and application of Poynting's theorem?

[harrylin]

[..] Yes It is the applied E field (owing to relative motion of other magnet in our preferred scenario) that drives the current, but equally it is the ramping current that creates the back emf exactly cancelling applied E. [..] where is the conflict?

Electrons cannot be driven by a zero field; if in the loop E=0, there can't be the necessary decrease in current for the decrease in magnetic field energy.

For a perfect conductor - and that is the necessary model for an Amperian loop, the necessary boundary condition is zero tangent component of E at the surface or interior. [..]

I don't know what you mean with tangent, but here you seem to reproduce my mistake.

Cheers,
Harald

 

[Q-reeus]

Electrons cannot be driven by a zero field; if in the loop E=0, there can't be the necessary decrease in current for the decrease in magnetic field energy.

I don't know what you mean with tangent, but here you seem to reproduce my mistake.

Cheers,
Harald

As you wish Harald ([STRIKE]btw, should that be two r's - I've forgotten[/STRIKE] - oh, I see your signature has returned and answered that one!). You may however like to grab some popcorn, or a beer, and just watch this show
When done, please come back and tell me what you conclude. That or grab the lecturers address and hound him for his ignorance!

 

[harrylin]

[..] just watch this show
When done, please come back and tell me what you conclude.[..]

Hehe I watched it, and indeed I was surprised to hear him start with such an absolute statement, and to repeat it as a mantra. It works for his topics of transmission lines and transformers, but even then not perfectly well. For example, I wonder if ever one of those puzzled looking students asked him how there can be local accumulations and depletions of electrons in the wires without any E-fields. :tongue2:

IMHO it is an over-generalisation based on EM shielding: https://en.wikipedia.org/wiki/Electromagnetic_shielding
In the case of a closed wire loop there is no boundary and thus no charge accumulation or reflection along the loop, and thus there can also be no shielding along that direction.

Now, to get back to the topic: I asked you how you explain a reducing current without a force to reduce that current.

 

[harrylin]

[..] The "Ohmic heating rate" is the rate at which the internal energy of the system is changing. [..] The energy transferred from EM field to matter is work. When work is done on the resistor, the internal energy of the resistor is changing.
If the resistor is kept at a constant temperature, heat conduction and work are being done at nearly the same time. The energy transferred by E.j is work, which is immediately converted into internal energy. This internal energy is immediately conducted out of the resistor. [..] The word heat sometimes means entropy time temperature, and sometimes means internal energy. You were fooled by the phrase "Ohmic heating rate". They really meant "rate that the internal energy would be changing in there was no thermal conduction." [..] "Ohmic heating" is sloppy physics jargon which can be confusing. "Ohmic heating" is defined as E.j.

I wasn't fooled by any of such, as I have not yet reached definite conclusions. And yes I understand it like you say. I now understand that some textbooks discussing Poynting (and apparently also Poynting himself) do not relate to a completely general case, but to energy flow, accumulation and dissipation inside a material.

[..] Maxwell's equations don't explicitly mention either temperature or entropy. In fact, there is nothing in Maxwell's equations that make it necessary for a system to reach equilibrium. [...]
The phrase "Ohmic heating" is deceptive because it implies that there is some random variables associated with
Thermodynamics comes into electrodynamics through the constitutive relations. Constitutive relations describe the properties associated with the substances. [..]
The article link mentioned by the OP tries to separate the mechanical energy of the particles from the electromagnetic field energies. However, it doesn't even try to include entropy and temperature. [..]
For example,the relationship between the electric field and the electron current is given by Ohm's Law, which is,
j=σE,
where σ is the conductivity of the material, j is the current density and E is the electric field.
The work done by the electric field is j.E. So the work, W, done by the electric field is,
W=σE^2
Note that in this case the work is rate of change of the internal energy. So,
dU/dt=σE^2
where U is the internal energy.
Basically, the atomic level dynamics of the electromagnetic system is characterized by the constitutive relations and the Lorentz force Law. These have to expressed in forms that don't violate the equations of state for your materials.

I'm not sure how to place those comments in the discussion... Do you agree that if one has simply a resistor in a circuit, the depleted EM energy in a volume element corresponds to E.j in that volume element? And what do you say about the generalisation of Poynting's theorem?

 

[Q-reeus]

Now, to get back to the topic: I asked you how you explain a reducing current without a force to reduce that current.

Sigh. Harald, if someone of Walter Lewin's standing fails to convince, it's an uphill battle for poor ol' me. Perhaps your familiarity with some of the GR side of things might help. As you know, an object in free-fall experiences weightlessness. But only if in free-fall at 1g acceleration wrt terra firma! If just sitting there on terra firma, it feels the full force F = mg. Can you see a possible analogy here with conduction charges in the surface of that loop? :uhh:
[Can't push the analogy too far - those charges generate their own electric 'inertial' field - but consider that as in effect the arrow of -ma 'inertial force' directly opposed to that of 'gravity' = qE_applied]

 

[harrylin]

Sigh. Harald, if someone of Walter Lewin's standing fails to convince, it's an uphill battle for poor ol' me. Perhaps your familiarity with some of the GR side of things might help. As you know, an object in free-fall experiences weightlessness. But only if in free-fall at 1g acceleration wrt terra firma! If just sitting there on terra firma, it feels the full force F = mg. Can you see a possible analogy here with conduction charges in that loop? :uhh:

Again no answer but an appeal to authority? Sigh indeed - appeal to authority has zero value in science. And amazingly, you seem to have no problem with work done on electrons without a force that can do that work!

However, I see an analogy, only not sure if that's what you have in mind: it looks very much to me referring to Escher's staircase (= your gravitation?), before rediscovering the definition of electric field and the paper that explained that such a potential concept isn't valid in this context, both to which I provided links.

Here's a link to a very basic discussion of Faraday's law with a neat drawing:
http://dev.physicslab.org/Document.aspx?doctype=3&filename=Induction_InducedElectricFields.xml
Please apply either my staircase analogy or your gravitational potential analogy to that drawing, and explain between which values of conductance an E-field will be present. Then we can get back to Poynting.

 

[Q-reeus]

Again no answer but an appeal to authority? Sigh indeed - appeal to authority has zero value in science.

Hey, I'm opposed to appeal to authority also, but that doesn't mean ignoring sound teaching from someone recognized as competent in the field. Thing is, what is claimed there is born out in practice. Faraday cages work. Metal foil really does reflect incident EM radiation just like the theory says. And so on in a host of real world applications.

And amazingly, you seem to have no problem with work done on electrons without a force that can do that work!

But it's not really like that. For a perfect conductor, there is zero work done on the electrons because there is always zero net field acting. They are acting, importantly, simply as conduits for energy exchange. By oscillating so as to maintain zero net E on themselves - and in doing so generating fields elsewhere. That's how it is in a metallic waveguide - power doesn't flow appreciably through the moving charges - it flows almost totally in the fields set up between the waveguide interior walls. Poynting vector! And that 'almost' would be 'totally' except that finite resistivity applies to real conductors, but the ohmic loss is a tiny fraction of the net power.

However, I see an analogy, only not sure if that's what you have in mind: it looks very much to me referring to Escher's staircase (= your gravitation?), before rediscovering the definition of electric field and the paper that explained that such a potential concept isn't valid in this context, both to which I provided links.

Not quite sure what you are saying here, but ok then forget the gravitational analogy. A basic fact is there has to be some mechanism that establishes equilibrium when an external influence - E field - impinges on a conductor. If that conductor is notionally perfect, and the impinging field acts along the surface direction, how is equilibrium established? Well obviously it has to be a dynamic equilibrium involving accelerated motion of the conduction charges. There is no other option. You cannot appeal to resistance, for there is none. But there is this thing called inductive reactance , and it guarantees no field exists inside a perfect conductor, and very little penetration for a good conductor.

Here's a link to a very basic discussion of Faraday's law with a neat drawing:
http://dev.physicslab.org/Document.a...tricFields.xml
Please apply either my staircase analogy or your gravitational potential analogy to that drawing, and explain between which values of conductance an E-field will be present. Then we can get back to Poynting.

Guessing somewhat but I'd say your real hangup is not with the fact a circular E field applies in that situation shown, but that there work is being done on those charges. Well the obvious conclusion for me is the unstated assumption is resistivity in that circuit is high and that is what limits the induced current and allows E.J work to be performed. Without resistance, a ramp current applies such that no net field acts on the circuit - and that has to be the case however crazy you may still find it. It gets back to the properties of a perfect conductor. If none of my efforts here impresses favorably, I would ask you Harald to supply a self-consistent alternate explanation - in particular for the behavior of a zero resistance loop subject to a time-varying B field. My - is it that time already! :zzz:

 

[harrylin]

* Note: it suddenly strikes me that in the particular example that I used, by chance "EMF" only corresponds in first instance to electric field in the "stationary" wire (compare Einstein's 1905 intro)! *
-http://www.fourmilab.ch/etexts/einstein/specrel/www/

[..] Faraday cages work. Metal foil really does reflect incident EM radiation just like the theory says. And so on in a host of real world applications.

Obviously, and that's the problem with rules (not laws!) based on such generalisations. In post #38 I referred to shielding after verifying the theory behind it, including links to why Faraday cages work plus my explanation as to why IMHO it doesn't apply. Even the online course to which I latest referred includes shielding - but with analysis and with E≠0 in their wire loops.

But it's not really like that. For a perfect conductor, there is zero work done on the electrons because there is always zero net field acting. [..]

Do you say that zero force is needed to slow down electrons? That would mean that their mass and magnetic field are both zero.

[..] A basic fact is there has to be some mechanism that establishes equilibrium when an external influence - E field - impinges on a conductor. If that conductor is notionally perfect, and the impinging field acts along the surface direction, how is equilibrium established?

There is no such problem as E is transient and there is also self induction - but in an extreme case if you put a big DC voltage on a thin wire with some resistance, it simply burns up.

Well obviously it has to be a dynamic equilibrium involving accelerated motion of the conduction charges. There is no other option. [..]

Good! I will ask you one more time, if as you insist E=0 always, then how do you want to bring about that accelerated motion of the conduction charges?

Guessing somewhat but I'd say your real hangup is not with the fact a circular E field applies in that situation shown [..]

You guessed wrongly: the real hang-up in this discussion is with your denial (although originally it was mine! ) of the law accordng to which a circular E field acts on the charges in that situation as shown.

Well the obvious conclusion for me is the unstated assumption is resistivity in that circuit is high

My conclusion is the contrary: their implied assumption is that R≈0 since they discuss conductors and put F=q.E.

It gets back to the properties of a perfect conductor.

It starts with "Recall E ( r ) = 0 in a perfect conductor." -> apparently it relates to an idealised situation that is not mentioned; what matters is the preceding chapter which we don't have. However I found a similar "missing link"
- https://www.google.com/url?q=http://www.ece.mcmaster.ca/faculty/nikolova/EM_2FH3_downloads/lectures/L11_PEC_Images_post.pdf&sa=U&ei=vr9VUKL4GKPA0QXg44DoAg&ved=0CAgQFjAB&client=internal-uds-cse&usg=AFQjCNH_KR8NfH9eDivvt65CxS77nTZccQ
Much of that does not apply to our discussion: we are accounting for transition effects which such a metal ignores, and pertinently the proof is based on "the conservative property of E" - which is invalid in this case!
If we have a magnet moving towards a conducting loop, the induced current is clearly the result of a driving force. There must be an EMF - an electric field - that is produced in the conducting loop.

Don't believe me? You will appreciate the following video by Walter Lewin:
http://www.academicearth.org/lectures/induction-faradays-law-and-non-conservative-fields
The whole video is interesting to watch, so now it's your time to grab a beer and watch. ;-)

Remember that in the context of "perfect conductors" he stated that "No electric field can exist inside an ideal conductor" (emphasis his) - and that he applied it to rather imperfect conductors such as the plate behind the black board?
Well, quite early in the context of our discussion (Faraday induction) he presents in this video the here-above cited contrary conclusion, and for equally imperfect conductors (he omits the self induction L but probably he has not yet covered that). No doubt he means with "ideal" conductor the same as discussed here above; and that's fine. Also, don't miss from minute 34 his explanation of why Kirchhof's rule (on which I and you based our opinion) is not true in this case.

If none of my efforts here impresses favorably, I would ask you Harald to supply a self-consistent alternate explanation - in particular for the behavior of a zero resistance loop subject to a time-varying B field. My - is it that time already! :zzz:

I hope that you had a good night's rest!
Now, I found that the explanation which I first gave and to which you now adhere is inconsistent with Faraday's law; most discussions of Faraday's law would be wrong and inducing a current in a superconductor would be impossible according to classical EM (and I found no such claim in the literature). I gave you my corrected explanation in posts #23 and #38.

However, at the point where Lewin says "not so intuitive" I say: "rather intuitive, as the emf acts on the electrons over three loops".

See also:
- http://www.physics.uiowa.edu/~umallik/adventure/nov_13-04.html

ADDENDUM: the following one is also quite good, but regretfully he contradicts himself exactly on this point ... anyway, I agree with his explanation at minutes 40-41, so that I cannot agree with his immediately following denial (probably due to simplification, exactly at minute 42) of what he explained. :tongue2:
http://www.youtube.com/watch?v=EYYNRubHIno&NR=1&feature=endscreen

 

[Q-reeus]

* Note: it suddenly strikes me that in the particular example that I used, by chance "EMF" only corresponds in first instance to electric field in the "stationary" wire (compare Einstein's 1905 intro)! *
-http://www.fourmilab.ch/etexts/einstein/specrel/www/[/QUOTE]
Einstein there is interested in a general relationship where emf *in* conductor is a loose, heuristic statement, emphasis being the relative motional aspect, not e.g. details of field penetration in conductors!

Obviously, and that's the problem with rules (not laws!) based on such generalisations.

What do you mean by 'rules' here? Are you suggesting application of ME's to reflection of EM waves at conducting surfaces is not applying laws, just inventing rules?

In post #38 I referred to shielding after verifying the theory behind it, including links to why Faraday cages work plus my explanation as to why IMHO it doesn't apply. Even the online course to which I latest referred includes shielding - but with analysis and with E≠0 in their wire loops.

I do have trouble following some of that. Anyway, you misunderstand things in #38:

Hehe I watched it, and indeed I was surprised to hear him start with such an absolute statement, and to repeat it as a mantra. It works for his topics of transmission lines and transformers, but even then not perfectly well.

The only 'not perfect' is when finite resistivity is factored in, but that is fully acknowledged there, as well as why the idealization of perfect conductivity works quite satisfactorily to establish the basic concepts. It is perfectly valid as the limit of vanishing resistivity, and that limit introduces no paradoxes.

For example, I wonder if ever one of those puzzled looking students asked him how there can be local accumulations and depletions of electrons in the wires without any E-fields.

You misunderstand. There are of course E-fields, but they are invariably exterior to the conductor interior and always normal to the surface, at the surface. What is always zero at the surface and interior is any tangent field component.

IMHO it is an over-generalisation based on EM shielding: https://en.wikipedia.org/wiki/Electromagnetic_shielding
In the case of a closed wire loop there is no boundary and thus no charge accumulation or reflection along the loop, and thus there can also be no shielding along that direction.

False - last part does not follow from the first bit. You again misunderstand the nature of shielding here. Perfect conductor = zero interior field *by definition* of being a perfect conductor! Real world EM shielding must deal with finite conductivity thus finite skin-depth etc. (also much there is about magnetic shielding, a quite different though related thing).

Q-reeus: "..For a perfect conductor, there is zero work done on the electrons because there is always zero net field acting. [..]"
Do you say that zero force is needed to slow down electrons? That would mean that their mass and magnetic field are both zero.

There is only 'zero force' = zero *net* E *because* of the back emf from the time-changing current. Inductance is fact. Hook up an ideal battery to a perfect inductor, and what do you suppose the circuit equation will read? Hint - apply Kirchoff's voltage law. If you get other than zero net voltage, start again. [I have since viewed relevant bits from that Lewin lecture you referenced btw, and above comments hold good. More later.]

[..] A basic fact is there has to be some mechanism that establishes equilibrium when an external influence - E field - impinges on a conductor. If that conductor is notionally perfect, and the impinging field acts along the surface direction, how is equilibrium established?

There is no such problem as E is transient and there is also self induction - but in an extreme case if you put a big DC voltage on a thin wire with some resistance, it simply burns up.

You start off basically conceding my point in mentioning self-inductance but then negate it with a bogus intro of resistance -> burn-up. Forget resistance. Stick with perfect conductor case!

Well obviously it has to be a dynamic equilibrium involving accelerated motion of the conduction charges. There is no other option. [..]

Good! I will ask you one more time, if as you insist E=0 always, then how do you want to bring about that accelerated motion of the conduction charges?

It's precisely because of the accelerated motion that net E=0. The equilibrium relation, necessarily dynamic, is E_applied+-dA/dt=0, where the -dA/dt owes to the accelerating surface current responding to the tangent applied E! Is that really so hard to grasp?

You guessed wrongly: the real hang-up in this discussion is with your denial (although originally it was mine! ) of the law accordng to which a circular E field acts on the charges in that situation as shown.

What denial is that?

My conclusion is the contrary: their implied assumption is that R≈0 since they discuss conductors and put F=q.E.

Jumping to conclusions - they nowhere specify the degree of conductivity in that loop - you assume the above. Anyway, it could represent a partial relation where only the applied E is considered. That happens. A total balance for perfectly conducting loop complies to what I wrote above. Must.

It starts with "Recall E ( r ) = 0 in a perfect conductor." -> apparently it relates to an idealised situation that is not mentioned; what matters is the preceding chapter which we don't have.

And we don't need it. Check any reputable resource on the web or in textbooks - that relation is universally acknowledged. Stop tilting at windmills Harald! :grumpy:

However I found a similar "missing link"
- https://www.google.com/url?q=http://...t65CxS77nTZccQ
Much of that does not apply to our discussion: we are accounting for transition effects which such a metal ignores, and pertinently the proof is based on "the conservative property of E" - which is invalid in this case!

Nonsense. The conservative properties there relate to electrostatic shielding component. The mention of zero tangent field at surface relates to electrodynamic shielding component. The two are perfectly complementary and generally both present in many situations.

In fact, in some cases an induced current is clearly the result of a driving force. There must be an EMF - an electric field - that is produced in a conducting loop. Don't believe me? You will appreciate the following video by Walter Lewin:
http://www.academicearth.org/lecture...rvative-fields
The whole video- is interesting to watch, so now it's your time to grab a beer and watch. ;-)

Re ~ 12-13 minutes in - induced emf = IR. Quite true - that is a lossy coil attached to an ammeter. It is *not* a shorted-out perfectly conducting loop! There is a fundamental difference!

Remember that in the context of "perfect conductors" he stated that "No electric field can exist inside an ideal conductor" (emphasis his) to rather imperfect conductors such as the plate behind the black board? Well, quite early in the context of our discussion (Faraday induction) he presents the here-above cited contrary conclusion, and for equally imperfect conductors (he omits the self induction L but probably he has not yet covered that). Obviously he means with "ideal" conductor the same as discussed here above; and that's fine. Also, don't miss from minute 34 his denial that Kirchhof's rule (on which I and you based our opinion) is true in this case. :-)

Re that bit about Kirchoff's law failing. True in a certain limited sense, and re the N windings bit - absolutely agrees with what I said back here However - you are missing something important there. That emf is the *open circuit value* - that measured across the terminals when no current flows. When the electrostatic field across those terminals is included in the circuit - Kirchoff's law does in fact hold good. Same if a resistor or capacitor is placed across the terminals. Lewin simply chose for his didactic purposes there to excise that contribution. If his test coil was truly perfectly conducting and the terminals shorted together - there would be, in accordance with Lenz's and Faraday's and Kirchoff's law, zero net emf around that coil. If you imagine Lewin was somehow contradicting himself re that other lecture - think again. Everything in proper context! Also from MIT: http://ocw.mit.edu/courses/physics/...netism-spring-2002/lecture-notes/lecsup41.pdf

I found that the explanation which I first gave and to which you now adhere is inconsistent with Faraday's law; most discussions of Faraday's law would be wrong and inducing a current in a superconductor would be impossible. I gave you my corrected explanation in posts #23 and #38.
However, at the point where Lewin says "not so intuitive" I say: "rather intuitive, as the emf acts on the electrons over three loops". :-)

See also:
- http://www.physics.uiowa.edu/~umalli...nov_13-04.html

Your point gleaned from there is? That eddy currents heat up conductors? Of course - a result of finite conductivity. That last bit about a magnet floating above a superconductor precisely reinforces my argument - such perfect diamagnetism in that case is exactly what a perfect conductor would exhibit. Accept it.

One last try Harald, and that's it. Please consider this article: "web.mit.edu/jbelcher/www/java/plane/plane.pdf"
worth reading all through, but pages 5-7 gives an approach you may find intuitively appealing and it's a bit different to that given so far. If that fails on you, sorry, I've expended more time than I can really afford. So please, concentrate, and open your mind to the possibility all those unanimous statements about zero tangent field might just be true! Think of it as the EM analogue of applying Newton's 2nd and 3rd laws. Push on a frictionless rail-car, and in order that no net force exists, it must accelerate such that F+ma=0. Analogue: q(E_applied+(-dA/dt))=0, where A is the vector potential generated by the surface current. Added 'benefit' in EM case is no field penetrates below the surface. Have I mentioned that before? Sigh - I dare not hope too much. Sigh. :uhh::zzz:

 

[Darwin123]

I'm not sure how to place those comments in the discussion... Do you agree that if one has simply a resistor in a circuit, the depleted EM energy in a volume element corresponds to E.j in that volume element? And what do you say about the generalisation of Poynting's theorem?

The problem is that don't know what "depleted EM" energy is. Unless you tell us what "depleted energy" is, we can't answer you. Further, you shouldn't use equivalent words unless you tell us what they mean. We don't know what "dissipated energy" is. We don't even know what "heating" is. All these words only have meaning if one considers the statistics on an atomic level.
When Ohm's Law applies, then E.j shows the rate at which the kinetic energy of the atoms and electrons in the system are increasing. There is no such thing as "depleted energy" on an atomic scale. On an atomic scale, there is only kinetic energy, electric field energy, magnetic field energy, and various types of nonelectromagnetic potential energy.
Ohms Law can be written
j=σE,
where J is the current density, E is the electric field, and σ is the conductivity. If σ>0, and σ does not vary with frequency, then one can imply that the carriers in the system are not accelerating. However, this is not a general hypothesis.

On an atomic level, -j.E is the decrease in energy density of the system. Without Ohm's Law, there is absolutely no way to tell whether the energy is "depleted", "dissipated", or "heated", or merely "reduced". In a way, Ohm's Law defines heat.
In terms of thermodynamics, you can't go wrong by saying "j.E" is the work done by the electromagnetic field. Calling it "Ohm heating" causes confusion.

 

[Darwin123]

Hey, I'm opposed to appeal to authority also, but that doesn't mean ignoring sound teaching from someone recognized as competent in the field. Thing is, what is claimed there is born out in practice. Faraday cages work. Metal foil really does reflect incident EM radiation just like the theory says. And so on in a host of real world applications.

But it's not really like that. For a perfect conductor, there is zero work done on the electrons because there is always zero net field acting. They are acting, importantly, simply as conduits for energy exchange. By oscillating so as to maintain zero net E on themselves - and in doing so generating fields elsewhere. That's how it is in a metallic waveguide - power doesn't flow appreciably through the moving charges - it flows almost totally in the fields set up between the waveguide interior walls. Poynting vector! And that 'almost' would be 'totally' except that finite resistivity applies to real conductors, but the ohmic loss is a tiny fraction of the net power.

Not quite sure what you are saying here, but ok then forget the gravitational analogy. A basic fact is there has to be some mechanism that establishes equilibrium when an external influence - E field - impinges on a conductor. If that conductor is notionally perfect, and the impinging field acts along the surface direction, how is equilibrium established? Well obviously it has to be a dynamic equilibrium involving accelerated motion of the conduction charges. There is no other option. You cannot appeal to resistance, for there is none. But there is this thing called inductive reactance , and it guarantees no field exists inside a perfect conductor, and very little penetration for a good conductor.

Guessing somewhat but I'd say your real hangup is not with the fact a circular E field applies in that situation shown, but that there work is being done on those charges. Well the obvious conclusion for me is the unstated assumption is resistivity in that circuit is high and that is what limits the induced current and allows E.J work to be performed. Without resistance, a ramp current applies such that no net field acts on the circuit - and that has to be the case however crazy you may still find it. It gets back to the properties of a perfect conductor. If none of my efforts here impresses favorably, I would ask you Harald to supply a self-consistent alternate explanation - in particular for the behavior of a zero resistance loop subject to a time-varying B field. My - is it that time already! :zzz:

If the conductor is perfect, then there doesn’t have to be an equilibrium established. There is no force on the electric charge carrier in a perfect conductor. Therefore, there is no way to “dissipate the energy” in the perfect conductor. If you set up a circuit with “perfect” conductors, then the electric charges just bounce back and forth between capacitor and inductor forever.
The only reason that equilibrium is ever established is because there are circuit elements with finite conductivity in them. The finite conductivity characterizes forces that the electrons undergo.
In electrodynamics, atomic scale motion is characterized by constitutive relations. For instance, Ohms Law implies that the system is in thermal equilibrium. The mathematical expression for Ohms Law, J=E, implies that the electrons in the conductor are under the influence of a frictional force so that they are not accelerating. If =0, then one would have to say that the electrons are always accelerating. In fact,  may vary with frequency. The variation with frequency shows that equilibrium is not established.
Part of the problem is that you are asking questions that don’t make sense on an atomic scale. You are asking about what brings the system to equilibrium. On a macroscopic scale, the system will reach thermal equilibrium. When the system reaches thermal equilibrium, then visible motion will cease on a macroscopic scale. However, the atomic constituents will never stop moving.
The concept of “thermal equilibrium” is intrinsically statistical. You can’t even define “thermal equilibrium” unless you have some way to distinguish atomic scale motion from “large scale motion.” There is no way to distinguish internal energy from kinetic energy.
There is no such thing as equilibrium on an atomic scale. All the atoms are constantly moving. Even when something has reached “thermal equilibrium”, the atoms are still moving. So on an atomic scale, one can’t really ask how equilibrium is established.
Poynting’s theorem shows how energy is conserved in a system of electric charges. Furthermore, Poynting’s theorem applies to all length scales. It applies extremely well on both an atomic scale. It shows that energy is always conserved on an atomic scale. However, the statistics of the system determine how much energy is dissipated and how much goes into mechanical energy..
Poynting’s Theorem is easier to interpret on an atomic scale than on a macroscopic scale. On an atomic scale, there is no such thing as “heat”. On an atomic scale, there is no such thing as “dissipation. All energy is either kinetic energy electric field energy, magnetic field energy, or some form of potential energy that is not electromagnetic in character. There are no statistics implicit in Poynting’s theorem “Heat” is not a specific form of energy on an atomic scale. Thermal conduction doesn’t exist on an atomic scale. “Heat energy” can be kinetic energy, magnetic field energy, or electric field energy on an atomic scale. “Work” can be kinetic energy, magnetic field energy or electric field energy on an atomic scale. In order to use the word heat meaningfully, you need a length scale to separate energy on the atomic scale from energy on the macroscopic scale. Poynting’s theorem does not tell
The phrase, “Ohmic heating,” makes no sense on an atomic scale. On a macroscopic scale, the "temperature" of the resistor goes up. On the atomic scale, there is no such thing as temperature. Each atom moves around faster because it has more kinetic energy. If the electron was accelerating in the resistor, then Ohm’s Law would make no sense.
Either way, Poynting's Theorem is valid. Whether you call a parcel of energy "internal energy" or "kinetic energy", Poynting's Theorem is still valid.
I even thing there is a quantum mechanical version of Poynting's Theorem somewhere. It isn't an issue of classical physics versus quantum physics. It is a case of classical physics versus classical thermodynamics.
Maybe the real issue is equilibrium. There is no equilibrium in Poynting's Theorem.

 

[Q-reeus]

If the conductor is perfect, then there doesn’t have to be an equilibrium established. There is no force on the electric charge carrier in a perfect conductor. Therefore, there is no way to “dissipate the energy” in the perfect conductor. If you set up a circuit with “perfect” conductors, then the electric charges just bounce back and forth between capacitor and inductor forever.

This much we are in agreement - except there is no LC oscillation involved. We are talking about modelling a so-called Amperian loop current which is entirely inductive. I'm running way overtime here, but just something quick. Often folks enter at various points in a long thread having never really absorbed what's gone on before. Maybe not your case, but I would ask you to go back to #12, and check out the sections I mention there in reference to article linked in #7. Do you have any answer to that author's points there - which on the whole I agree with? Unless the fundamental nature of the major contributor to magnetization is recognized, much argument can be totally skewed.

 

[harrylin]

OK, I now figured out that indeed Poynting's theorem is not generally valid, for reasons that already have been brought forward in the other thread. I'll come back later to show this based on the derivation in Wikipedia - it's very simple really, but I need time to write it down in full and provide proper references to earlier posts by others. I'll be back.

 

[harrylin]

@ Q-reeus: at the end of that video Lewin demonstrated the fact that Kirchoff's law does in fact not hold good for a non-conservative electric field, just as Faraday's law tells us. Also the last video that I linked explains this, as well as how it can be that we can use Kirchhof for a circuit with inductors.
But now that I see that anything that I find and refer to and even show is simply un-understood - incl. much of what I say - and reasoned away (and you may feel the same), it's no use to continue that side issue which distracts from the topic, and for which I want to find time to round it off. So, I agree that these were our last attempts as it was really becoming a waste of time for both of us.

 

[Q-reeus]

@ Q-reeus: at the end of that video Lewin demonstrated the fact that Kirchoff's law does in fact not hold good in such cases, just as Faraday's law tells us. Now that I see that anything that I find and refer to and even show is simply reasoned away, it's no use to continue that side issue which distracts from the topic, and for which I want to find time to round it off. Sorry, but it's really becoming a waste of time for both of us.

@harrylin: I admit, owing to time constraints, to not having viewed that lecture all the way through. So having now viewed the part where Lewin 'tears Kirchoff to shreds', I see why you say the above. Actually, Lewin is seen as a bit of a maverick on that matter, and I agree with many others that his argument is really bogus. When *properly formulated*, Kirchoff's second law always holds. It becomes a matter of definition and convention. Lewin chooses one approach that appears to overthrow Kirchoff. You may be interested to follow the lengthy PF thread debating Lewin's approach to that matter: https://www.physicsforums.com/showthread.php?t=453575 As you will find, there is no unanimity, but I side with those that believe KVL always hold - provided one consistently applies the rule; sum of emf's + sum of potential drops = 0 around any circuit. The one proviso here is it must be a physical circuit that includes at minimum conducting wire(s). Obviously a 'circuit' consisting of an imaginary line drawn in fresh air will fail KVL when time-varying B is present, but that is severely cheating!

But I agree it is a distraction - main point is to recognize the true nature of magnetization when it comes to applying Poynting power balance, or rather imbalance if certain assumptions are adopted. Now, do you finally accept that tangent field at a perfect conductor surface must be zero?

 

[vanhees71]

No, Lewin is right! It's a very good lecture and should help to understand Faraday's Law, which is usually the most difficult of Maxwell's equations to apply correctly. Of course, most of this is caused by not properly taking into account relativity when it comes to the application of the Maxwell equations with moving parts/media.

A good example is the (in)famous homopolar generator (Faraday's disk) or Feynman's disk. In this respect the Feynman lectures (vol. II) and good old Becker/Sauter (which is btw. available in English in a Dover paperback) are the best sources.

 

[harrylin]

[..] It becomes a matter of definition and convention. Lewin chooses one approach that appears to overthrow Kirchoff. You may be interested to follow the lengthy PF thread debating Lewin's approach to that matter: https://www.physicsforums.com/showthread.php?t=453575 [..] Now, do you finally accept that tangent field at a perfect conductor surface must be zero?

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]

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.

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]

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.

Sorry, please take those matters out of this thread.

 

[Q-reeus]

Sorry, please take those matters out of this thread.

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 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?

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]

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 it were our last attempts and won't come back to it.
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!

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!

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!).

Pass! :tongue:

 

[harrylin]

[..]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! [..]

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. :tongue2:

 

[harrylin]

[..] On an atomic level, -j.E is the decrease in energy density of the system. Without Ohm's Law, there is absolutely no way to tell whether the energy is "depleted", "dissipated", or "heated", or merely "reduced". In a way, Ohm's Law defines heat.
In terms of thermodynamics, you can't go wrong by saying "j.E" is the work done by the electromagnetic field. Calling it "Ohm heating" causes confusion.

That may be so, but I found that such textbooks simply cite Poynting on this:

The change per second in the electric energy within a surface is equal to a quantity depending on the surface — the change per second in the magnetic energy — the heat developed in the circuit.
[..]
the product of the conduction-current and the electromotive intensity, by Ohm's law, [..] is the energy appearing as heat in the circuit per unit volume according to Joule's law

https://en.wikisource.org/wiki/On_the_Transfer_of_Energy_in_the_Electromagnetic_Field

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

 

[Darwin123]

That may be so, but I found that such textbooks simply cite Poynting on this:


https://en.wikisource.org/wiki/On_the_Transfer_of_Energy_in_the_Electromagnetic_Field

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

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".