Energy flux direction in a conducting wire?

[nasu]

@bob012345 This is what I was talking about, from your post:
"Fields do not mysteriously jump out of wires at the generator source, flow along wires and suddenly jump back into the loads."

 

[bob012345]

@bob012345 This is what I was talking about, from your post:
"Fields do not mysteriously jump out of wires at the generator source, flow along wires and suddenly jump back into the loads."

Well of course you can make them do just that with antennas but I meant in the context of this discussion. The generator, such as a battery in a DC circuit, is not an antenna that send out fields into space, independent of the wires as I understand it. Again, I might be completely wrong in my understanding.

 

[vanhees71]

What's discussed in my above quoted writeup or in Sommerfeld, Lectures on Theoretical Physics, Vol. 3 was the DC case for a coaxial cable (an example chosen, because it's pretty easy to calculate), i.e., that's valid only for the situation after a sufficiently long time the circuit is "switched" on and you are in the stationary state ("magneto statics"). Then the energy transport from the source ("battery") along the cable is clearly due to the electric field in the free space between the coaxial conductors, because that's the only place, where the Poynting vector has a component along the direction of the wire (the $z$-axis in the calculation). This energy is dissipated into heat along the wire ("Ohmic loss"). You find the complete discussion also in my E&M manuscript, Sect. 3.5 (in German only):

https://itp.uni-frankfurt.de/~hees/publ/theo2-l3.pdf

To understand the transient state after switching on the circuit, you have to solve the wave equation (or "telegrapher's equation"). I guess you can also find this calculation somewhere, but I've no reference at hand at the moment.

 

[bob012345]

What's discussed in my above quoted writeup or in Sommerfeld, Lectures on Theoretical Physics, Vol. 3 was the DC case for a coaxial cable (an example chosen, because it's pretty easy to calculate), i.e., that's valid only for the situation after a sufficiently long time the circuit is "switched" on and you are in the stationary state ("magneto statics"). Then the energy transport from the source ("battery") along the cable is clearly due to the electric field in the free space between the coaxial conductors, because that's the only place, where the Poynting vector has a component along the direction of the wire (the $z$-axis in the calculation). This energy is dissipated into heat along the wire ("Ohmic loss"). You find the complete discussion also in my E&M manuscript, Sect. 3.5 (in German only):

https://itp.uni-frankfurt.de/~hees/publ/theo2-l3.pdf

To understand the transient state after switching on the circuit, you have to solve the wave equation (or "telegrapher's equation"). I guess you can also find this calculation somewhere, but I've no reference at hand at the moment.

Yes but originally this thread and my recent posts was about a conducting wire not a coaxial cable? Reading back through it it seems the discussion is confusing with different trains of thoughts intermingling. No pictures to help either...

 

[hutchphd]

If energy flows out of the battery and then is virtually all consumed in the resistor as heat, what flows out of the resistor and through or around the wire back to the battery?

If energy flows out of the battery and then is virtually all consumed in the resistor as heat, what flows out of the resistor and through or around the wire back to the battery? The current still flows the same in both paths into and out of the resistor. Aren't the Poynting vectors the same? I'm confused. No, I'm really confused.

Yes perhaps I can point out why.

Further consider, if the energy is carried outside the wire but used up in the load, what exactly is flowing outside the return wires if the current, fields and thus the Poynting vectors are the same? I think the Poynting vector must be different on the return path from the load.

The Poynting Vector shows the energy flow in the fields. There is no "return" path except by our naming convention

My last point was merely an observation that if energy flows along outside the wire, it must be less after the load on the return path that before it or energy would not be conserved. Do you disagree?

Their is no return path! I think you need to look at the Veritasium video again carefully. The Poynting vector always comes out of the battery. Everywhere. On one "leg" it is parallel to the current and on the other it is antiparallel. At the resistor it goes into the resistor. The pertinant image is at 8:00:


I hope that helps

 

[bob012345]

I'll look at it again but if there were a medium to completely dis-allow fields completely surrounding the wire do you say no energy would get to the resistor?

 

[Lord Jestocost]

Energy transfer in electrical circuits: A qualitative account
Igal Galili and Elisabetta Goihbarg
Am. J. Phys. 73, 141 (2005); doi: 10.1119/1.1819932

Understanding Electricity and Circuits: What the Text Books Don’t Tell You
Ian M. Sefton
Science Teachers’ Workshop 2002

Energy flow from a battery to other circuit elements: Role of surface charges
Manoj K. Harbola
American Journal of Physics 78, 1203 (2010); doi: 10.1119/1.3456567

 

[vanhees71]

Yes but originally this thread and my recent posts was about a conducting wire not a coaxial cable? Reading back through it it seems the discussion is confusing with different trains of thoughts intermingling. No pictures to help either...

The single wire is not different from the coax cable. It's only even less "realistic" ;-).

 

[bob012345]

I forgot it's just a shielded single wire.

 

[bob012345]

Energy transfer in electrical circuits: A qualitative account
Igal Galili and Elisabetta Goihbarg
Am. J. Phys. 73, 141 (2005); doi: 10.1119/1.1819932

Understanding Electricity and Circuits: What the Text Books Don’t Tell You
Ian M. Sefton
Science Teachers’ Workshop 2002

Energy flow from a battery to other circuit elements: Role of surface charges
Manoj K. Harbola
American Journal of Physics 78, 1203 (2010); doi: 10.1119/1.3456567

This is very useful! Thanks.

 

[bob012345]

Yes perhaps I can point out why.

The Poynting Vector shows the energy flow in the fields. There is no "return" path except by our naming convention

Their is no return path! I think you need to look at the Veritasium video again carefully. The Poynting vector always comes out of the battery. Everywhere. On one "leg" it is parallel to the current and on the other it is antiparallel. At the resistor it goes into the resistor. The pertinant image is at 8:00:


I hope that helps

Thanks. I am troubled by a couple of statements such as the energy is going out through the sides of the battery (7:47) and the energy is coming in from all around the bulb (8:13). I am not arguing the concept is wrong I just have questions.

Suppose the battery and or the light bulb were completely shielded (not to mention the wires)? One might accept the idea of a conventional filament light bulb glowing with stray EM fields impinging on it from all angles like a Nikola Tesla demonstration but a modern LED bulb? Or a precision motor where stray fields would disrupt the operation? The Poynting vector model is highly geometry dependent yet the result is completely geometry independent?

 

[hutchphd]

Honestly I don't know the detailed answers, because the physics makes perfect sense where I do know the answers. I would ask you to describe in detail how you would create the shielded ssituations you describe. I don't think you can create those situations. If so we will address them.

 

[bob012345]

Honestly I don't know the detailed answers, because the physics makes perfect sense where I do know the answers. I would ask you to describe in detail how you would create the shielded situations you describe. I don't think you can create those situations. If so we will address them.

I would simply build a Faraday cage around the battery and another Faraday cage around the actual bulb allowing only grounded coax leads through the plane of the cage to the bulb. But we don't need to get into a big debate on the subject. All I am really saying is some situations are not always as idealized as the image in the video. It is a very complex subject and I do not think everything is known as to the details.

 

[hutchphd]

The issue is how to feed the power wires into the Faraday cage. I do not desire a debate nor do I care about your unsupported opinion. I just want to analyze an actual situation. It is not really complex, but it may be subtle. You need to discuss specifics.

 

[vanhees71]

I would simply build a Faraday cage around the battery and another Faraday cage around the actual bulb allowing only grounded coax leads through the plane of the cage to the bulb. But we don't need to get into a big debate on the subject. All I am really saying is some situations are not always as idealized as the image in the video. It is a very complex subject and I do not think everything is known as to the details.

Yes, that's why the "very long coax cable" is a nice setup, because it's on the one hand simple due to its high symmetry and thus can be easily solved analytical and on the other hand it's complete, because it describes a complete closed circuit.

 

[bob012345]

FYI, here is a J.D. Jackson paper on the distribution of charge and the roles that plays in circuits. He analyzes a simple case which turns out not to be so simple.

https://pdfcoffee.com/surface-charges-on-circuit-wires-and-resistors-play-three-roles--pdf-free.html

Here is a bit lower level discussion of the topic;

https://matterandinteractions.org/wp-content/uploads/2016/07/circuit.pdf

Here is Jefimenko's early demonstration of surface charges around a circuit;

http://sharif.edu/~aborji/25733/files/Demonstration of the Electric Fields of Current-Carrying Conductors.pdf

 

[hutchphd]

FYI, here is a J.D. Jackson paper on the distribution of charge and the roles that plays in circuits. He analyzes a simple case which turns out not to be so simple.

https://pdfcoffee.com/surface-charges-on-circuit-wires-and-resistors-play-three-roles--pdf-free.html

Thanks for the article it is pretty interesting. Perhaps you misunderstand my point here. I am not saying the charge and currents can be ignored. The electrodynamic system consists of charges, currents, and fields. (If you want thermodynamics in materials you can couple to other degrees of freedom too!). One should not treat the current like water in a pipe. Wherever there are charges and currents there will be E and H and so they need to be included.
The Poynting Vector is often the simplest picture of the energetics and it is certainly not independent of the system spatial parameters and all the other degrees of freedom.

 

[bob012345]

Thanks for the article it is pretty interesting. Perhaps you misunderstand my point here. I am not saying the charge and currents can be ignored. The electrodynamic system consists of charges, currents, and fields. (If you want thermodynamics in materials you can couple to other degrees of freedom too!). One should not treat the current like water in a pipe. Wherever there are charges and currents there will be E and H and so they need to be included.
The Poynting Vector is often the simplest picture of the energetics and it is certainly not independent of the system spatial parameters and all the other degrees of freedom.

And I was not trying to say anything is wrong with this picture although I was perhaps expressing a little incredulity at the way the video graphically showed it by my questions.

 

[Philip Koeck]

I would also think that no energy (thermal or otherwise) is actually flowing along the wire.

I can offer the following thought experiment:
Let's say you have a very large charged capacitor, essentially a negatively charged slab of metal somewhere and parallel to that some distance away a positively charged slab.
The whole setup can be in vacuum.
Now you connect the two slabs with a wire.
The wire gets hot and gives of thermal energy in form of radiation so clearly there is some flow of energy.
If one wants to think that energy is flowing along the wire the first question would be: In which direction? I don't think there is a sensible answer to this question.

Assuming one believes that energy flows from the negative to the positive charge, that would mean that the amount of energy in the negative slab decreases during this process.
The problem with this picture is that there wasn't any excess energy localized in the negative slab to start with. The available energy was in the form of potential energy involving the potential difference between these slabs, so in a sense the available potential energy was in both slabs.
So it's really hard to maintain that the energy should flow in a particular direction along the wire when you connect the two slabs.

Does my thinking make sense?

 

[fluidistic]

So your point can be summed up as :
"Of course the energy flows in wires, they get hot"

And your paper explains that there is heating that is quadratic in J. I don't see why this disputes the Veritasium picture at all.

That's not how to sum up my point.

My main point can be summed up as $\vec{J_U}=J_r \hat r + \textcolor{red}{J_z \hat z}$, where the red part is what the youtubers claim is 0, but I show it isn't zero regardless of whether the resistivity vanishes or not.

I used cylindrical coordinates, z being along the wire, r being radial to the wire.

 

[hutchphd]

where the red part is what the youtubers claim is 0

Can you reference this? How can there be no J_z in any useful system ? I am lost as to your intent here...

 

[fluidistic]

Can you reference this? How can there be no J_z in any useful system ? I am lost as to your intent here...

Sure, e.g. Veritasium video's thumbnail is an example. And several of his statements (already alluded to in this thread).

 

[hutchphd]

Sure, e.g. Veritasium video's thumbnail is an example. And several of his statements (already alluded to in this thread).

They claim that there is zero net current along the wire? Definite reference please.

 

[fluidistic]

They claim that there is zero net current along the wire? Definite reference please.

Sorry for.the confusing notation, it's supposed to be energy flux. So their claim would be 0 energy flux along the direction of the wire, or along the direction of the current.

 

[hutchphd]

That's why I want the reference....I have lost track of what you are trying to say. This is why references are necessary and useful (and hearsay is not allowed in court).. Specific references please.

 

[fluidistic]

That's why I want the reference....I have lost track of what you are trying to say. This is why references are necessary and useful (and hearsay is not allowed in court).. Specific references please.

Ok, here are a few "Energy doesn't flow in wires" (thumbnail of veritasium).

Around minute 8:56 in Veritasium's video, the guy says that energy flux goes one way from the battery to the bulb (while in reality part of it goes from the bulb to the battery, but this is not showed nor mentioned anywhere in the video. They only focus on the Poynting vector when it comes to energy flux.)

Around minute 9:49 they claim the electrons don't carry the energy (dang, they again missed an energy flux term that is not part of Poynting's vector).

Then it continues like this, i.e. we can focus only on the Poynting vector to check the energy flux's direction. But this is wrong.

I have spent enough time on this for now, I'm done with this topic, I have already written a document for the curious. Too bad if it's not understood, but the thoughts are there.

 

[hutchphd]

the guy says that energy flux goes one way from the battery to the bulb (while in reality part of it goes from the bulb to the battery, but this is not showed nor mentioned anywhere in the video.

What are you talking about? The net energy flux is from battery to bulb. The electrical part is given by the Poynting Vector. Their are some small adjustments from nonideal wire.

 

[fluidistic]

What are you talking about? The net energy flux is from battery to bulb. The electrical part is given by the Poynting Vector. Their are some small adjustments from nonideal wire.

I am talking about the energy flux inside the wire, specifically. If the wire is ideal, Poynting vector vanishes there, yet there is still an energy flux going along the wire in the current's direction. That's the term in red I mentioned above. The term the youtubers mention its non existence.

 

[Philip Koeck]

I am talking about the energy flux inside the wire, specifically. If the wire is ideal, Poynting vector vanishes there, yet there is still an energy flux going along the wire in the current's direction. That's the term in red I mentioned above. The term the youtubers mention its non existence.

I have conceptual problems with this.
In my previous post I describe a setup with a capacitor and a wire something like this:

+H-

The vertical lines of the H are charged slabs of metal (with the charges indicated by + and -) and the horizontal line is a wire, which is the only load in this circuit.

Why would energy flow inside the wire in the direction of the electric current (from - to + ?)?
Why not in the opposite direction?
If I use a tube filled with salt water in stead of the wire, in which direction does the energy flow then?

 

[fluidistic]

I have conceptual problems with this.
In my previous post I describe a setup with a capacitor and a wire something like this:

+H-

The vertical lines of the H are charged slabs of metal (with the charges indicated by + and -) and the horizontal line is a wire, which is the only load in this circuit.

Why would energy flow inside the wire in the direction of the electric current (from - to + ?)?
Why not in the opposite direction?
If I use a tube filled with salt water in stead of the wire, in which direction does the energy flow then?

There's an energy flux which is a consequence of the thermodynamics relation $dU=TdS+\overline{\mu}dN$. A particle flux (associated to dN) is associated to an energy flux. The direction will depend on the sign of $\overline{\mu}$ and that of the particle's flux itself.