Current of AC transmission lines and electricity in general

[sophiecentaur]

The inside of the outer conductor is a excellent conductor. That makes it a good EM mirror. Any magnetic field incident with the inside surface will induce a perpendicular longitudinal current that will create a reverse magnetic field to cancel the incident field. Those two fields cancel everywhere outside the inner surface of the outer conductor.
You are hypothesising that the magnetic field inside the transmission line is caused by a current flowing “in” the conductor. But that current was induced in that mirror surface by an incident internal magnetic field. You are forgetting that the EM field within a coaxial cable is constrained to the dielectric by the surface currents on the reflective “walls”.
When you connect a transmission line to a signal you are connecting the dielectrics and the conductive reflective walls. You do that by making sure that longitudinal surface currents and electric field between the surfaces will not be interrupted at the interface.

Hypothesising your own personal theory is a most inefficient way of approaching the subject. It wastes your time and the time of those who answer your questions. You question the paradigm by proposing a simpler model of reality that does not fit the paradigm. You then call for someone to say why your poorly specified model is wrong. That requires they understand your immature model, which is different to their reality. It is better to read and understand the physics than to learn in an ever changing feedback loop where communications in the English language gets two chances to be misunderstood per cycle.

I'm not sure what you're implying here. Are you suggesting that the internal B field is eliminated due to reflections? (perhaps not) There is a B field inside the 'cavity, which is circumferential (Transverse). There are a load of links that show how this can be calculated using Ampere's Law and it is finite at the inner surface of the outer conductor and at the outer surface of the inner conductor. This link shows it in detail but there is a graph showing the results of the calculations and the way the field varies with the radius. It shows that the external field is zero and that it exists throughout the conductors (depending on the resistivity)
If tim looks at the link, above, he will see the actual situation and will not need to try an alternative personal approach.

 

[tim9000]

HI, thanks for the replies;

You can't just look at the outer because there has to be a return path for current to flow. The 'corkscrew rule' tells you that the magnetic fields add in the inside and cancel on the outside. Look at the diagrams further back in this thread. E fields are zero outside too. A

I am surprised that I'm getting the corkscrew rule wrong, could you please give me post number in the thread, to specifically refer to?

The inside of the outer conductor is a excellent conductor. That makes it a good EM mirror. Any magnetic field incident with the inside surface will induce a perpendicular longitudinal current that will create a reverse magnetic field to cancel the incident field. Those two fields cancel everywhere outside the inner surface of the outer conductor.
You are hypothesising that the magnetic field inside the transmission line is caused by a current flowing “in” the conductor. But that current was induced in that mirror surface by an incident internal magnetic field. You are forgetting that the EM field within a coaxial cable is constrained to the dielectric by the surface currents on the reflective “walls”.
When you connect a transmission line to a signal you are connecting the dielectrics and the conductive reflective walls. You do that by making sure that longitudinal surface currents and electric field between the surfaces will not be interrupted at the interface.

Hypothesising your own personal theory is a most inefficient way of approaching the subject. It wastes your time and the time of those who answer your questions. You question the paradigm by proposing a simpler model of reality that does not fit the paradigm. You then call for someone to say why your poorly specified model is wrong. That requires they understand your immature model, which is different to their reality. It is better to read and understand the physics than to learn in an ever changing feedback loop where communications in the English language gets two chances to be misunderstood per cycle.

That is harsh but pretty fair, but in my defense I didn't realize I was hypothesising my own personal theory, I thought I was just applying the corkscrew rule an illustration on the internet, I didn't realize that I was being overly reductionist and that it required a deeper level of understanding, hence I mistakenly expected a more simple answer than could be given [I do completely agree with the whole 'introducing two misunderstandings per cycle']. (also according to @sophiecentaur I'm applying it wrong, which doesn't help)
So I'm a little bit lost here "But that current was induced in that mirror surface by an incident internal magnetic field. You are forgetting that the EM field within a coaxial cable is constrained to the dielectric by the surface currents on the reflective “walls”.
When you connect a transmission line to a signal you are connecting the dielectrics and the conductive reflective walls. You do that by making sure that longitudinal surface currents and electric field between the surfaces will not be interrupted at the interface."
So are you saying that the current in the surface of the two conductors is caused by the magnetic field, and not the electric potential of the source? Okay, so the EM fields are contained within the dielectric, but what do you mean by 'interrupted at the interface'?

If tim looks at the link, above, he will see the actual situation and will not need to try an alternative personal approach.

Yeah I think I will need to look at that link to figure out what is going on with the B fields and how they are cancelling. Thanks

The bottom picture in my post #46 (particularly the top frame) I was trying to illustrate my interpretation of something(s) you said earlier:

It travels between the conductors, guided by the surface of the conductors.

And I was wondering if you could please comment on that.

There is a voltage difference between the conductors. So between the conductors we also have an electric field. The E and M fields are perpendicular. The cross product of those two fields gives the poynting vector which is the direction of energy flow. That direction is from the generator to the load.

When we measure the rate of energy transfer from generator to load by multiplying the current by the voltage to get power in watts, we are in effect (cross-)multiplying the electric and magnetic fields.
The energy travels through the insulation and air between the wires, guided by currents in the surface of the wires.

Yeah I think I more or less understand that, (and I am fascinated by the realisation that it is in essence the cross-product), and so (in the second half of that picture I drew in #46) I wanted to make a sort of hypothetical of well if the energy travels between them, what if they (the conductor and return conductor) were infinitely far spaced away from each other, but the source was a finite distance from the load, would energy ever actually be able to flow towards the load?Cheers

 

[sophiecentaur]

(also according to @sophiecentaur I'm applying it wrong, which doesn't help)

I have to backpedal here a bit. With a two wire feeder the B field between the two conductors will have contributions from both conductors but, of course, with a continuous outer, there is no contribution to the B field inside the cavity - if you consider the continuous outer as a number of parallel conductors with equal currents flowing in them, the 'corkscrew rule' will cancel the fields from diametrically opposite conductors. But Ampere's Law gives you the answer in a more pukka way.

what if they (the conductor and return conductor) were infinitely far spaced away from each other,

That's not an acceptable model to work with as you cannot connect a source or load in a conventional way. Your suggestion makes me think of radio communication between two antennae.

 

[Baluncore]

Are you suggesting that the internal B field is eliminated due to reflections? (perhaps not)

No, I'm saying there are no fields from inside the coaxial cable getting outside because the walls are mirrors. At a conductive surface the transmitted wave is canceled so it does not exist outside the coax.

 

[sophiecentaur]

No, I'm saying there are no fields from inside the coaxial cable getting outside because the walls are mirrors. At a conductive surface the transmitted wave is canceled so it does not exist outside the coax.

Yes, I see that now.
Also, Ampere's Law says what happens in any of these cases.

 

[tim9000]

I have to backpedal here a bit. With a two wire feeder the B field between the two conductors will have contributions from both conductors but, of course, with a continuous outer, there is no contribution to the B field inside the cavity - if you consider the continuous outer as a number of parallel conductors with equal currents flowing in them, the 'corkscrew rule' will cancel the fields from diametrically opposite conductors. But Ampere's Law gives you the answer in a more pukka way.

That's not an acceptable model to work with as you cannot connect a source or load in a conventional way. Your suggestion makes me think of radio communication between two antennae.

So with the conventional two wire feeder circuit (as I tried to illustrate in the top half of the bottom picture in #46) is that how the EM energy travels down the line? The B and E field vector orientations (if that is the right terminology) and so the cross product is down the line.

Ah yes, I see what you're both talking about with the continuous outer coax, thanks!

 

[sophiecentaur]

and so the cross product is down the line.

For a two wire feeder, there will have to be a finite radiation resistance, I think and this implies that the Power is mainly flowing down the line (TEM) but there will also be a slight divergence of the Pointing Vector field to account for the leaked power into free space. I guess that the E and B fields will have a small but finite in phase component.

 

[tim9000]

I was more interested in if the diagrammatic arrow representations of how you could think of the energy transfer component of the E and B actually looked, in the picture were accurate.
(also, what would this 'divergence' due to leaking power 'look like'?)

I think and this implies that the Power is mainly flowing down the line (TEM)

But I posed this before in about #12 and:

Why confuse things by using waveguide mode classification when phase velocity is not relevant because the distance between the wires is very very much less than a wavelength. EM radiation in space is TEM, just as are the fields between the good conductors that make up a circuit.

So are you saying that the conduction of electricity IS IN FACT a TEM model?

Cheers!

 

[sophiecentaur]

So are you saying that the conduction of electricity IS IN FACT a TEM model?

Why not? The E field is normal to the wire, the B field is in circles round the wire and the power flows along the wire. The fields are (at least nominally) transverse to the direction of power flow. (We ignore the forward component of the E field, which seems to get so many people steamed up because they think that field component is relevant)

(also, what would this 'divergence' due to leaking power 'look like'?)

Without bothering to actually draw it, I can describe it as having the Poynting Vector S parallel with the wires in the centre and very slightly spreading 'outwards' at locations near the wires. The divergence will be small as the radiation resistance is very low. If the wires were significantly resistive, part of the power would be 'into the wires' (more divergence, I guess) so the total flux (between the wires) would get gradually less and less. The explanation for this divergence is that the speed of propagation near the resistive wire (or the radiation leaves from sections of it) is a bit slower. The same effect can be seen when a Vertically Polarised Medium Frequency signal travels along the ground (a ground wave) and it is constantly 'dragged' and dissipated by the ground, giving a slight forward slope to the E field, directing Power down into the ground. It keeps the level of received signal higher than you'd expect because energy above the ground gets directed downwards. The 'shadow' of an MF signal, produced by the presence of metal buildings in a city, gets repaired by this mechanism and the received signal beyond the city gradually recovers.

 

[Baluncore]

So are you saying that the conduction of electricity IS IN FACT a TEM model?

How many different waveguide modes are possible on a coaxial cable?

 

[tech99]

How many different waveguide modes are possible on a coaxial cable?

If the circumference of the pipe is less than a wavelength, there are two modes. The ordinary TEM and the "single wire" TM mode. The latter is small for a small diameter cable and is not noticed, because its group velocity is the same.
If the circumference is greater than a wavelength, then conventional waveguide modes can start to occur, and if the cable is sufficiently large there is no limit to their number.

 

[tim9000]

How many different waveguide modes are possible on a coaxial cable?

I'm not talking about a Coaxial cable. (the single conductor and return path)

Why not? The E field is normal to the wire, the B field is in circles round the wire and the power flows along the wire. The fields are (at least nominally) transverse to the direction of power flow. (We ignore the forward component of the E field, which seems to get so many people steamed up because they think that field component is relevant)

I'm just being pedantic now, but how can there be a forward component of the E field if it's normal to the wire?
So what do you mean by 'relevant', could you elaborate (you don't have to if you don't want to), I think the original answer to my question was remember cross product and remember the E field is between the potential of the conductor (and on that second point, I imagine that each point of potential has fictitious field lines running to each other point along the conductor of lesser potential and that 'is where' the E lines are, as opposed to the B lines which just rotate around the conductor)

@sophiecentaur I'll need more time to think about the rest of your post, cheers.
Thanks for the replies.

 

[sophiecentaur]

I'm just being pedantic now,

Rightly so; you have to ask questions. I make no apology for saying that this is an 'Engineer's `thing' and it is perfectly acceptable to see this sort of problem as a set of shells; the outer shell would be the ideal / simplest model. This will suffice for many situations but it may be necessary to use more than the basic transmission line theory in some practical circs. The fact is that there is only a forward component of E when there is a non-ideal situation, involving loss of power as the wave travels. Nonetheless, this 'tilt' is very small in any normal transmission line. If you made a line out of nichrome (resistance) wire then you could imagine most of the power having dissipated within a couple of metres of line. Then you would really see some significant tilt or spread of the vector.

 

[tim9000]

Rightly so; you have to ask questions. I make no apology for saying that this is an 'Engineer's `thing' and it is perfectly acceptable to see this sort of problem as a set of shells; the outer shell would be the ideal / simplest model. This will suffice for many situations but it may be necessary to use more than the basic transmission line theory in some practical circs. The fact is that there is only a forward component of E when there is a non-ideal situation, involving loss of power as the wave travels. Nonetheless, this 'tilt' is very small in any normal transmission line. If you made a line out of nichrome (resistance) wire then you could imagine most of the power having dissipated within a couple of metres of line. Then you would really see some significant tilt or spread of the vector.

That is a nice answer. So the infra red radiated (heat loss) is explained from the poynting vector diverging (spreading) from it's forward direction in it's TEM path between and around the two wires.
Thanks heaps!

 

[sophiecentaur]

The "heat loss" is because of the resistance in the wires or the resistive element in the insulator / spacers. The other loss is due to EM radiation into space (the 'radiation resistance - which doesn't get anything hot until the EM is absorbed by something resistive out there.

 

[tim9000]

The "heat loss" is because of the resistance in the wires or the resistive element in the insulator / spacers. The other loss is due to EM radiation into space (the 'radiation resistance - which doesn't get anything hot until the EM is absorbed by something resistive out there.

I understand that the heat loss is due to resistance, I didn't consider that it was due to spaces in the conductor (minor insulation) I was just thinking of them (some of the electrons) absorbing some of the EM and then re-radiating it out as new photons off the conductor, but I suppose that is like a sort of insulation quality, then again this could just be two descriptions of the same thing? But now you're saying there is ANOTHER aspect, that of radiate resistance, so that means that a super-conductor would still radiate EM (and act as a transmission antenna)? So still has a resistance of sorts?

Also, just thinking about preparing to wind this thread up, of of my original post thesis was that I felt that the electrons were in them-selves acting as the medium for the ill-defined 'electricity', which I've come back around to thinking. So the electrons pass a sort of energy wave along the conductor as they slowly move (in DC) or oscillate back and forth without moving (in AC), as the Electric field is BETWEEN the conductor (and it's return path conductor) and the Magnetic field curls around the conductor (and it's return path) and I suppose the closest thing to what we call 'electricity', is the resulting poynting vector? [ of BxE or ExB (?) ]
And also just to double check there is no E field actually inside the conductor is there?

Cheers!

 

[sophiecentaur]

RF power is radiated from any structure - that's fundamental. But the radiation resistance of a superconducting coil is extremely low a couple of metres is a minute fraction of a wavelength at 50Hz so it's not a significant factor - particularly at DC.
From some of your comments, it seems that you are trying to mix macroscopic matters (Maxwell's Equations and EE in general) with a very superficial model of how electrons are actually involved in real conductors. You are bound to draw funny conclusions when (as you say) you have only limited knowledge of either. I, certainly would be reluctant to get involved in that sort of exercise. If in doubt I go to the textbook (or a local PF expert.)
The Poynting Vector was originally defined as
S = E_XH
H is Magnetic Field and B is magnetic flux density. Look it up if you feel like it but H and B tend to be used in different contexts and it's easy to get confused.
If you do it the other way round, the Power flows the wrong way. lol

 

[tim9000]

But the radiation resistance of a superconducting coil is extremely low

I thought that the current in superconductors flowed unimpeded forever. But if they have a (low) radiative resistance then this cannot be the case?

From some of your comments, it seems that you are trying to mix macroscopic matters (Maxwell's Equations and EE in general) with a very superficial model of how electrons are actually involved in real conductors.

I am guilty of having that nasty tendency, but I'm working on it. Though, how did I do that just before? Was it by saying that the electrons were what radiated the EM away? I didn't think really required Maxwell's equations (although I'm sure it would be consistent with them) I just thought I was taking an extremely superficial aspect of QM (not that I internally contexturalised that as a realisation when I said it).

And also just to double check there is no E field actually inside the conductor is there?

Thanks again!

 

[sophiecentaur]

I thought that the current in superconductors flowed unimpeded forever. But if they have a (low) radiative resistance then this cannot be the case?

The resistance is Zero for DC but 'very low' for AC. This link quotes nanoOhms for the resistance in a superconducting microwave cavity as opposed to milliOhms in a copper one, which shows that it's still worth using superconductors. Radiation Resistance is, like the poor, "always with us' but, of course, at DC it is zero, in any case.

Was it by saying that the electrons were what radiated the EM away?

That is really mixing your metaphors and can't lead you anywhere with certainty, I think. I always say that there is no point in bringing electrons into electricity except when you have no option. Maxwell certainly didn't (they hadn't been found in his time) and did well enough without them. If you think that using electrons has actually helped you with your 'understanding of electricity' then you are in good company but it's a bit of a delusion. I guess you could say that electron behaviour is a part of electricity and not the other way round.

 

[tim9000]

Ah, I ever so vaguely remember something like the BSC theory, (which my HS physics teacher called the 'BS theory') so that would make sense if that was for DC. As would be the case for levitating super conductors with a permanent magnet.

That is really mixing your metaphors and can't lead you anywhere with certainty, I think. I always say that there is no point in bringing electrons into electricity except when you have no option. Maxwell certainly didn't (they hadn't been found in his time) and did well enough without them. If you think that using electrons has actually helped you with your 'understanding of electricity' then you are in good company but it's a bit of a delusion. I guess you could say that electron behaviour is a part of electricity and not the other way round.

Yes, I agree about trying to neglect electrons from the 'electric model' which has been the big leap for my mind. I'm just trying to understand the role they play in their repulsion and behavior to be homogeneous in guiding the electric field for 'electricity' to happen ; so there is no electric field in the wire, I'm fine with that. But when I work back in the model, say from conductor to source from MMF, we're always taught to think of the loop of copper spinning cutting the flux and the 'current' to be induced in the wire. But using this model of the poynting vector etc. I'm trying to picture instead...what, the electric field is induced between the coils (between each turn and between one coil to the other) as they cut the magnetic flux? This is a bit for me to grapple with, but I'm trying.

Thanks