Current of AC transmission lines and electricity in general

[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