Speed of Electricity

Factual Questions
21

Hmmmm. Lets say you touched a charged wand to the end of a conductor… what would happen? It seems like the first thing is that all the charge would flow to the surface and then you’d have an unbalanced surface charge.

Now nature isn’t going to tolerate this so I guess the charge would start to propagate down the surface of the wire. But at the same time you have the transient EM wave outside the wire which would create a longitudinal E field inside the wire, which in turn would………….I don’t know. There’s all kinds of things going on and I’m confused. I guess if I had to guess I’d say once the transient field dissipated you’d end up with a surface current that would prevail until all the charge imbalance was gone. Corrections are welcome.

22

If you had the wire surrounded by a high dielectric constant region, the pulse could move quicker than the outside external radiation, but this doesn’t really match the real situation. I was thinking that for a wire in free space, the pulse would move slower than C, but would still be there. But I don’t really know.

Perhaps the hose analogy isn’t all that great in detail.

23

I’m in way over my head here, so I won’t presume to tell you that you’re wrong. But in the brief searches I’ve done, it appears that TEM waves are most often applicable in RF and microwave frequencies. Are you sure that the bulk of the energy of a trans-continental electric transmission line is carried in a TEM wave?

I could imagine a case where a massive switch is thrown in NY which energizes the line. High harmonics of the abrupt switch could travel down the transmission lines at near c, but the bulk of the energy (at 60 Hz) might take longer to get there.

The reason I’m questioning you is that all my life I’ve been told that electrical energy carried through wires travels significantly slower than c (.7 - .85 being the range I remember).

24

Last things first, the .7 to .85 C is reasonable for things like coax cables, printed circuit lines, things which would carry RF or microwave transmissions.

Electric transmission lines are usually treated as lumped load circuits, rather than transmission lines, because they are so short in terms of wavelength. For a 5000 km transcontinental transmission line at 60 Hz, that’s only 1 wavelength. Within a city, or even most states, the transmission paths aren’t long enough to worry about. This is why you wouldn’t usually hear about the transmission speed in this case.

All well and good, but is the bulk of the energy in a TEM wave? Well, strictly speaking, a TEM wave would exist only in the ideal case, with perfectly conducting wires, non-lossy air, and perfectly conducting ground. In the real case, that almost TEM mode is still there, and does carry the energy. There could be some energy carried between ground and the wires (although they try to minimize this). Any non-TEM modes are going to be cutoff at 60 Hz. Also, there could be some negligable delays at any substations where the voltage was changed. I’m going to assume we skip any high voltage DC transmission lines. I’m also going to ignore that the transmission path doesn’t follow a straight line (looking at a map of the US power grid, the path might be a 10 - 20 percent factor).

The issues which could plausibly affect the speed of the wave are the ground, the dielectric constant of the air (and any cover on the wires), and the loss in the wires. The wires (the ones I’ve seen, anyway) are up high in the air, much higher than the wire separation. The energy of the fields is predominantly located between or near the two wires, and falls off rapidly a few wire separations away. Also, at 60 Hz, even the ground is very conductive, so the fields don’t penetrate into the ground. Any covering the wires have is thin compared to the wire spacing, so most of the energy is in air.

This just leaves loss in the wire, and this was the part I thought had the best chance of having an effect. Since I crunched the numbers, I’m going to make you all look at them :p. In Fields and Waves in Communication Electronics (2nd Ed.), by Ramo, Whinnery and Van Duzer, there are formulas (with a little rearranging) for the velocity of the (almost) TEM wave in terms of the inductance, capacitance, resistance and conductance of a non-ideal line. See table 5.11 for the formulas (I’m using the low-loss formulas). I’ll give enough of the formulas that someone could check my work (all units MKS):

After assuming no conductance in air, I get
R = 2 * R[sub]s[/sub] / ([sym]p[/sym] * D) = 4E-6 / ([sym]p[/sym]D) (for copper, R[sub]s[/sub] = 2E-6 Ohms from Fig 3.16b. R[sub]s[/sub] = 1/([sym]sd[/sub]))
L = 4E-7 ln(S/D)
V(elocity) = C / (1 + R[sup]2[/sup] / (8 * [sym]w[/sym][sup]2[/sup] * L[sup]2[/sup])
where S is the wire separation, and D is the wire diameter.

8 * [sym]w[/sym][sup]2[/sup] = 8 * (2*[sym]p[/sym]*60)[sup]2[/sup] = 1.137E6

Assuming S = 4 meters, and D = 3 cm (these are WAGs), I get

L = 1.957E-6
R = 4.244E-5
V = C / (1 + 4.136E-4) = 0.9996 * C

25

ZenBeam

Assuming your are correct then Cecil is wrong and Marilyn is correct. Do you really want to go there?