The legal concept you refer to will have variable success depending on context. You may make your equitable argument and the judge may say 'nope, the law is the law'. BTDT. In this case, my main quibble with the video is the context and supposed implications, especially for the portion of the viewers that have a much more basic level of understanding. If you are within 100 feet of a power substation but due to some quirk of transmission line topology the route that the wires take to get to your house is 2000 miles, how long will it take your lights to come on after they throw the switch on? Will the power flow through the 2000 mile long route along the wires and take longer, or will it magically flow through space and get there in 100ft/c time? IMO Derek set that whole thing up quite deliberately to be, as Mehdi said, a trick question. So I'm less inclined than you are to cut him slack.
Shrug. To anyone less familiar with the subject, a practical answer to your version is fairly trivial -- within a cycle, less than the blink of an eye. Who could care whether it's 100ns or 10µs, right?
And, easy enough to add that, it's not just the straight-line distance, the wires also need to be in a specific configuration to observe the effect, i.e., having significant mutual induction. Distant transmission lines will not experience this, as we build power transmission lines deliberately to avoid it. So the answer is obviously the longer path (obvious, once this is included, that is). I'm not sure that this particular point was very well indicated in the video, in which case that would be a valid criticism as a missed or hanging point -- but also beside, or in addition to, the main point. If this thought occurs to someone, they can ask in the comments, they can ask friends or experts, or search around.
Anyway, with respect to mains frequency, and human experience, 10µs is just as irrelevant to the average user as the thought experiment's setup -- we don't have any 300Mm transmission lines into space, either.
There has to be a hook, of course. The dissonance between the expected highschool physics result ("current flows in wires duh") and actual EM theory, is what generates views. Again, that's ultimately driven by the dilemma he's explicitly been concerned about before. This production seems consistent with that dilemma.
Now for the specific question, I and surely many others immediately realized that closing Derek's switch would cause an EM response of some sort that would traverse the 1m of space. IIRC you were the first (here) to propose what so far has turned out to be the simplest model that matches scaled experiments so far. However, I'm not fully convinced that the actual response of the any reasonable version of the proposed setup--which has to include actual 1m spacing of the wires--will actually result in current that will light up any actual bulb in anything close to 3.3ns. If I haven't erred, a transmission line with 1cm diameter wire separated by 1 kilometer results in an impedance of 1400 ohms--so the circuit would still light a bulb if that were all there was to it. So I'm guessing that the transmission line is an incomplete model, and under these extreme separations--whether 1m or 1km--it will ultimately prove erroneous. And I mean entirely erroneous, not some nitpicking.
You mean to widen the problem, make the wires further apart? Presumably, because that has no apparent effect on the problem, beyond the scale factor (proportionally higher delay of the immediate wave)? And that you find this an unsatisfying result... but aren't quite sure why, I think..?
Well, why not?
Presumably, the biggest
practical problem to constructing a 1km-wide twin lead, would be its height over ground, no?
The problem makes no statement about ground; but we can see that it will have a significant effect, so we should go to lengths to avoid it, to keep the problem "pure". Perhaps we remove Earth from the picture entirely, just do the experiment somewhere in deep space. Fair enough, most of the TL is already floating up there, why tether the middle to some boring rock that makes things harder to work with?
It's interesting, in that the Earth is a mere 12Mm across, so makes up a small fraction of the largest length scale of the problem. But compared to 1m, or 1km, it's absolutely massive. So it certainly can't be ignored, if we must include it at all.
Notice how else we can treat the problem of ground effect. We can just as well scale it down to, say, 10m separation at ocean level (salt water ground plane), or say, 1mm separation of thin traces on a PCB (copper ground plane). In these cases, the ground effect will be substantial, and we have a mode that looks more like a pair of weakly coupled microstrips. And we know that the round-trip wave will be a great many times stronger than the immediate (coupled) wave.
But they will still be coupled, even if microscopically so. Like, even if it's a mere 1ppm, it's still nonzero, and more than enough to measure -- with a suitable receiver. Granted, we would have to apply quite a serious voltage to use a "lightbulb" as receiver -- we might very reasonably question whether it's worth considering a "lightbulb" as "lit" in that case.
A full description of the problem, i.e. with ground included, then needs to model the ground impedance and shielding effects. What we'll get at the load, is a small immediate step, at the expected straight-line delay, then eventually a very gradual rise as the shielding effect decreases for lower frequency components, and as the normal-mode wave launches off the limb of the Earth and the twin-lead mode takes over. So, we observe four characteristic times or frequencies:
1. Immediate wave: weak, proportional to coupling geometry (mutual induction), ratio of wire distance to ground height, those sorts of things. Delay: light speed between wires.
2. Ground reflections, soil waves, nearby mutual induction. If we're including real Earth earth in the mix, then soil has a fairly high dielectric constant, plus notable losses, giving a delayed and dispersive step response. If lines are elevated far above ground, then ground-wave reflections will be visible as step(s) delayed by [a] geometric factor(s). (Uh, if this is free from buildings, open sky, and ignoring ionosphere*, just the one ground wave, then.) Also, if the soil resistivity is notable, then high frequencies will be well shielded but low frequencies allowed to propagate, thus the coupling factor between lines will be higher at low frequencies.
This will give a delayed, and slow rising, response at the detector, probably in the µs to ms. (Such materials tend to have diffusion characteristics, so won't have a time constant as such, and will look more like a unsatisfying drool, as the level changes slowly over a range of time scales.)
3. Lack of ground reflections: the TLs clear the limb of the Earth, separation between wires dominates over ground, and a twin-lead mode takes over from the microstrip mode. The impedance rises, reflecting some energy back at a medium delay (~ms).
4. TL end reflection, 1s. Note that this has to propagate back through all the other stuff too, so will be weakened doubly; add on top of this, common mode (radiative) losses.
*Oh shit, this whole thing has to go through the ionosophere, doesn't it. Hah, well I suppose it might not make electrical contact, if we're insulating the lines well enough; bare lines I suppose ought to be shorted out a bit however. The conductivity isn't very much up there, with respect to something the diameter of a wire, but it adds up over the ~10s km layer thickness. Put another way: the waves are guided by the TL, but the waves propagate largely in the space between them, and that space happens to be loaded with ions which tend to absorb and reflect the waves, rather than allow them to propagate.
Nevermind somehow short circuiting
the entire motherfucking ionospheric current of the atmosphere. HAARP couldn't possibly dream of such power!
Tim
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