Electronic – transmission lines voltage drop

The lumped model of a wire (or any other element) is an approximation. It's not entirely accurate, but it can be useful in many circumstances.

The distributed transmission line model given by the telegrapher's equations is another approximation. It's useful in some circumstances where the lumped model becomes very inaccurate. But it will itself break down and be inaccurate in some cases.

If you are worried that the lumped approximation might not be accurate enough in your situation, you should solve your problem both ways (or maybe a small piece of your problem that will reveal the scale of the discrepancy between the models). If the difference is big enough to affect the final conclusions you are trying to draw from the model, then you should use the transmission line model. If the differences are too small to affect your conclusions, then you may be able to save some time and effort by using the lumped-element model.

“Persons were charged with stealing electricity by placing a large coil, somehow, near high voltage AC transmission lines.”

Is this feasible or was it perhaps an April fool’s article that I swallowed hook line and sinker in my youthful naivety.

Entirely feasible.
Farmers were occasionally charged with power theft in this country (New zealand) in the past. I haven;'t heard of a case in a decade or few - maybe they are getting cleverer at it :-).

This is the same principle as used for "IPT" / "Inductive Power Transfer as seen in phone chargers, industrial monorail powering, electric vehicle charging and much more.

I started to say that if the pickup coil was symmetrical with respect to two phases that were perfectly balanced that you'd get zero pickup, and then suddenly realised that I've always done IPT with essentially a single phase, and that with a 3 phase system with 120 degrees phase separation you should get the advantage of the full load current even if the two phases were fully balanced.

You are essentially getting fields produced by the current, not the voltage, and the voltage is essentially irrelevant as long as you observe the normal conventions that apply to any other dealing with xxx kV.

Energy Harvesting from Electromagnetic Energy Radiating from AC Power Lines - FAR more energy can be obtained than they achieve.

Worked example - I suspect some of the conclusions are suspect A Solution to the RWP for Exam 1 - Stealing Power

Low technical content - high relevance

Directly relevant but low technical value Electromagnetic Harvesters: Free Lunch or Theft!

Several related stack exchange questions with variably useful content.

• How would an electric company detect wireless theft of electricity?

• https://skeptics.stackexchange.com/questions/3520/is-it-possible-to-obtain-current-indirectly-from-power-lines

• Stealing energy from radio towers or power lines

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Online vehicle transfer - I do not have access to this paper but it is probably at least relevant as it will have examples of dual linear conductors and a pickup coil.

Mythbusters getting it wrong

Related:

Industrial monorail

Maximising transfer

Capacitive - but impressive: