Keith Dysart wrote:
How is it that this exhibits transmission line behaviour?

The equation for a single-wire transmission line over
ground is well known to be Z0 = 138*log(4D/d)

As a data point, take a look at:

http://www.w5dxp.com/coil512.ez

Here is the current for each turn as reported by EZNEC.

Load 1 Current = 1.02 A. at -3.15 deg.
Load 2 Current = 1.121 A. at -11.28 deg.
Load 3 Current = 1.211 A. at -17.09 deg.
Load 4 Current = 1.289 A. at -21.59 deg.
Load 5 Current = 1.352 A. at -25.22 deg.
Load 6 Current = 1.401 A. at -28.29 deg.
Load 7 Current = 1.436 A. at -31.0 deg.
Load 8 Current = 1.459 A. at -33.5 deg.
Load 9 Current = 1.47 A. at -35.89 deg.
Load 10 Current = 1.468 A. at -38.25 deg.
Load 11 Current = 1.454 A. at -40.66 deg.
Load 12 Current = 1.427 A. at -43.21 deg.
Load 13 Current = 1.387 A. at -46.04 deg.
Load 14 Current = 1.332 A. at -49.34 deg.
Load 15 Current = 1.261 A. at -53.5 deg.
Load 16 Current = 1.17 A. at -59.25 deg.
Load 17 Current = 1.057 A. at -68.49 deg.
Load 18 Current = 1.039 A. at -71.74 deg.

The auto transformer would appear to be unnecessary
... Do we really need it?

I don't know the answer to that question. I didn't
want any reflections from the coil.

How did you route this wire?

I used an aluminum ground plane for that "wire".
Since the wire is very short at 4 MHz, I assumed
not much transmission line effects in the wire.

Should I expect the same results if
I measure the voltage?

I doubt it. But the subject was the current through
a loading coil, not the voltage.
--
73, Cecil http://www.w5dxp.com