Gene Fuller, W4SZ wrote:
"This is getting more interesting by the moment."

There are plenty of coils in boxes which have different currents into
and out of their two ends.

A coil in a box used to be a common way to resonate a too-short 1/4-wave
(90-degree) whip. A company I worked for had many Land Rovers, trucks,
boats, and ships on and around the Argentine side of the island of
Tierra del Fuego.These were equipped with H-F SSB tranceivers. Mobile
amntenna was a stainless whip mounted atop a substantial fiberglass box.
The box contained the loading coil which was accessible for preselecting
the right coil tap to resonate the whip with the vehicle for a
particular operating frequency. The box also contained a motor-driven
band-switch to automatically change taps on the coil when the frequency
was changed on the radio.

I am well aware of the ability to resonate a 90-degree whip with no more
than the proper coil in series with the short whip on a base insulator.
I tuned every one of those coils for each of the frequencies we used in
Argentina with my own hands.

ON4UN has a graph, Fig 9-22 on page 9-15 of "Low-Band DX-ing" which
shows current distribution of a base-loaded whip, In his example, the
whip is 45-degrees long.. The loading coil provides the extra 45-degrees
required for resonance.

Current at the base of ON4UN`s whip is one amp times the cosine of
45-degrees, or 0.707 amp. The loading coil has an input of one amp.

With 1 amp into the loading coil and 0.707 amp out of the loading coil,
the coil definitely does not have the same current at both ends.

Best regards, Richard Harrison, KB5WZI