Tdonaly wrote:
"In order to show that an inductor can be treated as a transmission
line, in the way that you want to do it, you have to show that your
inductor has an exponential potential gradient along its length when
terminated in a certain impedance."

Inductors are used to replace a missing length of an antenna which often
would be located at the inductor. The coil is an antenna length
surrogate. Its delay and impedance characteristics match that of the
missing length of straight wire.

The logic is simple. Natural growth or decline is a change based upon a
certain fraction of the available energy. One segment of of a radiator
or a line extracts a certain energy fraction. The next similar segment
extracts the same percentage, but the extraction is larger or smaller
because the remaining energy it has to work with is is larger or
smaller. It`s a natural law of growth or decline.

It is "exponential" because that`s the name given to change "as a
percentage of the energy of the energy involved". It`s growth or
shrinkage at the "natural rate".

It is exactly due to agreement in the amplitude and phase behaviors of
antennas and transmission lines that Terman refers his readers to his
transmission line section to explain antennas.

Best regards, Richard Harrson, KB5WZ