Art, KB9MZ wrote:
"Taking this point further, one wonders why inductors in the real world
are not designed to be a point load, albeit in a two dimensional world."

Seems we exhausted this topic some time ago. The ends of a coil do not
have to be 180-degrees out of phase due to the configuration and
composition of connections external to the coil. Waves traveling in
opposite directions through the coil can produce a standing wave within
the coil regardless of coil position. Energy into one end of a coil does
not necessarily equal energy out because radiation and conversion to
heat may not be uniform throughout the coil.

Nevertheless, I`m elated. I`ve found my copy of Terman`s "Electronic and
Radio Engineering".
On page 11, Terman says:
"Inductance in microhenrys = (F)(nsquared)(d)
n = number of turns
d = diameter of coil measured to center of wires
F = constant that depends only upon the ratio of length to diameter,
given in Fig 2.2"

The inductance formula above is for a single-layer solenoid. The
footnote says:
"A comprehensive collection of such formulas is given by F.E. Terman,
"Radio Engineers` Handbook" pp 48-64, McGraw-Hill Book Company, Inc.,
New York, 1943."

On pages 59 and 60 of Terman`s "Handbook" he treats a "Flat Retangular
Coil". He gives a formula (47) for its inductance, which is complicated
by multiple dimensions, length, width, etc. Inductance is nevertheless
proportional to the square of the number of turns as in the case of a
solenoid.

My Terman`s Handbook is difficult for me to read due to its damage in a
flood a few years ago. Its pages are stuck together and torn, but it`s
worth trying to use.

Doubts about radiation from shortened antennas can be resolved by
reference to "Terman`s "Radio Engineers` Handbook". On page 795 Terman
says:
"Top loading has the same effect on field distribution in a vertical
plane as a greater height."

Terman also says of a loading coil inserted in an antenna a little way
down from the top:
"This method of top loading gives results equivalent to those obtained
with a capacity top."

Maybe a flat coil is more equal than a solenoid. Were it of great
importance, Terman would have told us.

Best regards, Richard Harrison, KB5WZI