Cecil, W5DXP wrote:
"My statement was limited entirely to lumped inductors, a purely
imaginary conceptual model."

Sorry I didn`t get the picture. An inductor that provides no phase shift
is similar to a capacitor that holds no charge. Inductors and capacitors
store energies in their magnetic and electric fields. Current lags in
the inductor and leads in the capacitor. Pure reactances have a
90-degree phase shift between applied voltage and resulting current by
definition.

An inductor sans phase shift is salt without savor or sugar without
sweetness.

Lumped inductance means coiled in place of straight wire, to me.
Reference to toroidal coils in this thread implied to me an absence of
external field, for which I chose a shielded coil with a straight-axis
for my example.

I agree with Cecil that a 90-degree antenna which includes only a
45-degree length of wire needs another 45-degree phase-shift in its
length to reach the full 90-degrees.

As the coil is in series with a resistance, and the resistance the coil
experiences depends upon its position between drivepoint
(low-resistance) and far end (high resistance) at the end of the
element, the inductance required to produce the same required phase
shift, varies with its position in the element.

Where the resistance is low, so is the required inductance. Where the
resistance is high, so is the required inductance, and it is all for the
same number of degrees that the antenna is short.

Best regards, Richard Harrison, KB5WZI