Cecil Moore wrote:

If you want to know the velocity factor of a piece of
transmission line, the easiest thing to do is find
its first self-resonant frequency. A little math
will yield the VF which allows prediction of the
phase shift through any reasonable length of
tranmission line.

If you want to know the velocity factor of a coil,
the easiest thing to do is find its first self-
resonant frequency. A little math will yield the
VF of the coil which allows prediction of the
phase shift through any reasonable length of coil.

If the inductor in question does not take much advantage of mutual
induction across its length nor has much capacitance across its length
(say, a straight conductor, strung with ferrite toroids), then I can
see the similarity with a transmission line. But as the inductor
approaches a lumped inductance with significant inter winding
capacitance and mutual inductance coupling the current across a
significant part of its winding length, I see on reason to assume the
transmission line method (delay independent of frequency) strictly
applies. It might, but it would take more than you saying so to
assure me that it is a fact.

In other words, transmission line concepts like uniform inductance per
length and uniform capacitance per length get rather muddled in a real
inductor.