On Mon, 27 Mar 2006 15:17:35 -0800, Roy Lewallen
wrote:

What most people would call "self capacitance" -- the equivalent
capacitance from one terminal to the other.

Hi Roy,

Not strictly speaking. It ("self capacitance") is with respect to a
very remote reference, not merely the two plate formulation of the
terminal's geometries to each other (that is more part of the
distributed capacitance).

There are two measures of capacitance. Self capacitance is any body's
capacity to store charge. You don't need a second plate to do that in
the classical math - merely a reference point from which the voltage
is determined (yes, another dimensionless oddity that makes this more
easily said than done). Mutual capacitance, two plate construction,
is the more usual form we all have come to expect - so much so that
the term mutual has fallen into disuse and most express only the
second, isolated term - capacitance.

Tom, a week or so back, asked about the infinitesimal capacitance of a
coil with 15 meters (or so) of wire. He speculated that as the
"second" plate of the (mutual) capacitance was withdrawn to infinity,
that it forced the value to zero. I, on the other hand showed that in
the practical universe:
C = 2 · Pi · epsilon0 · L / ( ln(b/a) )
a = 1m (after all, thin is relative at infinite dimensions)
L = 15m
b= 1,000,000,000,000,000,000,000,...000m (10³³³ meters away)
epsilon0 = 0.00000000000885

C = 12 femtofarads

This was certainly at the limits of my usual Capacitor Bridge to
measure to this resolution 30 years ago, but time has marched on. This
sized capacitance is certainly encountered every day in my new field
of nanotech, and 1 femtofarad is measured by charge transfer
techniques.

Consider, Einstein's estimate of the radius of the Universe is roughly
10 Billion Light Years (±3dB) As this result above is vastly further
away than Einstein's guess (by more than 300 orders of magnitude),
lets look at again from his number:

C = 12.5 picofarads

Oddly enough, this value is on par with the distributed capacitance of
the coil's we've been pounding away on (and even more convergent, is
this is roughly the same amount of wire used in them).

I extracted this correlation from reports of the coils' self resonant
frequency and their inductance.

Self Capacitance is nothing more than Mutual Capacitance with a second
spherical plate, with a radius of this 10 Billion Light Years.
However, this capacitance is the total bulk of the coil rather than
that distributed to form a transmission line.

Anyway, thinking of a coil in terms of Mutual Capacitance, Distributed
Capacitance, Self Capacitance, Self Inductance, and Mutual Inductance
is a tantalizing prospect to investigate and elevate the topic to this
mythic status of transmission line - but I seem to lack the motivation
to go there. The extraordinary farce is more entertaining.

73's
Richard Clark, KB7QHC