# Isotropic Capacitance

``` Richard Hull <hullr-at-whitlock-dot-com> wrote:

> The charge figured relative to a point infinitely distant is a nice
> concept.  But, to aquire a charge, anywhere in the real world, work must
> be performed in a dielectric (space in this case) by sparating this
> charge relative to something (the point far off).  Metals can't have

Ahhh... but the point that originally sparked this exchange was your quite
correct comment that the formula used for the capacitance of a sphere does
not match the measured values. And the reason for this is that the
assumptions made to derive the capacitance do not match anything that can
be done in the real world. Since most real-world problems don't have any
exact, closed-form mathematical solution, (at least that we've yet been
able to find) we are forced to either work with approximations or go with
computer-based numerical solutions. These are still approximations, but we
can usually make them very, very close to what's really measured.

But looking for a closed-form solution, we often end up having to assume
away reality in order to make the problem simple enough to be solvable.
That equation for a spherical capacitor that coilers tend to use assumes
a universe that's absolutely empty, except for that charged sphere.
There's not even a "second plate" to the capacitor, since capacitance by
definition does not require one; only a voltage that varies in proportion
to the charge.

Considering all this, your original comment that the measued value can be
off by 20% is really quite encouraging. (I prefer to see it as the
measured value is __only__ off by 20%.) From time to time we'll see
comments that this or that thing doesn't match "theory". Now, while there
are real-word measurements that don't match the best available theory, I
wonder how much of that truly exists in the coiling world. That's not to
say there's none there, but that what many coilers think of as "theory"
was known from the beginning to be only rude and crude approximation.

Things like the equation for the capacitance of a sphere were never
intended to be more than ballpark indication of where the capacitance
should be. If someone really really needed a close prediction of the
capacitance in a real-world situation, they'd need to apply something
like the Method of Moments on a decent computer with a good matrix
inversion routine that can handle some hefty sized matrices in something
less than the expected lifetime of the universe. In a lot of cases, say,
with changing values of dielectric constants, even this would be far too
simplistic a solution.

It might be nice if we could derive equations that just let us plug in
some numbers and get an exact solution for whatever problem we faced.
I suspect that the universe wouldn't be nearly as interesting as it
actually is, so I'd never wish for such a thing. In reality, there are
even very simple problems that can be mathematically proven to have no
closed-form solution; the classic three body gravitation problem is
probably the best known. There's no reason to expect that the problems
we face as coilers should have closed-form solutions, but numerical
computer modelling should certainly be able to give predictions to the
precision we need; that is if we really need them. The cut-and-try
methods used by many coilers, added to net communication like this
have allowed various coil designs to evolve in a most rapid and
startling fashion, without the need for accurate prediction
beforehand.

> separating the charge.  Naked monopolar charges are suppossedly not
> allowed anymore than magnetic monopoles.  Theory is great, but it must be
> self-consistent when viewed from every angle.

This is an interesting comment; I wasn't even aware that magnetic
monopoles were not "allowed"; simply that there's no evidence for
their existence. Maxwell's Equations could easily be retrofitted to
handle them; in fact the absence of monopoles causes us to leave out
terms that really look like they belong there. That's not to say that
I expect monopoles to exist. There are Grand Unification Theories
that don't allow them, of course. There's also at least one that
requires one or more to exist. All of these GUTs represent a lot of
really excellent and really hard work, though no more than one of
them can be correct, and perhaps none of them are even close. I
could be wrong, but I suspect that no consensus has been reached,
and the jury is still out on this one. (Personally, I expect we'll
find a unicorn before we find a monopole, but my track record at
prediction has been less than remarkable...)

If I read you right, it seems that you're saying that separate
electric charges can't exist? Are there any published experiments
that might support such a claim? It's quite a remarkable thing
to say.

> A fantastic book I am currently wading through calls into question some
> aspects of Maxwell's equations especially as regards displacement
> currents and their hypothesized attendant magnetic fields and further
> points up and mathematically proves that some of his equations have no
> demostrable causal relationships.  This is a very well done piece of work
> by Dr. Oleg Jefmenko, professor at West Virginia State Univ.  If anyone

You omitted the title of the Good Doctor's work. As you mentioned in a
personal note, I suspect we're straining the limits of what's allowed
on this list, and I am trying to turn the subject back toward coiling
at every opportunity. Certainly, if there is a problem in Maxwell's
Equations, it could affect our coiling predictions. However, if it's
wise to suspect the validity of established scientific conventions, it
might seem even wiser to also suspect the validity of its challengers,
as there are so many more instances of the challenges falling apart than
the conventions. To this effect, if you can again describe a published
experiment that backs up such a claim, it would be helpful. I kinda
like seeing old established ideas getting swept away, but really good
revolutionary ideas are rare things. Separating them from the "also-rans"
requires much careful examination. If it's inappropriate for this list,
I'd certainly be interested in continuing by E-Mail.

By the way, in my last note I asked wether you had any data concerning
measured toroid capacitance compared to the equations that get passed
around. That short sentence must have been lost amid the rest of my
voluminous verbiage, but I'm really interested in hearing of whatever
you've found. They have the look of empirical equations, fitted to
data, rather than something derived, which adds a bit more uncertainty
on my part, so I'd greatly value your experience in the matter. Thanks
for the interesting discussion & take care.

Wes B.

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