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Re: Spheres vs Toroids
Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br>
Tesla list wrote:
> Original poster: "Gerry Reynolds" <gerryreynolds-at-earthlink-dot-net>
>> A very thin toroid has zero capacitance, but it must
>> be -very- thin.
> I interprete thin to mean small minor diameter and not thin conducting
Yes. Only the shape of the surface is important.
> Also, I'm presuming that as the minor diameter go to zero and the
> toroid/capacitance vanishes, that there is no interconnecting surface that
> would normally make connection from the center to the inner surface of the
> toroid contributing to your capacitance calculation. Would this be correct?
Yes. Otherwise the toroid would be reduced to a thin disk,
that has C=4*e0*diameter in meters. A toroid with the hole closed by
a disk seems a quite complicated object for a closed-form solution.
As a curiosity, The (open) toroid that has the same capacitance of
a thin disk with the same diameter has:
minor diameter = 0.07556682*major diameter.
> Is the distribution of charge on the outer surface of the toroid (for
> typical and fixed geometry that we use for TCs) uniform or is there a
> guassian like distribution across this outer surface. Does this
> distribution (whatever it is) affect the capacitance calculation?
The distribution is not uniform. It has a maximum at the outer diameter
and a minimum at the inner diameter, that is zero only if the hole
is closed (Maj. D.= 2* Min. D.). The shape of the distribution, as
far as my studies are, is a complicated series of Legendre functions.
Antonio Carlos M. de Queiroz