Re: capacitance of a disk

[brian whatcott <inet@INTELLISYS.NET>]

At 17:04 2/10/01 -0500, David wrote:
> // the exact general result for the
> capacitance (to infinity) of an arbitrary conducting oblate spheroid of
> semimajor axis a and eccentricity e (the formula being simple enough to
> readably write in ASCII), it is
>
> C = 4*[pi]*[epsilon]_0*a*e/arcsin(e)   .
>
> David Bowman
> David_Bowman@georgetowncollege.edu


An innocent reader (like me) might easily speculate on how exact
 a result can be which depends for its magnitude upon
 a physical quantity like epsilon_0  - the permittivity of free
space, six decimal places known with certainty from my data
 book reference.

 The permittivity of air could contribute a difference
in that sixth decimal place?
(Relative permittivity of air = 1.000536)

Coulomb reports that he was disappointed in an effort to find a
change of capacitance in a trial of transferring charge to an
isolated conductor coated with shellac.
The charge delivered did not vary from that passed to an uncoated
conductor.   (1)

 But Faraday, in investigating dielectrics (his coinage) chose
shellac and sulphur as offering the best bulk resistivity and
 found an effect by transferring a measured charge using a
sufficiently thick dielectric layer even though the dielectric
constant of these materials at 3 or 4 is not high.  (2)

    If capacitance takes effect over a medium which extends to
infinity, then even great thicknesses of dielectric would provide
 a vanishingly small proportion of the permittivity of the total
 medium in question one supposes.



1) Coulomb:   Memoires de l'Academie    1787 p.452-3
   as mentioned in
2) Faraday:   Researches Series IX  1835   para 1253