Re: Capacitance to free space

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Gerry Reynolds" <gerryreynolds-at-earthlink-dot-net> 

Hi Jared,

It will also be true that the exact solution assumes no proximity effects
from other objects like a secondary coil.

Gerry R



 > Original poster: "Jared E Dwarshuis" <jdwarshui-at-emich.edu>
 >
 > There are approximations for top end capacitors to free space, but the
 > exact solutions are just as easy to use if not easier, and are fairly
 > easy to derive.
 >
 >                                (all metric)
 >
 > Spherical capacitor:    C = (4 pi) (8.85 x 10 -12) (radius)
 >
 > Cylinder capacitor:     C = (2 pi) (8.85 x 10 -12) (length) / ( -ln
 > radius )
 >
 > Toroidal capacitor:     C = (4) (pi sqrd) (8.85 x 10 ? 12) ( R) / (- ln
 > radius )
 >
 >   r is the small radius and R is the average of the large radius where
 > (R1 + R2)/ 2 = R
 >
 > Interestingly the exact solutions for the cylinder and toroid become
 > negative solutions when r is greater then one meter (as ln goes
 > negative). Seems odd that the exact solutions would say this but they
 > do!
 >
 > These are in close agreement with the approximations you typically see
 > except when the capacitors are very large (over 50 pf), then the
 > approximations come up short.
 >
 > From: Jared and Larry
 >
 >