Re: Capacitance to free space

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

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