Re: Capacitance to free space

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

Original poster: "Antonio Carlos M. de Queiroz" <acmdq-at-uol-dot-com.br> 

Tesla list wrote:
 >
 > 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.

The exact capacitance of the sphere is easy to derive. The toroid case
is more difficult, but known. The cylinder case I don't know if is
known.

 >                                (all metric)
 >
 > Spherical capacitor:    C = (4 pi) (8.85 x 10 -12) (radius)

Ok.

 > 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 )

?!?!?! You can't take the ln of a value with dimension.

 >   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!

Obviously, something is seriously wrong. Capacitances are always
directly
proportional to the size, if the shape is kept.

For some capacitance formulas, see:
http://www.coe.ufrj.br/~acmq/tesla/capcalc.pdf

Antonio Carlos M. de Queiroz