Re: Spheres vs Toroids

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

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

Tesla list wrote:

 > Original poster: "Godfrey Loudner" <ggreen-at-gwtc-dot-net>

 > u = 4Pix10^(-7) NA(-2) exact and c = 299792458 m/s exact. Then use
 > epsilon = 1/uc^2.

So, e0=8.85418781762038985E-0012

But, if the error in c is +/-1 m/s, the error in 1/(u0*c^2) is:
-/+e0*2/c=0.000000059e-12. So, only 8 digits are significant, so
e0=8.8541878e-12.

To see the level of precision, consider that Q=C*V=e0*C0*V, and so
dQ=de0*C0*V. The minimum dQ is the charge of one electron, e=1.6e-19 C.
The voltage that corresponds one electron of error in the charge
is then V=e/(de0*C0). With de0=5.9e-20 and C0=1 (a capacitor of 8.85
pF),
V=2.7119 V. So, we can calculate the charge of our toroids with about
100000 electrons of precision.

 > My estimate say to use 69 terms to get 20-place value accuracy. To be sure,
 > I
 > used 100 terms. In my Mathematica session, I asked for 20 significant
 > figures;
 > which in the case of D = 90 cm and d = 30 cm, translates to 18-place value
 > accuracy. Using Mathematica, I get 40.583973310804090804 pf.

The best that I can get is with extended precision, calculating e0 from
your value of c is:
Error=1e-15, 15 terms: 40.58397331080408980000 pF
Error=1e-17, 17 terms: 40.58397331080409070000 pF
This is the limit. More terms don't add anything, and the terms of the
series become numerical noise.
If this is correct, we can measure charges in small fractions or one
electron...

Antonio Carlos M. de Queiroz