# Re: Spheres vs Toroids

```Original poster: Paul Nicholson <paul-at-abelian.demon.co.uk>

Antonio wrote:

> But the toroid is in air, not vacuum. Would this cause the
> difference?
> I have a book here that lists e0=8.85418e-12, +/-0.000002e-12.

That looks like the vacuum value, which is the figure I gave.

For air, multiply epsilon by a factor 1 + x * 10^4, where
x is taken from:

Temperature   Humidity     x
--------------------------------
0 deg C      dry       5.76
20 deg C      dry       5.36
20 deg C      25%       6.0
20 deg C      60%       6.6
20 deg C     100%       7.4
40 deg C      dry       5.1
40 deg C     100%      10.8

> I get C=40.5839741468 pF for the 90x30 cm toroid in free space.

I get 40.5839789 - I think yours will be better because I'm
numerically integrating the P and Q functions.

> Do you have some idea about how to calculate the electric field
> at the toroid surface?

Of course, that varies with position.  You have to use say, the boundary
element method to obtain the surface charge distribution, which
gives you the surface field strength.

Bart wrote:
> I also ran Fantc at a level 10 (off my pc as I can set the code
> for higher details).  Anyway, it showed 40.55. I would say your
> 40.5648 is doing quite well

which is an example of the boundary element method with the toroid
decomposed into 50 charge rings.  I would say the boundary element
method does ok (less than 0.1% error in this example) even at this
modest level of detail.  Similar comparisons can be done for other
exactly computable capacitances, such as discs and spheres.

Cheers.
--
Paul Nicholson
--

```