Re: Charge distribution on a Toroid (was 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: Paul Nicholson <paul-at-abelian.demon.co.uk>

 >  > I made a document showing the algorithms:
 >  > http://www.coe.ufrj.br/~acmq/tesla/capcalc.pdf

 > Thanks.  I haven't been able to download it yet, host roma.coe.ufrj.br
 > doesn't seem to be responding,

Maintenance in the power lines, heavy rains, etc.

 > First, a cylinder 1 metre diameter and 1 metre long

   rings   tssp        Inca
    10     62.469 pF  62.965 pF
    20     63.178 pF  63.481 pF
    40     63.572 pF  63.740 pF
    80     63.779 pF  63.869 pF
   200     63.919 pF  63.947 pF

Do someone know an exact capacitance formula for a hollow cylinder?
Doesn't seem so complicated to calculate exactly. Maybe a distorted
toroid, with the tube flattened to a belt.
The capacitance of a disk can be deduced from the capacitance of
a flattened sphere, so the general idea is not so strange.

 > Now a cone, 1 metre diameter across the base, 1 metre high,

   rings      tssp      Inca
    10     45.701 pF   46.118 pF
    20     46.359 pF   46.628 pF
    40     46.724 pF   46.883 pF
    80     46.920 pF   47.010 pF
   200     47.050 pF   47.087 pF

The rings produce faster convergence, because at least around the
figure the modeling is exact. I am placing the rings exactly at
the centers of their sections of the line that generates the figures.
I could stretch the arrangement, moving the outermost rings to
the edges. This would increase the capacitances to above the correct
value. I would have then two limits for the correct capacitance.

 > How about looking at mutual capacitance between two objects?  You'll
 > have to tag the rings to remember which electrode they belong to, then
 > sum the charges separately for each object.
 >...

I will have to reorganize my program for this, allowing a list of
objects and then computing the capacitance matrix for the objects.
I could also use images of the objects to calculate the capacitance
between an object and a perfect ground plane at some distance
below it. Maybe in the next days.

 > That's a nice page.  The obstacle remaining is a good self potential
 > formula for the tape ring.  If the performance of tube rings is as
 > good with mutual capacitances as it is with isolated objects, then
 > I might be able to switch to using tubes.

The ideal would be to have a truncated conical ring. A problem
appears to exist with the mutual influences too. Points or rings
are located at exact points, but a belt is spread along a line
where the potential due to another belt varies. Where in the line
of the belt would the potential be calculated? The problem of
the self-potential falls in a similar problem, that is where to
place the other "dummy" belt where the potential would be the
same of the self-potential. But where in the dummy belt?
If that the correct place is at the center of the line, we are
back to the infinitely thin rings.

 >  > There is a gnu C for DOS: http://www.delorie-dot-com/djgpp
 >
 > Yes, I wrote a program with this once.  It produces 32 bit code and
 > requires a DPMI environment to run in, so it's ok in the 'dos boxes'
 > on windoze and linux.  Works well, I recall.  Has a full set of
 > libraries for video graphics, etc.

The produced code is very fast.

Antonio Carlos M. de Queiroz