Re: Charge distribution on a Toroid (was spheres vs toroids)

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

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

Antonio wrote:

 > 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,

: abelian:/root# ping www.coe.ufrj.br
: PING roma.coe.ufrj.br (146.164.53.65) from 158.152.63.229
: 17 packets transmitted, 0 packets received, 100% packet loss

but I'll keep trying.

 > Do you have some cylinders or cones calculated?

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

rings   tssp
  10     62.469 pF
  20     63.178 pF
  40     63.572 pF
  80     63.779 pF
200     63.919 pF

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

rings   tssp
  10     45.701 pF
  20     46.359 pF
  40     46.724 pF
  80     46.920 pF
200     47.050 pF

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.

An easy one is two concentric spheres, say radius 0.5m and 0.3m,
C = 4 * pi * epsilon Ra * Rb / (Rb - Ra) = 83.448756 pF

rings      tssp
  10      80.341 pF
  20      81.887 pF
  40      82.643 pF
  80      83.045 pF
200      83.289 pF

In these figures, each object is given the specified number of rings.

If neither object encloses the other, we must be specific about
which capacitance we are measuring...

For two discs, 1 metre diameter, spaced 10cm apart, I get

rings   tssp total    tssp mutual
  10      94.596 pF     75.263 pF
  20      97.845 pF     78.245 pF
  40      99.633 pF     79.896 pF
  80     100.604 pF     80.796 pF
200     101.572 pF     81.699 pF

The capacitances are obtained by putting 1 volt on one of the objects,
with the other(s) fixed at zero volts.  The 'mutual' capacitance is
obtained by determining the charge induced on the zero volt object(s),
and the 'total' capacitance of the 1 volt object is obtained by
looking at the charge on the 1 volt object.  In this example the
two objects are the same size, but if you modelled two different
sized objects, you would have to present four capacitances.

 > http://hermes.phys.uwm.edu/~russell/projects/masters/index.html
 > It has the derivation of the potential of a ring, exactly as I
 > obtained it. Shows also the potential of a belt, but doesn't solve
 > the integral.

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.

 > 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.

By why bother - just erase that nasty little boot virus called
windows and install an operating system.
--
Paul Nicholson
--