Re: ark voltage

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

Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz <twftesla-at-qwest-dot-net>" <acmq-at-compuland-dot-com.br>

Tesla list wrote:
> 
> Original poster: "by way of Terry Fritz <twftesla-at-qwest-dot-net>"
<Kidd6488-at-aol-dot-com>
> 
> I'm kind of curious about the voltage coming off the toroid...
> Is it still 70kV/inch (35kV/Cm)
> 
> It doesn't seem like my wimpy 20" sparks are (20 * 70,000)= 1,400,000 Volts!

The actual relation is nonlinear, and depend on the shape of the
electrodes. A good discussion about this appears in the book by North
"High-power microwave-tube transmitters" (there is a copy on Terry's
site),

http://hot-streamer-dot-com/TeslaCoils/OtherPapers/NorthReport/

chapter 7. A formula is given there for the voltage between 2 spheres of
radius R and separated by d (meters):

V=E*4*d/(d/R+1+sqrt((d/R+1)^2+8))

E is 3000000 V/m in normal conditions. The relation tends to V=E*d for
d<<R and to V=2*R*E for d>>R. 
The formula in the book actually gives E as function of V. The text says
that the expression is exact (really?). It agrees reasonably with tables
that can be found in several places.
For a ball and a plane, simply double d and divide V by 2:

V=E*4*d/(2*d/R+1+sqrt((2*d/R+1)^2+8))

I would like to see a formula for spheres of different sizes.

Antonio Carlos M. de Queiroz