# Re: Toroid Design .

```At 06:47 AM 1/5/99 -0700, you wrote:
>Original Poster: "John H. Couture" <COUTUREJH-at-worldnet.att-dot-net>

>  It is my understanding that it is not Coulomb's Law but Faraday's ice pail
>discovery in 1824 that makes the VDG possible. Electrical potential is a
>work function and can be cumulative. This was noted by Faraday when he found
>the addition of charges on the inside of the pail could increase the voltage
>on the outside of the pail beyond limit.
>

Hello list.

Actually, the voltage on the outside of the pail cannot be increased
without limit. Consider a typical belt driven VDG with a large, smoothly
rounded, and insulated, metal electrode.

Suppose a negative surface charge of density: s Coulomb/metre^2 is sprayed
onto a belt which is: b metres wide and which moves vertically at a speed
of: v metres/second. The charging current carried by the belt to the
colector is:

I = b*v*s   (Amps)

In a time: t seconds, a charge Q = I*t is deposited on the electrode whose
potential V is Q/C where C is the capacitance to earth of the high-voltage
electrode. Obviously, in the absence of any loss of charge, an unstable
situation prevails and the potential V would rise to infinity. In practice,
a steady state is established at a terminal voltage V where the charging
current is balanced by a discharge current which includes the load current
and losses due to corona and leakage along insulating surfaces. If all
these paths have a combined resistance of R, then the discharge current is:

I = V/R   (Amps)

So the terminal voltage is (by combining the two equations):

V = b*v*s*R   (Volts)

Reasonable practical values for the quantities involved above are R= 10^13
Ohm, s = 10^-6 C/m^2, v = 10 m/s and b = 0.1 m. Here, the theoretical
potential of the high voltage electrode is 10 MV.

Safe coiling,

Gavin Hubbard

P.S. I have paraphrased the above from some photocopies which were given
out at a lecture I attended last year. The author's name and the original
publication are not recorded.

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