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# Re: Toroid Design .

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Gavin -

I agree the voltage of the pail cannot be increased without limit. But how
about an isolated sphere in space. What would limit the voltage?

In your post using the equation

Volts = b x V x s x R

the capacitance of the terminal to ground of 0.1 pf is unrealistic.

Cap = Q/V = 10^-6/10^7 = o.1 pf

Also the 1 ucoulomb\m^2 is unrealistic. Refer to Antonio's post where he
derives 26.5 ucoulombs/m^2 or 1 coulomb/58.5 inch^2. I used 50 inch^2/1
ucoulomb or 31 ucoulombs/m^2 in my post as value based on tests.

Was this matter brought up in the lecture you attended?

John Couture

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At 11:02 PM 1/5/99 -0700, you wrote:
>Original Poster: Gavin Hubbard <ghub005-at-xtra.co.nz>
>
>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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