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Re: Toroid Design
At 10:02 PM 1/3/99 -0700, you wrote:
According to my cypher'n:
1 meter dia sphere capacitance= 4 PI E0 R = 111 pF
Energy stored -at- 1 million volts= .5 C V^2 = 55.5 Joules
To double the voltage on the sphere (quadruple the power to 222J)=
222-55=167J; add 167 joules
The next voltage doubling will require adding (888-222=) 666 Joules }:-)
>> Original Poster: Terry Fritz <twf-at-verinet-dot-com>
>> Reading from Tipler's book, the work required to bring a charge Q1 from
>>an infinite distance to within a radius r of another charge Q2 is:
>>
>> W = k x Q1 x Q2 / r [joules]
>>
>> The voltage or potential of a point charge at a distance r is:
>>
>> v = k x Q / r (since Q / v = capacitance, the capacitance of a sphere =
>r
>> / k Farads/meter radius)
>>
>> where
>>
>> k = 1 / (4 x pi x e0) ==~ 9 x 10^9 [N-m^2/C^2]
>>
>> e0 = 8.85 x 10^-12 [ C^2/N-m^2 ] = [Farads/meter]
>>
>> So if we have a Van de Graaff sphere 1 meter in diameter charged to 1
>> million volts the charge is:
>>
>> 1000000 = k Q / 1 .... Q = 111.1 uCoulomb
>>
>> So if we want to double that voltage in 1 second, we need to add 111.1 uC
>> to the sphere in 1 second.
>> How much power (in watts) does it take to support this charge rate?
>>
>> The work in joules is:
>>
>> k x (111.1 x 10^6)^2 / 1 which is 111.1 joules / sec or 111.1 watts if
>> the sytsem is running continuously.
>>
>> That works out to 111 watts to keep the generator charging at the
>1MegV/sec
>> rate.
Adding constant power will result in a limit being reached. That limit
itself will be limited far more practicaly by the poor insulation systems
available. I would just love to have a meter-diameter diamond or sapphire
for an Inertial Electrostatic-confinement thermo-nuclear fusor.
Forunately for Tesla-philes, the realm of dynamics offers far higher
potentials and powers with the pulse-power paradigm.