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Re: Toroid Design .
Hi John and All,
Although Van de Graaff generators are a fringe topic for this list, let me
explain the energy principles the best I, and Paul Tipler's College Physics
text, can. Also demonstrating that we just don't make this stuff up :-))
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.
Since the motor is supplying 111 watts (0.15 Horse Power) it can easily
slow down if it is not very strong. Van de Graaff motors are often weak so
when the belt falls off the track, or any of a number of screw-ups happen,
the motor will do minimal damage.
If the generator is turned off, there is a lot of charge on the top
terminal. It is possible, if the belt moves freely, to reverse the process
and use the stored energy to turn the belt in the opposite direction.
One side of the belt is charged by the top terminal and is attracted to the
ground. On the other side, the belt is at ground potential and is
attracted to the top terminal. So the belt can start turning. In a real
system the process is likely to start in the opposite direction but with a
"push" the belt could turn by itself in the same direction. 111 joules is
a lot of energy so this is possible on very large systems and has been
observed.
Note that there is mechanical friction in this system but ideally it is
very low and has no real effect. There are a few issues with how the
charges are created and transferred at the top and bottom of the machine to
the belt but nothing to serious. Needle points are used to create high
field stresses that arc and "suck" the charge from the belt. The fact that
the potential in the sphere is zero (relative to other objects in the
sphere) helps this process of charge transfer. It works in reverse when
the machine is turned off. The belts are electrostatically charged by
needle points driven by a high voltage power supply at the base. It is
possible to use friction (triboelectric effect) to charge the belt but this
method is not very good in a REAL machine.
Refer to any modern (Van de Graaff wasn't that old) physics book in the
electrostatic potential section for more details. Many use the Van de
Graaff machine as an example and give homework problems on how much work it
takes to charge them. Read the part about work and potential between point
charges for the real theory involved. "Coulomb's Law" is the real heart of
all this. John - If your "physics and engineering texts" don't mention ANY
of this, throw them away and get new ones. The books (probably lectures)
Coulomb learned from, won't mention any of this either :-))
It is interesting to note that the French physicist Charles Augustin de
Coulomb (1736-1806) figured all this out 214 years ago.
Robert J. Van de Graaff was born in 1901 (young by great physicist
standards) but I doubt if he is still living.
I hope I did all this right. In college I was attracted to girls more that
point charges :-))
Terry
terryf-at-verinet-dot-com
At 06:58 AM 1/2/99 +0000, you wrote:
>
> Ed -
>
> The "pelletron" website was interesting but did not contain any
>information on work regarding the VDG. I also was not able to find any info
>for VDG work on any other site or in physics and engineering texts. I wonder
>if anyone has ever considered this problem. Have you found info on VDGs that
>mentions work involved? It appears to be complex and to require a lot of
>empirical data from real world VDGs.
>
> I believe understanding about the work required to charge the VDG terminal
>would help in undestanding the work involved with charging the Tesla coil
>terminal.
>
> In your description "that as the belt moves up etc" cannot be possible
>because there is no charge on the inside of the terminal to repel the charge
>on the belt. No charge inside the terminal is the electrical magic that
>surprised Faraday. If the belt was on the outside of the terminal the
>charges would repel as you stated but that is not what happens.
>
> You say that the "belt backed away". That could indicate a possible
>repelling effect but not necessarily an increasing repelling effect with an
>increasing terminal voltage.
>
> It is obvious the work to get the charge on the VDG terminal must come
>from somewhere. This work appears to be in the form of belt friction
>creating electrical charges or from a separate power supply. The electrical
>friction would be a load on the belt motor but would be a very small part of
>the total motor load. This electrical friction load would be a constant so
>would not slow up the motor as the voltage on the terminal increases. If
>there is a separate power supply there would be no electrical friction load
>on the belt motor. The work to charge the terminal would come from the power
>supply.
>
> Determining the electrical input for the motor would be easy but
>determining the part needed for the charging load may be impossible. It is,
>however, possible to determine the work to charge the terminal by Work = Q
>x V where Q is in coulombs.
>
> Note that I have not been able to verify the above VDG work theory in any
>text.
>
> Sorry to hear about your eye problems. I also am limited by my eyes as to
>time at the computer screen.
>
> John Couture