Re: Toroid Design .
> Original Poster: "John H. Couture" <COUTUREJH-at-worldnet.att-dot-net>
> Jim -
> This is the first time I have heard that the Van deGraaf motor slows
> because of the upper electrode voltage. I thought the transfer of charges
> from the belt to the inside of the sphere was because the potential on
> inside of the sphere was less than on the belt.
The motor slows because the load increases. Assume, first, that the upper
electrode has NO charge (no potential difference between the bottom and
top). In this case, the work required to move the charge the distance
between the bottom and top is zero (no net field to work against). Now, as
the charge accumulates on the top electrode (more properly, the collector),
the voltage increases (V = Q/C) causing an electric field to appear between
the two electrodes. The charge is now moving against an imposed field (that
is, the little "packet of charge" on the belt is charged the same as the
collector: like charges repel: moving against a force requires work, etc.)
In the little Van de Graaf systems we're talking about, the motors are
fairly small, so the mechanical work to push against the electrostatic
forces is fairly significant and noticeably loads the motor down.
You can approach this another way, There is stored energy in the system in
the form of a voltage on a capacitor (500 kV at 10 pF, for example, is
about a joule). That energy had to get there someway, and it is from the
mechanical energy input to the belt moving the charge. For a small
generator like mine, the electrical output is about 10 uAmp at 250 kV, or,
2.5 Watts. The motor is probably something like 1/20 HP, if that, or 40
Watts, so the "electrostatic load" is 5-10% of the motor output, enough to
audibly load the motor down as it charges.
The discussion of why the charge moves to the outside of the sphere is a
bit off topic for this list. Perhaps the High Voltage list might be a
better forum for these discussions anyway.