Re: [Phys-L] measure voltage of van de Graaf

[John Denker <jsd@av8n.com>]

On 08/13/2013 06:41 PM, Carl Mungan wrote:

> I'd like to measure more precisely. Obviously either a measurement of V or
> Q would work.

I'd measure the /force/.  I estimate the force to be on the order 
of 1 newton, which should be measurable without too much fuss.

> Simplest idea I can think of is to progressively reduce the plate spacing
> until I get arcing and then assume V = (3 kV/mm) * (arcing plate spacing).

That's the one thing that won't work at all, assuming the gap
is changing under conditions of constant Q.  Each field line 
begins and ends on a charge.  Constant Q means constant field.

Starting with a large gap and then reducing it (at constant Q)
lowers the voltage.  Starting from 100 kV, a modest reduction 
suffices to get the voltage down to where ordinary instruments
can measure it.

If that lowers the voltage by a factor of ten, then 10 kV
divided by 100 megohm is only 0.1 mA and 1 watt, so you can 
use off-the-shelf resistors to to make a voltage divider.
With a capacitance of 10^-11 C and a resistance of 100 megohm, 
the RC time is a millisecond, so the discharge should be 
readily observable on a storage scope.  1000 megohm resistors
are available but somewhat more scarce.  Beware that you
have to /clean/ any high-value resistors or you'll get the
wrong answer.

If you were thinking of changing the gap at constant V, to
find the breakdown point, there are easier ways of measuring 
the V.  Basically you are just measuring the open-circuit
voltage of the generator.  Doing that is easier and safer 
/without/ the capacitor.

A field mill is fine way of measuring large electric fields.
Measure the field near the generator and integrate to get 
the voltage.
  http://a-tech.net/ElectricFieldMill/