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

[John Denker <jsd@av8n.com>]

My previous answer is "in need of improvement".  Strictly speaking
it's not wrong ... but it's not clever.

On 08/13/2013 08:07 PM, I wrote:
> I'd measure the /force/.  

So far so good .....

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

That 1 newton is how much you would get if you measured 
the force on the entire capacitor plate.  It would be much 
cleverer to do a *bead pull* measurement.  This is a standard 
technique;  I get 23,000 hits from
  http://www.google.com/search?q=%22bead-pull+method%22+OR+%22bead-pull+measurement%22

It is commonly used to measure the high-frequency (microwave)
fields in particle accelerators ... but it works fine for DC
(electrostatic) fields also.

If done right, this can be quite accurate.

Loosely speaking, the physics of the thing is that there is
energy in the electrostatic field, and there is less field
inside the dielectric bead, so the energy of the system is
less when the bead is in a high-field region.  To find the
voltage, measure the force on the bead at various locations 
and integrate.

If the bead is small, you can measure the field without
greatly perturbing it.

Do you see why the tube is necessary, surrounding the
filament that holds the bead?  It's a waveguide beyond
cutoff.  Without it, we could not guarantee that the
region inside the Faraday cage was a field-free region.
By fiddling with the shape of the tube, you can spread
out the force on the bead, to make it easier to measure 
and easier to integrate.  (Measuring a force that is
nearly a delta-function is not so much fun.)

The cage should be mostly made of metal screen, so you 
can see what's going on inside.

The scale needs to be battery-powered.  The positioner
needs to be battery powered and controlled via optics
or via bluetooth.  Lego robotics is one possibility.
Again it should be protected by waveguide that is beyond 
cutoff at DC ... but not beyond cutoff at optical or 
bluetooth frequencies, so we can still control it.

Note that the scale /moves/ depending on the force on
it ... but its position-versus-force characteristic
can be calibrated in advance and taken into account.

You can get some very fine fibers by cutting open a
piece of Kernmantel (aka kernmantle) rope.

This setup has a fair number of parts, but each one
has an obvious purpose, so the overall cognitive
workload shouldn't be too bad.

It demonstrates a real, practical technique.  It 
demonstrates some interesting physics.  I don't see
any obvious safety problems, in the sense that it's
no worse than the original capacitor.