IONS/forces

[Ludwik Kowalski <kowalskiL@Mail.Montclair.edu>]

On 10/7/98  Bob Sciamanda wrote:

> ... A conductor, either carrying a net non-zero charge and/or
> within the influence of external charges,  IS ALWAYS IN
> TENSION due to electrostatic fields acting on its surface
> charges, never in compression. That is: wherever there is
> a non-neutral surface charge, those charges are being forced
> OUTWARD by the combined electric force of the rest of the
> conductor and the rest of the universe.  You can in fact (using
> Gauss' law) get quantitative: F/A =1/2 (sigma/eps) - the force
> per unit area is equal to 1/2 the surface charge density/epsilon).
>
> This is what classical E&M concludes to be the bottom line, net
> effect - existing electric forces are trying to rip any excess charges
> straight out from the conductor surface (there is no escape from
> this conclusion - don't spin your wheels!).  Why don't the
> charges move?  Classical E&M responds only that there is no
> conductivity in that direction.  The mechanism behind this
> "blocking" non-conductivity is not addressed.
>
> By unspoken hypothesis, no mechanism is required: Classical
> E&M is here taking non-conductivity as a presumed given -
> unless you move along or into a conductor!  (You presume
> that motion can occur unless there is a blocking force; in
> contrast, this model presumes that motion is forbidden
> unless there is conductivity.) .....

Everybody knows how to calculate a repulsive force
between two identical point charges, Q/2, separated by
a distance r.  For example, F=22.5 N when Q=0.001 mC
(r=1 cm),  2250 N when Q=0.01 mC, etc.

Suppose that a charge Q=0.001 mC is distributed
uniformly over the INNER surface of a DIELECTRIC
spherical shell whose radius is 1 cm. Then, if thinking
in terms of forces is not forbidden, the pressure exerted
on the shell is 0.24 atm (it would become 240000 atm
if the net charge were 1 mC; electrostatic pressure is
proportional to the square of Q).

1) Clearly a thin shell (of r= cm) would burst under
the electric pressure of one millicoulmb. How thick
should the shell be to hold 1 mC? Suppose that the
mechanical properties of the material are the same
as for steel. I do not know how to find the necessary
thickness d when the gas pressure is given. Can
somebody suggest a clerver way of estimating d? Or
summarize a ready-made recipe?

2) Suppose that the dielectric shell is very thin and
supported (to prevent bursting) by a very thick
metallic shell. Induced charges on the inner surface
of the metallic shell will at once remove the electric
pressure and the charge Q will appear on the outer
metallic surface. Now Pauli is in charge of all charges.
Like charges still repel but they are not free to escape
into a vacuum, unless E is excessive (for example,
10^9 V/m or so).

Thick dielectric=closed jail.
Metal=open jail, and a tunnel to escape.
Ludwik Kowalski