Re:IONS/metal pedagogy

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

The specification "due to the rest of the universe", which appears
in two Bob's messages, is not clear to me. What is its significance?
My understanding of the difference between (1/2)*sigma/epsilon and
(1)*sigma/epsilon has nothing to do with the "rest of the universe",
only with total charges on the objects under consideration. In the first

place the field due to sigmas exists on both sides of the surface while
in the second case the field of sigmas exists on one side only. Am I
missing something more significant to our debate?

Bob Sciamanda wrote:

> The net electrostatic force per unit area (DUE TO THE REST OF
> THE CONDUCTOR AND THE REST OF THE UNIVERSE) =
> (1/2) sigma^2 /epsilon - always an outward force.

An electrostatic voltmeter (essentially a capacitor whose one plate
is spring-supported rather than rigidly-fixed) is based on this formula
because sigma can be expressed in terms of d.o.p.

An additional d.o.p. between already electrified plates "tries to help
charges" to escape from the surface. But they do not escape as plates
move toward each other. There must be an attractive force of some
kind between excess charges (outside the volume of the plate) and
the plate itself.

A free body diagram, applied to the movable plate in equilibrium,
will have the force of the spring acting in one direction and the XXX
force acting in the opposite direction. This is not an action-reaction
pair (both forces are acting on the plate, one is due to the spring and
another must be due to surface charges). The XXX force must be
numerically equal to the force with which the plate attracts its
surface charges.

I am assuming that the voltmeter is connected to a HV source and
that the d.o.p. was increased slightly so that the average sigma can
be used in the force formula.

What is the nature of the XXX force? Some said it is electrostatic
(due to electrostatic induction) others said its nature can not be
explained in classical terms. These positions contradict each
other. And nobody wants to say  "free body diagrams are not
applicable to situations of that kind." A paradoxial situation.
Please help to resolve it.

Ludwik Kowalski