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Re: IONS/metal pedagogy



Hi Ludwik,

Your springs cannot be made without violating Earnshaw's theorem!

I can see some of these schemes (like Joe's) perhaps consistently working
(given QM's having already made stable neutral matter with available
bound states). The problem is that this raises a perhaps much more
serious problem. If the excess charge on a conducting surface is in
equilibrium under only electrostatic forces, then Gauss' law is in
trouble. Again - what do we give up? Is not the internal field zero?
must not a negative surface charge terminate a field line from the
outside? Something of the classical model of a conductor and its surface
must give. (And this might be the way to go!)

-Bob

Bob Sciamanda
Physics, Edinboro Univ of PA (ret)
trebor@velocity.net
http://www.velocity.net/~trebor

-----Original Message-----
From: Ludwik Kowalski <kowalskiL@Mail.Montclair.edu>
To: phys-L@atlantis.uwf.edu <phys-L@atlantis.uwf.edu>
Date: Friday, October 09, 1998 11:52 PM
Subject: IONS/metal pedagogy


On October 9, 1998 Bob Sciamanda wrote:

The first job of QM is to construct a NEUTRAL
atom/molecule/object by keeping equal and
opposite charges APART! This is the first defiance
of Earnshaw.

We can do this without QM. Suppose small metallic balls are
charged with Q1, Q2, Q3, Q4 etc.; some are positive others are
negative. We connect these balls with springs made from a
dielectric material. Some springs will stretch, others will
compress and an equilibrium will be established. The sum of
all charges does not even have to be zero.

The system of charges is stable because in addition to
electrostatic forces we added elastic forces (which are
ultimately electric). Why should "defying" Earnshow's
theorem with QM be more acceptable than defying it with
classical springs. In both cases we are trying to escape the
tyranny of the word "electrostatic" which appears in the
theorem (see below).

The attractive surface forces preventing electrons (on the
outer surface of a charged sphere) from escaping into the
vacuum could perhaps be explained classically. We must
invent such forces to preserve the validity of the Fnet=m*a.
This is better than to say that F=m*a does not apply to our
macroscopic system.

I suspect that a classical explanation of attractive surface
forces (acting on electrons) is possible. What is wrong with
the suggestion made this morning by Joseph Bellina?

On September 29, 1998 From Bob Schiamanda wrote:

A home-brew proof of Earnshaw's Theorem (actually a
corollary thereof): If there were a point in empty space
(no charge there) where a positive test charge would be
in stable equilibrium under only electrostatic forces, the
electric field would have to be zero at that point, and at
every point on the surface of a neighboring sphere
(centered on that point) the field would have to point
inward toward that point. (outward if you use a negative
test charge). Since E lines are continuous and only start
and terminate on charges (Div E(r) = 0 in charge free
space), this is impossible. QED