Re: IONS/metal pedagogy

[jmclean@chem.ucsd.edu (James Mclean)]

Bob Sciamanda wrote:
> Any scheme to make a stable system out of only Coulomb forces must answer
> to Earnshaw!  We need a conceptual bridge to QM's defiance of Earnshaw.
This may be another view of something already said, but I don't see that QM
is defying Earnshaw at all.  Earnshaw is about static charge distributions
and electrostatic forces.  The orbiting-electron atom is *stable* as far as
electrostatics is concerned, and it doesn't violate Earnshaw because the
electron is moving.  QM is only needed because the orbiting-electron atom
is unstable due to electro*dynamics*.

Coming back to the charged metal sphere, the electrons in there aren't
static.  It's kind of like the atom.  So the first point in the pedagogy:
although the macroscopic charge distribution looks static, the individual
carriers are all bopping around.

Concerning Gauss's Law being in trouble:  if it really is in trouble, then
we needn't resort to mystical quantum situations to see the trouble.  The
Gauss's Law argument which has been presented with regard to excess
electrons applies equally well to a charged conducting sphere and a small
like-charged pith-ball near the sphere's surface.  The argument would have
the pith-ball repelled, but we know it is not.

I think the problem is that the argument assumes spherical symmetry in
using Gauss's Law.  But because of induction, the charge on the conducting
sphere is not spherically symmetric.  And the induction was allowed because
the carriers in there aren't static.

-- 
--James McLean
jmclean@chem.ucsd.edu
post doc
UC San Diego, Chemistry

PS. Anyone notice how this thread, with it's like charges attracting due to
induction, cross-pollinates the one about electrostatics with sticky tape?