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Re: IONS/metals EUREKA



Hi Ludwig,
You are speculating that this "induction" effect (that's what Jeans is
referring to) will overpower the other effects and hold the excess charge
on the surface. No need to speculate. The following classical textbook
arguments take this and all classically operative electrostatic effects
into account and come to some definite conclusions:

Given a conductor, either neutral or charged, either isolated or under
the influence of external charges, there are two possibilities:
either
1) the carriers (partially) making up the conductor keep moving forever
under the existing E fields, or
2) they ultimately achieve a static situation in which the carriers
(subtracting random thermal motion) are at rest.

We reject possibility (1) as unobserved and/or intractable and proceed
under the assumption that situation (2) ensues after the lapse of some
finite "relaxation time" ( experimentally a fraction of a millisecond,
for metals).

Therefore, once electrostatic equilibrium has been achieved::
1) The electric field at any interior point must be zero (or carriers
would still be moving).

2) Applying Gauss' law it follows that the net charge density at any
interior point must be zero (aside: Note that this assertion - unlike
(1) - would not necessarily follow if Coulomb's law were not exactly an
inverse square law).

3) It follows that any excess charge must reside on the surface.

4) It also follows that the electric field (due to the universe)
existing just off the surface - and exerting a force on any excess charge
residing there - must be perpendicular to the surface and point
outward/inward if the excess charge on that surface is positive/negative.
(Cuz the carriers would still be moving if there were any tangential
component to E_universe acting on them - outward is the only direction in
which they cannot move.)

(Jeans comes to just this conclusion a few paragraphs before your quote.)

Additional conclusions follow, but this much serves to show that :
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.)

No more basic model is classically offered for conductivity vs.
insulation; in fact Jeans explicitly says that the difference is only a
matter of degree. Quantum mechanical "trapping" - requiring a threshold
energy rather than a threshold "anti-frictional" force - was not an
extant idea.

-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: Tuesday, October 06, 1998 9:55 AM
Subject: Re: IONS/metals EUREKA


Bob Sciamanda wrote:

No sale!

If an electron tries to leave the surface of a NEUTRAL conductor, it
will
of course be attracted back by the now positively charged "mother"
body -
separated charges will naturally try to re-combine!. That is pure
Maxwellian.

Your problem was the stability of an unbalanced charge deposited on
the
surface of a body.

What is wrong with unbalanced electrons on the "outer
surface" polarizing the neutral medium deeper inside?
That is what James Jeans was referring to, I think.

".... The relation which, as we have seen, must be
supposed to occur at the surface of charged conductors
between 'matter' and 'electricity', can now be interpreted
simply as systems of forces between electrons and the
remainder of the matter. Up to a certain extent these
forces will restrain the electrons from leaving the
conductor, but if the electric forces acting on the
electrons exceed a certain limit, they will overcome
the forces acting between the electrons and the
remainder of the conductor, and an electric discharge
takes place from the surface of the conductor."