Re: IONS/metal pedagogy

["Bob Sciamanda" <trebor@velocity.net>]

Hi Brian,
Let me first outline the textbook classical argument without using the
word "tension".

Presuming electrostatic equilibrium:

1)  From Gauss' law => the electric field produced by a flat sheet of
uniform charge,  just off that sheet and near its center = (1/2)
sigma/epsilon (on each side of the sheet) ; away/toward the sheet as
sigma is positive/negative. (This gives the exact field in all external
space in the limit as the width & length of the sheet increase without
limit.)

2) Also from Gauss' law => the total (net) field, due to the universe,
just off a conducting surface = sigma/epsilon; outward/inward as sigma is
positive/negative.

3)   From (1), exactly half of this field is due to the local charged
surface element (dA) - so that the net field acting on that conducting
surface element (due to the rest of the universe) is (1/2) sigma/epsilon;
out/in as sigma is positive/negative.

4.) The net electrostatic force of all other things on the charged
conducting surface element (dA) is therefore
dF = (1/2)*( sigma^2)* (dA)/epsilon; always outward - ie; away from the
conductor's interior.

For those who see a slippery speciousness in the argument of (3),  let it
be noted that the conclusion (4) also follows from "virtual work"
arguments (beyond the scope of most intro courses).


The semantics of tension:
Model a rope as a line of point masses connected by springs.  When two
external forces pull the ends in opposite directions with equal force,
each constituent mass is in "tension"; ie -  being pulled apart by its
connected springs.  We say the rope itself is in tension  (being pulled
apart).  The end masses are each in tension under a single spring force
and an external force.  The external force agents are being pulled toward
each other.  (I like to say a rope is a one dimensional, uni-directional
rigid body - it will support tension, but not compression, and only in
one dimension - or: "You can't push a rope!")

Apropos to the electrostatic forces on a conductor, textbooks often sum
up by saying the conductor is at most in tension (being pulled apart),
never in compression (as would be an object submerged in deep water).  I
think this term "tension" is properly applied to the entire conducting
object, and not just to a single surface element as my previous language
wrongfully did - mea culpa!  The point is: the net electrostatic force on
each charged dA is OUTWARD.

-Bob

Bob Sciamanda
Physics, Edinboro Univ of PA (ret)
trebor@velocity.net
http://www.velocity.net/~trebor
-----Original Message-----
From: Brian McInnes <bmcinnes@pnc.com.au>
To: phys-l@atlantis.uwf.edu <phys-l@atlantis.uwf.edu>; PHYS-L
<phys-l@atlantis.uwf.edu>
Date: Sunday, October 11, 1998 10:06 AM
Subject: Re: IONS/metal pedagogy


> Hi Bob,
> I see where you are coming from.  If there is a net electrostatic force
on
> the surface charge then there has to be a (magic) force to balance this
out
> or there is a (magic) proscription: thou shalt not move off the edge of
the
> metal!
> Now I accept that as you say "the standard classical line of reasoning
> (hinging largely on Gauss' law) says that a conductor (charged or
neutral -
> in an external field or not) is under a force of tension wherever there
is a
> surface charge".
> However, I want to check out the details of the argument (none of my
> classical electricity books are here at home).
>
> In the meantime, one point that really worries me is the reference to
"force
> of tension".  Tension is what you get when molecules are too far away
from
> one another: examples are a stretched string or the surface of a liquid.
> When the molecules are too close we have compression as in the body of a
> liquid (which leads to the phenomenon of pressure) or in a table leg.
> Forces of tension are attractive and, importantly, leave any particular
> molecule along the string or in the surface in equilibrium: NO NET
FORCE*.
> Similarly for forces of compression.  Now what the classical line calls
a
> force of tension surely can't be the same as that, or is it?  Anyway, I
want
> to follow it up early this week.
>
> *Twenty or so years ago, Warren, in his excellent book, Teaching of
Physics,
> pointed out how flawed most (all?) textbook diagrams are on this point.
>
> Brian McInnes
>
>
> *******************************
> > Hi Brian,
> > I apologize - my statement was hurried and vague - but of serious
import.
> > I was referring to a line of reasoning which I earlier outlined:  the
> > standard classical line of reasoning (hinging largely on Gauss' law)
says
> > that a conductor (charged or neutral - in an external field or not) is
> > under a force of tension wherever there is a surface charge.  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.  This (says the classical model) is the net electrostatic force
> > due to the universe, per unit area of charged conductor surface. IE;
the
> > NET ELECTROSTATIC FORCE is not zero - it is outward.  If our scheme
says
> > the conducting surface is in equilibrium under only electrostatic
forces,
> > this (largely Gauss based conclusion) is in question.  I really hope
> > something is wrong with my reasoning here, because it looks to me like
> > any classical model has to include some non-electrostatic force to
> > achieve equilibrium here (as we feel forced to do within the nucleus).
> > Please straighten me out!
> >
> > Bob Sciamanda
> > Physics, Edinboro Univ of PA (ret)
> > trebor@velocity.net
> > http://www.velocity.net/~trebor