Re: IONS/metal pedagogy

["Brian McInnes" <bmcinnes@pnc.com.au>]

Hi Bob (and others interested in this strand),
Let's follow up some of your comments.

snip
> 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.
end of snip

I've got no problem with any of that, except to remark that I'd rather think
of and talk of intermolecular forces (electrostatic ion origin) rather than
'connected springs'.  Key points are that elements of the string is being
pulled away from each other and that the elements (and the string) are in
equilibrium. 
Forces due to the rest of the universe (everything outside the string;
forces from the hands and the earth) are exerting a net force on the end
elements of the string.  Yet those end elements, like all the elements
within the string, are in equilibrium.

snip
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.
end of snip

Okay, the analogous system for the string is a solid, say a rubber cube,
that is being pulled out everywhere (for example, it could have hooks on
each face and someone is pulling on the hooks).  We'd say that the cube is
under tension.  The net external force on any surface area dA is OUTWARD. 
However each element of surface is in equilibrium under the combined effect
of external forces and molecular forces from the cube. 

Now, back to our charged conductor.  Does "the rest of the universe" include
the interior of the conductor?  
As Joe carefully pointed out, there is a redistribution of electrons in the
interior.

He wrote
snip
What happens if we put a 
charged object on the surface of that metal, say for example another 
electron, so that metal now has a net charge.  The electrons in the metal 
near that charge will be repelled leaving a positive region in the metal 
which serves to attract that electron and keep it from drifting off into 
space.  Now lets add a second electron.  You might think that since the 
metal already carries a negative charge, the next electron would be 
repelled.  It is, as long as the electron is not too near the surface.  
By not too near I mean far enough away not to induce a redistribution of 
the electrons in the metal.  However when the electron gets close enough, 
it repels the electrons in the metal just as the first one did, and 
creating a positive region which attracts the second electron.  Even 
though the metal carries a charge, the induced interaction is 
stronger than the coulomb one, and the electron is bound to the surface. 
 This happens because the Coulomb force falls off as the square of the 
distance, so the positive region near charge on the surface has a much 
greater influence than the distributed charge further away.  Of course 
as I add more and more electrons, the coulomb repulsion gets bigger and 
bigger, and eventually other things happen.
end of snip

So what I see is the conductor in "tension" but also in equilibrium being
acted on 
by equal and opposite electrostatic forces, external and internal to the
conductor.

This gives an explanation in terms of classical forces and preserves the
consequences of Gauss' law.

Brian McInnes