Re: Re IONS/metals pedagogy

[sample@idcomm.com (John D. "Chip" Sample)]

At 9:24 PM on 10/8/98, Ludwik Kowalski wrote:

> What are we arguing about? Certainly not about superiority
> of quantum physics. We are talking about a conceptual
> dilemma a teacher of elementary physics faces while
> interpreting most basic electric demonstrations. A piece of
> metal is touched with an electrified rod and electrons
> distribute themselves over the outer surface.
>
> Here is a gedanken experiment. Two likely electrified pith balls
> are placed in the middle of a sealed tube (which has no air) and
> released. They repel each other and travel toward the opposite
> ends of the tube. There is no bouncing and they remain as far
> as possible from each other. Each pith ball is at rest because the
> net force acting on it is zero (Fnet=Fcoul+Freact). If there were
> no reaction forces at the tube's endings the balls would travel
> to infinity.
>
> Now back to charges which are distributed on the outer surface
> of a metallic sphere. What keeps them at rest? Unless we say
> that Fnet=m*a does not apply to electrons on the sphere (a=0
> means Fnet=0) we MUST invent a force. Some say this can only
> be done by using QM. And then they say that the concept of F
> does not belong to the arsenal of its tools. Even if the concept
> of F ("Pauli F") was acceptable, the QM can not be used to explain
> things before students learn it.
>
> Something is not right somewhere. There must be an attractive
> force acting on each bunch of electrons; it must be equal and
> opposite to the repulsive force exerted on it by other bunches.
> Admitting our inability to explain this force in terms of what we
> already know (in a given course) is much better than saying that
> a=0 when Fnet is not zero.
It seems to me that if you are looking for a qualitative understanding of
why excess charge (up to some limit) does not fly off a charged metal
surface, then the expanation is relatively simple and can be understood in
purely classical terms.

Imagine two negatively charged conducting spheres.  Is it possible that
they could feel an electrical attraction?  Coulomb's Law would seem to say
"no", but Coulomb's Law applies to point charges or *spherically symmetric*
charges.  If one of the spheres is smaller than the other and is brought in
the near vicinity of the other, it will polarize the larger sphere and give
you a non-spherically symmetric charge distribution.

          <------R1---->
              .
            -   :
          -      +
         -        +    3-         (poor attempt at ascii art)
          -      +
            -   :
              .
                  <-R2->

In this case it's possible to have two net negative charges attracted to
each other because the positive charges on the left ball, even though fewer
in number than the negative charges on the left ball are significantly
closer to the negative charges on the right.  Compare R1 and R2.

The case of the electron leaving the surface of the metal is an extreme
case of what is going on above...the electron is MUCH smaller than the
remaining sphere, but the effect is the same.

The key is that the larger charge can't be considered a point or spherical
charge from the point of view of the electron.

Another somewhat analogous example comes to mind in which the "usual rules"
fail.  The north poles of two bar magnets are brought near each other.
Normally we expect a repulsive force between them, but if one magnet is
much stronger than the other it can temporarily or permanently polarize the
weaker magnet in the opposite direction and an attractive force results.
So a strong north pole is attracted to any south pole but also to weak
north poles as well.

J. D. (Chip) Sample                    Lockheed Martin Astronautics
(303) 471-2808                         (303) 971-2744
sample@idcomm.com                      john.d.sample@LMCO.com