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Re: IONS/metals EUREKA



I knew there were a classical (Maxwellian only) way
of justifying the attractive forces which keep electrons
on the surface of a metal. And I found it in old books.

I was blinded because I took the conventional model
(E=0 everywhere in a piece of metal) too literally, as
if the space inside was nothing but pure vacuum. It
is not true that electric fields do not penetrate into a
very thin layer of metal. The whole idea of surface (in
Gauss Theorem) is only a mathematical abstraction.

A piece of metal (inside) is a neutral mixture of
positive ions and negative electrons. But the neutrality
does not apply to a region which is very close to the
outer surface. In a metallic layer close to the surface
electrons are being pushed toward the inside by
electrons which are outside. This creates a layer which
is positively charged and which attracts outside
electrons. Here is how the work function was explained
in a book published in 1942 (Introduction to Modern
Physics, by Richtmyer and Kennard, p. 103).

"... If, for any reason, an electron escapes from the
metal, as it moves away, it will be drawn back by an
attraction that may be regarded as arising from its
'electrical image' in the surface of the metal, this
image being caused by the repulsion of the other
electrons by the escaping one and the consequent
exposure of positive charge. Thus, in escaping, the
electron will do a certain amount of work against
this attraction, which will be denoted by ...."

The model is presented in the context of the
photoelectric effect; it explains the work function.
But I do not see why it can not be used to explain
stability of excess charges on metallic surfaces.
The net force on each charge is now zero due to pure
Maxwellian forces. No Pauli is needed. The same
general idea was expressed in "The Mathematical
Theory of Electricity and Magnetism" by James Jeans
(first published in 1908, long before QM).

".... 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."

An electric surface tension? Mutual repulsion between
electrons exposes them to positive charges. The surface
tension analogy is quite obvious. A little bit like static
friction forces, more you pull larger the opposing force,
up to a limit. Is this an acceptable model for an
introductory physics course? It explains things in terms
of what students already know rather than in terms of
what some of them may possibly learn in the future.

Ludwik Kowalski