Ions, dielectrics

["Ludwik Kowalski" <KowalskiL@Mail.Montclair.edu>]

NOT A SINGLE MESSAGE FROM PHYS-L SINCE YESTERDAY
(30 HRS).  FRUSTRATING WHEN ONE IS WAITING TO SEE
REPLIES TO THREE POSTED MESSAGES. I SUSPECT THE
PROBLEM IS HURRICANE RELATED. TO KEEP MY MENTAL
INERTIA GOING I AM POSTING ANOTHER MESSAGE, WITH
A LOT OF HESITATION.

The conceptual model of a dielectric (randomly oriented dipoles)
must be used (somehow?) to explain its behavior. Let me try.
Suppose a point charge is placed in the middle of a large volume.
Due to the Coulomb law of repulsion it will be at once surrounded
by a layer (or several layers) of dipoles. If the initial charge is
negative then the outer ends of the dipole layers will also be
negative. The degree of polarization, P, will decrease with the
distance from the initial charge. The entire polarized region
will have the net positive charge.

How will the net charge be distributed? The non uniformity of
the field created by the original charge leads a cloud of net
negative charge (layer by layer) whose density decreases with
the radius. Now consider two point charges. In the vacuum (for
example in empty space between atoms of a metal) they would
push each other as far as possible. But not in the dielectric.
Why? Because they are no longer point charges; they are large
spheres made from layers of dipoles. Spaces between atoms are
too small for such spheres.

The net charges still repel each other (Coulomb's law) but this
leads to an internal tension rather than to a displacement. Is
this explanation acceptable? What kind of experiment can be
conducted to validate it?

The initial question (see below) can perhaps be answered. How
much charge can be loaded into a dielectric before the internal
tension is too large to keep the solid material in one piece?
Think about a similar problem for a liquid dielectric, the
famous liquid drop model of Niels Bohr. The issue was how
much charge can be present in an atomic nucleus before it
fissions spontaneously (by mutual repulsion)? This question,
by the way, was not formulated before a factologist, Lise
Meitner, recognized fission in the data published by O. Hahn
and F. Strasmann.

The answer produced by Bohr was that the  Z^2/A ratio must
exceed a critical value of about 50. Cohesive forces, keeping
molecules (of a solid) in fixed (more or less) positions,
correspond to binding nuclear forces. The electric disintegration
of a charged block of an insulating material will occur when
the internal tensions are larger than some characteristic value,
probably more for solid glass than for solid paraffin.

Does this make any sense? Somebody certainly was addressing
this problem before me. References to this, or any related,
topic will be highly appreciated. I am contemplating an
experiment.

********* the initial posting is quoted below ************

> ... Suppose that a pure dielectric, such as SiO2, is "loaded"
> with a uniform cloud of net negative charge. This can be done,
> for example, by stopping beta particles inside. Would the cloud
> remain uniform (as the charge density goes up) or will charges
> be drifting toward the surface, as in metals, due to mutual
> repulsion? What is the maximum possible charge density (order
> of magnitude) inside a solid?
*************************************************
Ludwik Kowalski