In reading M. Faraday (Experimental Researchers in Electricity, 1837)
I see a description of the phenomenon of "charge penetration" into
dielectrics. We touched upon this in another thread; was it a year ago
or two? But the context of this thread makes the topic more interesting.
Can somebody comment on space charges in dielectric materials?
A naive thinker could come to a conclusion that an ideal dielectric
crystal should never be able hold electrons inside; such electrons
would go to the conduction band and migrate to the surface, as in
metals. But in real cold materials electrons may be trapped below the
conduction band. That is a way of rationalizing experimental data
of M. Faraday (see below).
Is there a theoretical limit for the number coulombs per cubic
millimeter in a typical solid? Does anybody know about recent
experiments on static space charges? Any other ways of squeezing
net charges into limited volumes? The rest is just a description of
Faraday's observations.
Ludwik Kowalski
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A material, such as shellac or sulfur, was electrified by Faraday in
contact with two metallic walls (in a high voltage spherical capacitor)
for long time. Then the metallic walls are shortened and the material
is removed to examine its surface charges. The side of the dielectric
which was in contact with the negative metal becomes positive while
the other side becomes negative. Today we call these things "bound
charges" and we understand them in terms of alignments of dipoles.
But after this charge disappears, presumably due to the randomizing
effect of thermal agitation, the charges of opposite sign appear on the
surfaces. According to Faraday, the effect is reproducible; he observed
it in several materials. The reappearing charges often represent large
fraction of the original charge, depending on the material. Here is a
quote.
from paragraph 1234
"... Again, if after having been charged for some time, as fifteen or
twenty minutes, it was suddenly and perfectly discharged, ... , then
apparatus being left to itself, would gradually recover a charge,
which in nine or ten minutes would rise up to 50% or 60%, and
in one instance to 80%."
from paragraph 1238
"The electricity which in these cases returned from an apparently
latent to a sensible state, WAS ALWAYS OF THE SAME KIND
WHICH HAS BEEN GIVEN BY THE CHARGE." Emphasis added.
In other words, as I understand it after reading the entire report,
the reappearing charge was of the same polarity as that which was
initially applied to the adjacent metallic wall. Here is another quote.
from paragraph 1245
"The effect appears to be due to an actual penetration of the charge
to some distance within the electric, at each of its two surfaces, by
what we call conduction; so that, to use the ordinary phrase, the
electric forces sustaining the induction are not upon the metallic
surface only, but upon and within the dielectric also, extending to
a greater or smaller depth from the metal linings."
This is illustrated by Faraday's Figure 10 showing a parallel
plane capacitor. Symbols a, b, c refer to metallic plates and the
dielectric while symbols n and p refer to dotted lines inside the
dielectric plate (p facing a and n facing b). He writes:
"Let c be the section of a plate of any dielectric, a and b being
the metallic coatings; let b be uninsulated [grounded?], and a be
charged positively; after ten or fifteen minutes, if a and b be
discharged, insulated, and immediately examined, no electricity
will appear in them; but in a short time, upon a second examination,
they will appear charged in the same way, though not to the same
degree, as they were first."
from paragraph 1246
Figure 11 is used to describe a similar experiment. This time the
dielectric plate is made of two layers. After discharging the capacitor
Faraday separates touching dielectric layers and finds net electric
charges on each of them. The half plate which was close to the
positive plate is found to be positive while the other half is found
to be negative.
from paragraph 1247
"Thus it would appear that the best solid insulators, such as shellac,
glass and sulphur, have conductive properties to such an extent, that
[STATIC] electricity can penetrate them bodily, though always subject
to overruling condition of induction." [I added the word "static"].
from paragraph 1248
"The condition of time required for this penetration of the charge is
important. ..."In the next paragraph Faraday refers to presumably well
known "diffusion of electricity" into the "uncovered portions of the
glass" in the Leyden jar. The name "residual charge" is used to what
I would call a space charge in a dielectric.