Suppose billions of electrons are deposited at one spot of a metallic
ball. A moment later a layer of charge is distributed over the surface.
The same is true for a Faraday cup; we deposit a charge at a spot on
the inner surface and a moment later the excess appears on the outer
surface. We say the charge was transferred (or redistributed) due to
mutual repulsion of electrons. Electrons which appear on the outer
surface are not those which were received from outside but the net
result is the same as if they were.
The energy approach does not care about the "who is who". The
potential energy of the initial configuration (a bunch of electrons
close to each other) is higher than the energy of the final
configuration (electrons are as far away as possible from each
other). There is no intermediate configuration at which the
potential energy is higher than the initial one. The system evolves
"spontaneously" from the higher potential energy to lower.
Here are my questions. Suppose that the metallic sphere, or the
Faraday cup, is replaced by an identical vessel made from a pure
dielectric, such as fused silica or plexiglas. The initial potential
energy (electrons deposited at one small spot) is higher than the
energy of the configuration in which electrons would be far away
from each others. But the system does not evolve "spontaneously"
from the higher potential energy to lower. Electrons remain
where they are initially deposited. Why?
According to Coulomb's law charges do repel each other in a
dielectric. (The force is K times less than in a vacuum; K for
plexiglas is 3.4). What forces prevent mutually repelling
electrons from spreading? In other words, what is responsible
for the potential energy minimum presumably existing around
the initial configuration? We say that insulators do not allow
currents because they have no free carriers. We are providing
carriers but they do not move away from each other, as in
metals. Why?
What keeps carriers together in one spot? Or maybe they do
move a little to reach a potential energy minimum somewhere
below the initially high energy hill. An electric barrier of
some kind (?) must exist between the initial high and final
low states if electrons are to be prevented from establishing
the lowest possible energy state. I am assuming that
non-electric forces acting on electrons, such as gravitational,
etc., are negligibly small.
What evidence do we have that at least some dilution, of the
initial high concentration of charges, does not take place in
dielectric materials? What stops this process?