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Re: Charge interactions in media



--- Bob LaMontagne <rlamont@POSTOFFICE.PROVIDENCE.EDU> wrote:
pvalev wrote:


V_metal = V_vacuum / D /1/

where D is the dielectric constant of the intervening material.
The
inspection of the physical picture or an experiment would convince
them that V_m is practically zero, i.e. D is extremely great. But
then they may find that, in accordance with Coulomb's law

F = k(q1*q2)/Dr^2 /2/

the attraction between the plates has also vanished. (After all,
the
plates can be ragarded as two charged bodies that obey Coulomb's
law). But this would be a wrong conclusion - the same physical
picture that showed vanishing of the voltage now shows INCREASE of
the force of attraction:


What is the justification of your last sentence? If the metal
totally
fills the region between the plates, it shorts out the capacitor.
There
must be an insulating gap next to the plates. Let's assume it's
vacuum
for simplicity. The extremely low field in the metal is due to the
canceling of the original field before the metal is inserted by the
induced field produced in the metal because of its induced surface
charges. The field in the vacuum gap between the inserted metal and
the
plates is still the same as before the metal was inserted.


You are right if the plates are infinite or at least large (compared
to the distance between them). In this case the attraction before and
after the insertion will be the same. If the plates are small
(roughly speaking, the capacitor is not a true capacitor anymore),
the attraction after the insertion will be greater. Let us consider
an oversimplified model: two dipoles are inserted between the (small)
plates. Before the insertion, the situation looks like that:

+++++++

(+) (-)
(-) (+)

-------

After the insertion, one of the dipoles undergoes reorientation:

+++++++

(-) (-)
(+) (+)

-------

Clearly, the reorientation of the dipole increases the attraction.
The conclusions can be generalized. When a solid body is
inserted between the plates, irrespectively of its shape and size,
the attraction between the plates CANNOT DECREASE. On the other hand,
formulas in textbooks are consistent with the Coulomb's law in the
form /2/ above. For that reason, calculations based on these formulas
would lead to the conclusion that the attraction decreases.
Strangely, in the few textbooks I have checked texts that could
expose the problem are missing as if the authors had removed them
deliberately. I hope this impression of mine is illusory.

Pentcho