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Re: Induced dipole moments



I quote Slater, <Quantum Theory of Matter>, p. 377-8 (in
relevant part, only):
There are three principal parts of dielectric behavior...
any individual atom can be polarized by the field,...the displacement
of ions with positive charge, with respect to ions with negative
charge...[and] molecules with permanent dipole moments.

You have excluded the third case. Which of the first two cases are you
trying to understand? They are quite different.

Slater goes on to point out that if you calculate the classical
polarizability of a conducting sphere of atomic dimension, you get the
right order of magnitude for your answer. Perhaps this is the best
approach for those who don't want to get into quantum mechanical
arguments.
Regards,
Jack

On Sun, 31 Dec 2000, Ludwik Kowalski wrote:

I understand what David is saying. So let me present the
same dilemma in a different way.

1) To simplify I am dealing with a single molecule (other
molecules are far away, as in a low-pressure gas). The
external field E is uniform. I want to understand "induced
polarization", as described by Tipler.

2) The separating forces, +qE and -qE, are constant. The
attractive (restoring) force is distance-dependent. To
allow for a stable equilibrium the attractive force MUST
increase with the distance between + and -. The process
of separation would stop when the restoring force reached
the value of qE. At shorter distances the repulsion would
prevail, at larger distances the attraction would prevail.
Right or wrong?

3) If the answer is "right" then how to explain the
required relation between the restoring force on the
distance between the centers of charges?

************************
Another (related) question:

4) Suppose we have two "rigid clouds". A rigid cloud,
by definition, is a set of identical point charges which
can not move with respect of each other. Yes, it is a
highly unrealistic model; I do not care what keeps
particles at fixed positions with respect to each other.
Two such clouds can penetrate through each other
because distances between particles (inside of each
cloud) are large.

5) One cloud is made of electrons and another is
made of protons. Let d be a distance between the two
centers of charge. The attractive force between the clouds
is proportional to 1/d^2 when clouds are separated. What
is wrong by assuming that this relation holds even when
the two clouds are overlapping?
Ludwik Kowalski

David Bowman wrote:

Regarding Ludwik's "conceptual difficulty with a non-polar molecule":
...
4) But Tipler states that the attractive force is due to
Coulomb's interaction. Coulomb force decreases with
the distance. Therefore this force does not become large
enough to stop the process of separation of + from - by
the external electric field E. The Coulomb force is infinite
when separation is zero and no finite field should be able
to induce a dipole moment in a molecule or atom. Right?

No, wrong. The Coulomb force is only of the 1/r^2 form for the force
between 2 *point* charges. In the case of an atom or molecule the
negative charge distribution is continuously spread out over a few
Angstrom's even though the positive charge distribution is concentrated
into one or a few more (effectively) point charges. Not only is the
negative charge spread out, it *surrounds* the positive charge. The
Coulomb force between the negative and the positive charge distributions
would only begin to approximate the 1/r^2 form if they both were widely
separated from each other so only the monopole contribution from the
negative charge distribution interacted dominantly with a point positive
charge.

5) Am I missing something important? If my objection is
valid then how to explain dipole moments? Is this another
case (like hydrogen atom) in which an explanation is not
possible in classical physics?

I think the important thing you are missing is that the negative
charge distribution for a given atomic configuration is a continuous
distribution, not a point distribution.

David Bowman
David_Bowman@georgetowncollege.edu


--
While [Jane] Austen's majestic use of language is surely diminished in its
translation to English, it is hoped that the following translation conveys
at least a sense of her exquisite command of her native tongue.
Greg Nagan from "Sense and Sensibility" in
<The 5-MINUTE ILIAD and Other Classics>