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Re: Induced dipole moments



Jack Uretsky wrote:

Ludwik-
I spare the readers a repeat of your posting.
Have you forgotten that the net force on the system is zero,
since it is neutral? The center of mass therefore does not move.
The nucleus at the center is thousands of times heavier than the
electronic cloud, so the nucleus also does not, to a good approximation,
move; only the cloud does. I will look at the rest of your calculation
with this in mind, but cubes are less tractable than spheres for
simple calculations.

1) The net force exerted by the field was zero in my illustration.
Fextrn=Q*E-Q*E=0
2) Yes, I did ignore mass differences because I considered them to
be irrelevant. It would be relevant (I think) only if I wanted to know
by how much each part (+Q and -Q) moved in the lab frame when
E>0. I was considering their relative motion. Therefore, in the
limit of M>>m the proton is at rest while the cloud is being pushed
by the field (the CM is at rest if M=infinity).
3) I think that a cubical cloud is mathematically easier. Try to derive
the force formula for a cloud of radius L. The left segment of your
sphere will become a meniscus lens whose volume would not be
a linear function of x. I will accept your claim "cubes are less
tractable than spheres" after I see your derivations. Perhaps you
have a good shortcut that is OK for an introductory course.
4) There was a typing error in the formula for Emax; it is obvious
that the denominator should have been L^2 and not L.
Regards, Ludwik