Re: Induced dipole moments

[Jack Uretsky <jlu@HEP.ANL.GOV>]

        The statement is correct, although less relevant than I had
thought at first blush.  At any point inside or outside of the spherical
charge distribution, the field is identical to that of two point charges,
separated by a distance vector d.  Outside of the distributed charge, for
simplicity, the potential is proportional to
                (1/|r +d/2|) - (1/|r-d/2|)
where r is the vector from the midpoint between the point charge and the
center of the distributed charge.  Expanding this expression in
multipoles, you find an infinity of multipoles present; the dipole
dominates for r>>d.
        Contrast this with the induced potential by a constant E-field
on a uniformly conducting sphere which is a pure dipole.
        Incidentally, before going to bed last night I convinced myself
that there is no static spherical charge distribution (for, say, the
negative charge) for which the asymptotic dipole field is proportioal
to the external constant E-field, which is the hallmark of polarizability.
So, again I return to the conducting sphere as the better classical model.
        You might wish to attempt to verify my result.
                                Regards,
                                        Jack


On Sun, 31 Dec 2000, Herb Schulz wrote:

> >         Put another way, the field of a spherical negative charge
> > distribution and an off-center point positive charge is not a simple
> > dipole.
> >                                 regards,
> >                                         Jack
>
> Howdy,
>
> Jack, I don't understand this statement.  If you are OUTSIDE the
> spherically symmetric negative charge distribution is MUST act like a
> point charge at its center from Gauss' Law.  I assume that you meant
> the E-Field INSIDE the negative charge distribution is not that of a
> point charge.
>
> As a matter of fact, if the negative charge distribution is
> approximately uniform and spherically symmetric the E-Field inside is
> linearly increasing with distance out.  Maybe that might help in
> understanding why an increasing external E-Field will increase the
> separation and therefore the dipole moment of the atom.
>
> Good Luck,
> --
> Herb Schulz
> (herbs@interaccess.com)

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