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E&M simple polarizability question

  1. Jul 12, 2014 #1
    this is a homework problem i realized after posting it. so could a moderator please move this question to the hw section? thanks

    one of Griffiths' example:

    A primitive model for an atom consists of a point nucleus surrounded by a uniform charged spherical cloud of radius "a". Find the atomic polarizability of such an atom.

    (reference equation):

    $$\vec{p}=a \vec{E}$$
    -------------------

    First step:

    the field (produced by the electron cloud) at distance d from the center of a uniformly charged sphere is

    $$E_e=\frac{1}{4\pi \epsilon_0}\frac{qd}{a^3}$$

    ---------------


    so why is that the field produced by the shifted electron cloud?

    ie, how does one go from

    $$E_e=\frac{1}{4\pi \epsilon_0}\frac{q}{a^2}$$

    to..

    $$E_e=\frac{1}{4\pi \epsilon_0}\frac{qd}{a^3}$$

    (where "d" and "a" are not equal)?
     
    Last edited: Jul 12, 2014
  2. jcsd
  3. Jul 12, 2014 #2

    UltrafastPED

    User Avatar
    Science Advisor
    Gold Member

    It's a dipole field.
     
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