# E&M simple polarizability question

1. Jul 12, 2014

### iScience

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):

$$\vec{p}=a \vec{E}$$
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First step:

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

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

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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. Jul 12, 2014

### UltrafastPED

It's a dipole field.