# Why can we assume dielectric induced dipoles are pure dipoles?

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1. May 12, 2015

### Happiness

1. The problem statement, all variables and given/known data
Griffiths was trying to prove that when calculating the electric field inside a dielectric, we may assume the dipoles induced in it are "pure" dipoles, although they are in fact "physical" dipoles, as long as we view the field as a macroscopic field, one that is averaged over a sufficiently large region of space.

I don't follow his argument in the last paragraph of page 174, the one just before equation (4.19).

2. Relevant equations
Page 174 (attached) of "Introduction to electrodynamics" by Griffiths

3. The attempt at a solution
I calculated that

$V(r)=\frac{1}{4\pi\epsilon_0}\int_{inside}\frac{\hat{\eta}\cdot P(r')}{\eta^2}d\tau'=0$

if $P(r')$ is constant throughout the inside volume. ($\eta$ is Griffiths' script r.)

How does this relate to equation (4.19) and the argument about using a uniformly polarised sphere?

Pages 173-175 (Enlarged)

The same pages in their original size:

Last edited: May 12, 2015
2. May 17, 2015