Different expressions for the dipole moment

[Niles]

Hi

In my book (Griffith's) there are two different expressions for the induced polarization, namely
[tex]
P = \frac{N}{\text{volume}}<d>
[/tex]
where <d> is the average of the dipole operator and N the number of atoms. The other expression listed is
[tex]
P = \text{Re}[\varepsilon_0 \chi E]
[/tex]
where E is the electric field and χ the susceptibility. The latter is of course only valid in the case where the the electric field is not too strong, so it is valid to go to first order only. In that respect, is it correct to say that the first expression listed is more correct than the latter, in the sense that it is not an approximation?

 

[Valerie Park]

Yes, the first expression is more general and correct since it is not an approximation. It accounts for all orders of the electric field, while the second expression is valid only in the first order.