How Does Displacement Affect Material Polarization?

[agrianne]

Homework Statement

Show that the polarization of a material is P=Nqx where x is the displacement between the center of the electron cloud and the atomic nucleus.

Homework Equations

P=Nqx is given and I went ahead and subbed (q/m) * E[1/(w₀^2 - w^2)] for x.

The Attempt at a Solution

After that I'm kind of stuck. I tried some basic manipulation with P=E($$\epsilon$$₀-$$\epsilon$$), but I'm just shooting in the dark here. I feel like I'm missing some basic information that makes this a simple question.

 

[gabbagabbahey]

Homework Statement

Show that the polarization of a material is P=Nqx where x is the displacement between the center of the electron cloud and the atomic nucleus.

Are you given any other info? Is this exactly the way the question is stated?

To me, this sounds like you are supposed to assume that each atom is modeled by a positively charged nucleus, surrounded by a spherically symmetric elecron cloud and that the material contains $N$ atoms per unit volume. But that's just an educated guess.

Homework Equations

P=Nqx is given and I went ahead and subbed (q/m) * E[1/(w₀^2 - w^2)] for x.

Huh?

Reading the question, I thought you were being asked to prove that P=Mqx, not that you are supposed to take it as given. Where is x=(q/m) * E[1/(w₀^2 - w^2)] coming from?

 

[agrianne]

Yeah, that's the exact question and no more information is provided.

The value for x is something I plucked out of my book for the avg distance between the nucleus and electron cloud. Really, it was just grasping at straws.

I understand, in a broad conceptual way, why P=Nqx, but I'm not sure how to "show" that.

 

[gabbagabbahey]

Yeah, that's the exact question and no more information is provided.

The value for x is something I plucked out of my book for the avg distance between the nucleus and electron cloud. Really, it was just grasping at straws.

I understand, in a broad conceptual way, why P=Nqx, but I'm not sure how to "show" that.

Well, how is Polarization defined? How is Dipole Moment defined? What is the dipole moment of a single atom?