How Does Displacement Affect Material Polarization?

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Homework Help Overview

The discussion revolves around the relationship between displacement and material polarization, specifically focusing on the equation P=Nqx, where x represents the displacement between the electron cloud and the atomic nucleus. Participants are exploring how to demonstrate this relationship and the underlying concepts involved.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the given equation and attempt to manipulate it, expressing uncertainty about their approaches. Questions arise regarding the assumptions made about the atomic model and the origin of the displacement value x. Some participants reflect on their understanding of polarization and dipole moments, seeking clarification on how to demonstrate the relationship.

Discussion Status

The discussion is ongoing, with participants sharing their interpretations and questioning the assumptions behind the problem. There is no explicit consensus, but several lines of reasoning are being explored, particularly around the definitions of polarization and dipole moments.

Contextual Notes

Participants note the lack of additional information provided in the problem statement, which may affect their ability to approach the question effectively. The reliance on values from textbooks and the need for clarification on definitions are also highlighted.

agrianne
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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([tex]\epsilon[/tex]0-[tex]\epsilon[/tex]), but I'm just shooting in the dark here. I feel like I'm missing some basic information that makes this a simple question.
 
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agrianne said:

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 [itex]N[/itex] 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? :confused:

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?
 
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.
 
agrianne said:
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?
 

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