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?

 

[paranormal]

I would like to clarify that polarization of a material is a fundamental property that describes the behavior of electric dipoles within a material under the influence of an external electric field. It is defined as the dipole moment per unit volume of the material and is denoted by P. The equation P=Nqx, where N is the number of dipoles per unit volume and x is the displacement between the center of the electron cloud and the atomic nucleus, is a simplified representation of the polarization of a material.

To further understand this equation, we can consider the fact that when an external electric field is applied to a material, the electron clouds around the atoms will be slightly displaced from their equilibrium positions. This displacement, denoted by x, is directly proportional to the strength of the electric field. Thus, the equation P=Nqx indicates that the polarization of a material is directly proportional to the number of dipoles present in the material and the strength of the applied electric field.

Now, in your attempt at a solution, you have substituted q/m * E[1/(w0^2 - w^2)] for x, where q is the charge of the electron, m is its mass, E is the electric field, and w0 is the natural frequency of the electron cloud. This substitution is incorrect as it does not take into account the number of dipoles present in the material. Moreover, the equation P=E(\epsilon0-\epsilon) that you have tried to manipulate is not applicable in this context.

In conclusion, the equation P=Nqx is a simplified representation of the polarization of a material and it is important to keep in mind that it is not a comprehensive equation that takes into account all the factors that influence polarization. To fully understand the polarization of a material, one must consider the properties of the material, the external electric field, and the behavior of the dipoles within the material.