Griffiths Problem 4.10: Finding Sigma for Polarization Vectors

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So, the summary of the conversation is: "In summary, the person is asking for clarification on a problem similar to one in Griffiths. The problem involves a sphere with polarization P(r)=kr and the question asks for more information and equations needed to solve it."
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m0nk3y
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Homework Statement


I have a problem exactly like problem 4.10 in griffiths, however that problem is not being much help since it seems to me that they just plug in P(r).

For those who do not have griffiths the question is:
A sphere of radius R carries a polarization P(r)=kr
where k is a constant and r is the vector from the center

Homework Equations



[tex]\sigma[/tex]=P*nhat

The Attempt at a Solution


answer is sigma=kR

Thanks:smile:
 
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  • #2
What do you mean? You need to use the definitions of bound surface and volume charges, which are dependent on P. If by plug in you mean they plug it into the equations, then yes, you just use the definitions.
 
  • #3
You are right, but that question asks for more
 

FAQ: Griffiths Problem 4.10: Finding Sigma for Polarization Vectors

What is Griffiths Problem 4.10 about?

Griffiths Problem 4.10 is a problem in the field of electrodynamics that deals with finding the value of sigma, the conductivity, for polarization vectors in a material.

Why is finding sigma important in polarization vectors?

Sigma is a measure of a material's ability to conduct electricity. In polarization, it determines how much charge can be stored in a material and how fast it can be discharged. Therefore, finding the correct value of sigma is crucial in understanding the behavior of polarization vectors in a material.

What methods can be used to find sigma for polarization vectors?

There are several methods that can be used to find sigma for polarization vectors, such as the Drude model, the Lorentz model, and the Debye model. These models use different equations and assumptions to determine the value of sigma.

How do the different models for finding sigma differ?

The Drude model assumes that electrons in a material are free and undergo collisions with other particles, while the Lorentz model takes into account the effect of anharmonic oscillators on conductivity. The Debye model, on the other hand, considers the relaxation time of electrons in a material. These differences in assumptions and equations result in different values of sigma for polarization vectors.

Can sigma change for different materials?

Yes, sigma can vary for different materials depending on their properties such as composition, structure, and temperature. Conductivity also depends on the frequency of the electric field applied, so different materials may have different values of sigma for the same polarization vector.

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