Deriving the local field and Clausius Mossotti formula in a dielectric

In summary, the local field is derived from the Lorentz field and the Clausius-Mosotti formula. The local field is calculated as a contribution of two parts, E_{out} due to all the charges that lie outside the sphere and E_{near} due to charges inside the sphere. The local field is considered to be zero for regular distributions.
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(My last https://www.physicsforums.com/showthread.php?p=4424810#post4424810 post did not get much attention so I try again without all these formulae. Think this will be more clear...)

To derive the local field in a non-polar dielectric you assume a very small spherical cavity in which (since there is an applied field to it) you have made up surface charges. Integrating over those made up surface charges you get the Lorentz field from which you can derive the Clausius-Mosotti formula. My question is: when you integrate over those made up surface charges, why don't you also integrate over the real surface charges on the outside of the dielectric? Don't these two fields (made up and real) cancel each other?
 
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I think you're right, maybe the problem is that you found a simplified(or elemental) explanation that's why it doesn't make much sense. Here is how the real thing is: to calcculate the local field([itex]E_{i}[/itex]) you take,as you explained, a spherical cavity and next calculate the local field as a contribution of two parts 1)[itex]E_{out}[/itex] due to all the charges that lie outside the sphere which includes all free charges and all bound charges which can lie not only on the external surface but could also be volumetric bound charges(div P≠0) 2) [itex]E_{near}[/itex] due to charges inside the sphere and is demostrated to be zero for regular distributions so the result is:
[itex]E_{i}=E_{out}+E{near}=E_{out}[/itex] and this is the desired result.
You can find a good explanation in Grifiths an also in Jackson
 
  • #3
facenian said:
I think you're right, maybe the problem is that you found a simplified(or elemental) explanation that's why it doesn't make much sense. Here is how the real thing is: to calcculate the local field([itex]E_{i}[/itex]) you take,as you explained, a spherical cavity and next calculate the local field as a contribution of two parts 1)[itex]E_{out}[/itex] due to all the charges that lie outside the sphere which includes all free charges and all bound charges which can lie not only on the external surface but could also be volumetric bound charges(div P≠0) 2) [itex]E_{near}[/itex] due to charges inside the sphere and is demostrated to be zero for regular distributions so the result is:
[itex]E_{i}=E_{out}+E{near}=E_{out}[/itex] and this is the desired result.
You can find a good explanation in Grifiths an also in Jackson

Thanks, that makes me more Confident that there is more to it. I don't Think I will read Jackson in a while (I know it is chapter 4), but when I do I will keep all this in mind.
 

1. What is a dielectric?

A dielectric is a material that can polarize in the presence of an electric field, creating an electric dipole moment. This means that the material is able to store electrical energy.

2. What is the local field in a dielectric?

The local field in a dielectric is the electric field that is experienced by each individual atom or molecule within the material. It is caused by the interaction between the external applied field and the induced dipole moments in the material.

3. How is the local field related to the Clausius Mossotti formula?

The Clausius Mossotti formula is used to calculate the polarizability of a dielectric material, which is a measure of how easily the material can be polarized. The local field is a key factor in this formula, as it is used to determine the strength of the induced dipole moment in the material.

4. What is the significance of deriving the local field and Clausius Mossotti formula?

Deriving the local field and Clausius Mossotti formula allows us to better understand the behavior of dielectric materials in the presence of an electric field. This knowledge is crucial in the design and development of various electronic devices and technologies.

5. How is the local field and Clausius Mossotti formula used in practical applications?

The local field and Clausius Mossotti formula are used in a variety of practical applications, such as the design of capacitors, insulators, and other electronic components. They are also used in the study of dielectric materials in fields such as material science, electrical engineering, and chemistry.

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