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Let's assume we have a polarized charged sphere which is uniformly polarized (it is one of the Griffiths example). Since it is uniformly polarized, I assumed the material is dielectric. What would be the case if the sphere is conducting? Can I still use the surface bound charges to find the potential.

For example:

$$\sigma_b = P\cdot \hat n = P cos \theta$$ ???

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  • $\begingroup$ That depends. Is your conductor permittivity real or complex? Or are you taking an ideal conductor with $\epsilon = -\infty$? $\endgroup$
    – Feel My Black Hole
    Commented Aug 2, 2019 at 7:02
  • $\begingroup$ I'm confused a little. From my understanding whenever we say "conductor", it assumes the real one, right? It's because ideal conductor exits only in theory. Another thing is that, can we carry on the real conductor case and after applying some approximation, converting the real case? $\endgroup$
    – user193422
    Commented Aug 2, 2019 at 7:19

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If the sphere is conducting then it is polarized due to an external electric field.. An example is a Faraday cage. So you can have induced dipole moments, like that of a Faraday cage, and non induced dipole moments, like that of a dielectric. The difference is the dielectric dipole moment is the result of an insulator having molecules where the electronegativity of its atoms is normally non symmetrical.

Hope this helps

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  • $\begingroup$ Could you please give the equations for dipole moment in the two cases too? It would be helpful to understand the scenarios. $\endgroup$
    – user193422
    Commented Aug 2, 2019 at 8:58
  • $\begingroup$ @user193422 For a general equation for calculating dipole moments and some worked out examples, check the following: chem.libretexts.org/Bookshelves/… $\endgroup$
    – Bob D
    Commented Aug 2, 2019 at 13:34

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