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Ambiguity of electrostatic polarization?

  1. Jun 3, 2012 #1

    Jano L.

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    Gold Member

    Hello everybody,

    I have a doubt about the section of the Wikipedia page on the polarization:

    https://en.wikipedia.org/wiki/Polarization_density

    especially the section in the end where the writer claims the polarization is ambiguous.

    In the example about Alice, the writer states that the pairing of +/- particles is ambiguous and hence the polarization is ambiguous. I think he incorrectly interprets the meaning of the polarization.

    The writer even states that Alice can back up her strange pairing procedure by ascribing the crystal surface a non-zero density of (free!) charge. This is ridiculous. The crystal is a dielectric and there is no free charge. All polarization comes from displacements of the bound charges. There will be only bound surface charge.

    I think the proper way to define the polarization of the crystal at [itex]\mathbf x [/itex] is to average the dipole moments of the smallest neutral cells k hitting the averaging volume V, which is centred at [itex]\mathbf x[/itex]. The polarization is then

    [tex]
    \mathbf P(\mathbf x) = \frac{1}{V} \sum_k \mathbf \mu_k
    [/tex]


    What do you think - is not this unambiguous definition?
     
  2. jcsd
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