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Homework Help: Volume distribution of charge

  1. Feb 13, 2010 #1
    1. The problem statement, all variables and given/known data

    A rod of dielectric material is spun about it's axis with angular velocity [tex]\omega[/tex]. A uniform magnetic field B exists in a direction along the axis of the bar. Determine a charge distribution which produces the same electric field as does the rotating rod. The electric susceptibility of the material is xE

    2. Relevant equations

    3. The attempt at a solution

    The force on a charge q at a distance r is F=q*[tex]\omega[/tex]*r*B and the electric field is E=r*B*[tex]\omega[/tex].
    The polarization of the rod at distance r is P=xE*[tex]\epsilon[/tex]0*[tex]\omega[/tex]*B*r.
    So the volume distribution of charge should be -div P = -([tex]\partial[/tex]Pr) / ([tex]\partial[/tex]*r). But according to the book it should be
    -div P = -([tex]\partial[/tex]Pr) / ([tex]\partial[/tex]*r) - (Pr) / r .

    Could somebody please explain why it should be that way?? thx
  2. jcsd
  3. Feb 14, 2010 #2


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    Staff Emeritus
    Science Advisor
    Homework Helper

    That is the divergence in cylindrical coordinates.

  4. Feb 15, 2010 #3
    Thank you thank you thank you! :!!)
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