1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Redbelly98

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    That is the divergence in cylindrical coordinates.

    http://hyperphysics.phy-astr.gsu.edu/Hbase/diverg.html#c3
     
  4. Feb 15, 2010 #3
    Thank you thank you thank you! :!!)
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook