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Confused about Poisson equation

  1. Jan 31, 2009 #1
    Hello everybody

    I've been searching this today but I am a bit lost now. I've encountered two forms of Gauss law in its differential form, Poisson equation :

    del2V(r) = -p(r)/e

    del2V(r) = -4*pi*p(r)/e

    where V:e.potential, p:charge density, e:permivity

    Now, what's the difference between these two /or/ where does the (4pi) in the second one comes from?

    Mathematically they are not equivalent, but they are presented as such. Any opinions?
     
  2. jcsd
  3. Jan 31, 2009 #2
  4. Jan 31, 2009 #3
    Hi snapback,

    I've already came across this link during my search, but the equation in mind was with "e".

    I encountered the equation in Holst book of poissn-bltzman eq., I can't see it as a mistake as he built upon it later.

    Thanks for the reply
     
  5. Jan 31, 2009 #4
    Hi mysubs,

    do you mean http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.9.9570 by "Holst" ?

    Yes, he is indeed using the form with "e" rather extensively. Now, I think this is the CGS version of the the macroscopic form of Poisson equation for a medium with permittivity "e". "Macroscopic" means the version of Poisson eq. where you have actually grad(e grad V(r))=... and it is assumed that it is a linear medium, so that "e" is a scalar.

    I haven't seen this version before, and will add it as another chapter in "my personal book of annoyance with different unit systems in electrodynamics" ;-)

    cheers
     
  6. Feb 1, 2009 #5
    Yes, that one. I thought it might have something to do with this but couldn't think of any connection mathematically.

    Now it all works out, and I feel like a complete human being again. Thanks for the help!
     
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