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Mandl and Shaw, page 16, eqn (1.56)

  1. Feb 28, 2009 #1
    1. The problem statement, all variables and given/known data
    [tex]\int{E}_L^2d^3x = \int\frac{\rho(x)\rho(x')}{4\pi|x - x'|}d^3xd^3x'[/tex]

    2. Relevant equations
    [tex]{E}_L = -\nabla\phi[/tex]
    [tex]{\nabla}^2\phi = -\rho[/tex]


    3. The attempt at a solution
    [tex]\int{E}_L^2d^3x = \int(\nabla\phi)^2d^3x = -\int\phi\nabla^2\phi d^3x = \int\rho(x)\phi(x)d^3x[/tex]
    I suppose to finish up, I need to see why
    [tex]\phi(x) = \int\frac{\rho(x')d^3x'}{4\pi|x - x'|}[/tex]
    But I don't see it. Or am I on the wrong track.

    By the way, I have the 1993 revised edition.
     
    Last edited: Feb 28, 2009
  2. jcsd
  3. Feb 28, 2009 #2

    malawi_glenn

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    Last edited: Feb 28, 2009
  4. Feb 28, 2009 #3
    Thanks malawi_glenn, that's what I needed.
     
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