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Homework Help: Point charge potential

  1. Feb 10, 2007 #1
    Hallo!

    1. The problem statement, all variables and given/known data
    Consider electrostatic Potential of point charge at point (0,0,0)
    [tex]\phi = 1/r[/tex]
    I'm trying to calculate [tex]\Delta\phi[/tex]

    2. Relevant equations

    3. The attempt at a solution
    Actually it's not a difficult problem outside (0,0,0):

    [tex]\nabla\phi = -\frac{\vec r}{r^3}[/tex]
    [tex]\Delta\phi = 0[/tex]

    But i also know, that i should become Dirac-Delta function (charge density for point particle). What is the problem in point (0,0,0)?
    I understand that Potential goes there to infinity, but how can i work it out mathematically?
     
    Last edited: Feb 10, 2007
  2. jcsd
  3. Feb 10, 2007 #2

    Meir Achuz

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    Science Advisor
    Homework Helper
    Gold Member

    Using the integral definition of div, it can be shown that
    div(r(vec)/r^3)=4pi delta(r).
    This can also be shown by appying the div theorem and taking the limit as r-->0.
    What book are you using? Graduate texts do this.
     
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