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Homework Help: Partial differential equation

  1. Jun 8, 2010 #1
    1. The problem statement, all variables and given/known data

    Using Cartesian coordinates show that [tex]\Phi = 1 / r[/tex] satisfies [tex]\nabla^2\Phi=0[/tex] for r not equals to 0.

    2. Relevant equations

    3. The attempt at a solution

    I tried to let [tex]r = x+y+z[/tex], then [tex]\nabla \Phi = ( \frac{1}{r^2} , \frac{1}{r^2}, \frac{1}{r^2})[/tex], but [tex] \nabla . \nabla \Phi [/tex]is obviously not zero
  2. jcsd
  3. Jun 8, 2010 #2


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    Science Advisor

    You didn't do the differentiation correctly. What is the partial derivative of 1/r with respect to x?
  4. Jun 8, 2010 #3
    ..and [itex] r^2=x^2+y^2+z^2 [/itex] would work better too...
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