Partial differential equation

  • Thread starter cloudone
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  • #1
cloudone
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Homework Statement



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

Homework Equations





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
 

Answers and Replies

  • #2
phyzguy
Science Advisor
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You didn't do the differentiation correctly. What is the partial derivative of 1/r with respect to x?
 
  • #3
Mmmm
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..and [itex] r^2=x^2+y^2+z^2 [/itex] would work better too...
 

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