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Homework Help: Vector integration

  1. Mar 22, 2010 #1
    1. The problem statement, all variables and given/known data
    Prove [tex] \int\int_{S}r \times dS=0 [/tex]
    for any closed surface S.


    2. Relevant equations



    3. The attempt at a solution
    i used divergence theorem but i didn't make it...
     
  2. jcsd
  3. Mar 22, 2010 #2

    gabbagabbahey

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    Well, how far did you make it with that? Show us what you've got and we'll be better able to help you.
     
  4. Mar 22, 2010 #3
    the value of r= x^2+y^2+z^2
     
  5. Mar 22, 2010 #4

    gabbagabbahey

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    First,

    [tex]r=||\textbf{r}||=\sqrt{x^2+y^2+z^2}\neq x^2+y^2+z^2[/itex].

    Second, is this the entirety of your attempt at the problem? What does this have to do with computing the integral

    [tex]\int\int_{\mathcal{S}}\textbf{r}\times d\textbf{S}[/tex]

    ??
     
  6. Mar 22, 2010 #5
    i dont know sir...
     
  7. Mar 22, 2010 #6

    gabbagabbahey

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    Try applying the divergence theorem to the vector field [itex]\textbf{c}\times\textbf{r}[/itex], where [itex]\textbf{c}[/itex] is any constant (position independent) vector.... What does that give you?
     
  8. Mar 22, 2010 #7
    thank you sir...
    but can i have the complete solution of it sir..
    thank you
     
  9. Mar 22, 2010 #8

    gabbagabbahey

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    No. We do not provide complete solutions here. It is unethical and it doesn't really help you learn any problem solving skills.

    You need to make some effort and show your work in order to receive further help.
     
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