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Flux through a sphere?

  1. Dec 23, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the flux of the vector field F(x,y,z)=(z,y,x) across the unit sphere x^2+y^2+z^2=1



    3. The attempt at a solution
    My Answer: 3(pi)^2/8

    Book answer: 4(pi)/3
     
  2. jcsd
  3. Dec 23, 2007 #2

    Dick

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    The easy way to do this is to use the divergence theorem which immediately gives you the book answer.
     
  4. Dec 23, 2007 #3

    nicksauce

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    The book answer is correct. Can you show your work?
     
  5. Dec 26, 2007 #4
    divergence theorem: triple integral of the divergence of the vector field, in this case the divergence is just 1, so you're just essentially finding the volume of the sphere
     
  6. Dec 26, 2007 #5
    RIght, I just had problems with the surface integral but it's just d(theta)d(psi)

    by letting x=theta, y=psi so the jacobian is 1.

    All correct?
     
  7. Dec 26, 2007 #6
    yes but no need for spherical coordinates since its just the triple integral:

    SSS1dV = volume of sphere over the domain d = { (x,y,z): x^2 + y^2 + z^2 = 1 }
    ( sorry no latex )
     
  8. Dec 27, 2007 #7

    Gib Z

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    If dexter still posted regularly, I'm sure he would have made a point to say Volume *enclosed by* the sphere =] Welcome to PF Dmak! (And don't mind that comment, really just semantics).

    EDIT: Wow Dick has 2^(12) posts =]
     
    Last edited: Dec 27, 2007
  9. Dec 27, 2007 #8

    In the first attempt, I wasn't trying to use the divergence theorem but the surface integrable dS. It was the long way but I wanted to know that I could do it.
     
  10. Dec 27, 2007 #9


    haha thanks Gib_Z :p
     
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