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Homework Help: Flux of F through S

  1. Dec 3, 2008 #1
    1. The problem statement, all variables and given/known data
    Verify Stokes' Theorem for F and S
    F=(y^2)i+(z^2)j+(x^2)k
    S is the first octant portion of x+y+z=1

    2. Relevant equations



    3. The attempt at a solution
    I know that it should be equal to -1 from Stoke's theorem, but I keep getting 1/4 when I use the normal surface integral way. (I have to do it both ways)

    The integral I am using is
    [tex]\iint x^2 + y^2 + (1-x-y)^2[/tex]

    What am I doing wrong?? :(
     
  2. jcsd
  3. Dec 3, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    I don't think you took the curl of F before you dotted with dS.
     
  4. Dec 4, 2008 #3
    “The line integral of [tex]\v{F}[/tex] around any closed contour C equals the surface integral (flux) of [tex]curl \v{F}[/tex] over any surface bounded by C

    [tex]\oint_{C}\v{F}\bullet\v{dl}=\int_{S}\left(Curl\v{F}\right)\bullet\v{dS}[/tex]

    Found these in some of my old undergrad notes...
     
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