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Flux through surface

  1. Apr 26, 2009 #1
    1. The problem statement, all variables and given/known data

    Compute the flux of the vector field, [tex] \vec{F} [/tex] , through the surface, S.
    [tex] \vec{F} = y\vec{i} + 7\vec{j} - xz\vec{k} [/tex] and S is the surface [tex] y = x^2 + z^2[/tex] with [tex]x^2 + z^2 \leq 36[/tex] oriented in the positive y direction.

    2. Relevant equations



    3. The attempt at a solution

    [tex] \int\limit_R ((x^2+x^2)\vec{i} + 7\vec{j} - zx\vec{k}) \cdot (-2x\vec{i} -2z\vec{k} + \vec{j})dA [/tex]
     
  2. jcsd
  3. Apr 27, 2009 #2
    Are you trying to evaluate

    ∫∫R ( (x2+z2) i + 7 j - zx k ) · (-2x i + j -2z k) dA

    where R is the disc x2 + z2 ≤ 36 in the xz plane?

    So take the dot product, then convert to polar coordinates in the xz plane, is this what you mean?

    I think this is correct if the unit normal to S is pointing "right" (i.e., into the parabolic bowl), but negate it if the unit normal to S is pointing "left" (i.e., out of the bowl). Also, you are assuming the bowl has no "lid."
     
  4. Apr 27, 2009 #3
    thanks!
     
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