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Flux Integral Over Cylinder

  1. May 21, 2009 #1
    To compute the flux integral over a cylinder's walls oriented along the z axis:

    Can I do:

    [tex]\int\int \vec{F}\cdot\nabla G(x,y,z) dA[/tex]

    [tex]G(x,y,z) = r^{2}=x^{2}+y^{2}[/tex]

    [tex]\nabla G = <2x, 2y, 0>[/tex]

    [tex]\int\int \vec{F}\cdot <2x,2y,0> dA[/tex]

    Is this a correct approach?
  2. jcsd
  3. May 22, 2009 #2
    Assuming a positive orientation, the easiest way to do it is by Divergence Theorem.

    (1) Find the divergence of [tex]\vec{F}[/tex]

    (2) Integrate this over the solid cylinder.

    The other way is to split the cylinder into 3 pieces the Top, Bottom and Side and the sum the flux contributed from each piece.
  4. May 22, 2009 #3
    Thanks for the reply.

    Yeah, I specifically want to solve it as a flux integral without the div theorem.

    Also know how to split it up. Is this a proper way to compute it over the cylinder walls though?
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