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Flux of vector field

  1. Apr 21, 2009 #1
    1. The problem statement, all variables and given/known data
    Question is:

    Compute the flux of the vector field, \vec{F} , through the surface, S.
    [tex]\vec{F} = 7\vec{r}[/tex] and S is the part of the surface [tex]z = x^2 + y^2[/tex] above the disk [tex]x^2 + y^2 \leq 4[/tex] oriented downward.

    2. Relevant equations

    3. The attempt at a solution

    [tex]\int\limits_R (7x\vec{i} + 7y\vec{j} + (x^2 + y^2)\vec{k}) \cdot (2x\vec{i} + 2y\vec{j} - k) dA[/tex]
    [tex]\int\limits_R (14x^2 + 14y^2 - (x^2 + y^2)) dA[/tex]
    [tex]\int\limits_R (13x^2 + 13y^2) dA[/tex]
    [tex]13 \int\limits_R (x^2 + y^2) dA[/tex]
    [tex]13 \int^{2\pi}_0\int^4_0 r^3 dA[/tex]
    [tex]13 \int^{2\pi}_0 64 dA[/tex]

    is this correct?
  2. jcsd
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