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Flux through surface

  • Thread starter -EquinoX-
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  • #1
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Homework Statement



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.

Homework Equations





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]
 

Answers and Replies

  • #2
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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."
 
  • #3
564
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thanks!
 

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