Hi,

I need help with this question;

Find the outward flux of the vector field F = <y,x,-z> through the boundary of the solid inside the cylinder (x^2) + (y^2) = 4 between the plane z = 0 and the paraboloid z = (x^2) + (y^2)

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- April 19th 2009, 09:20 PMhtata123question on outward flux (Vector calc.)
Hi,

I need help with this question;

Find the outward flux of the vector field F = <y,x,-z> through the boundary of the solid inside the cylinder (x^2) + (y^2) = 4 between the plane z = 0 and the paraboloid z = (x^2) + (y^2) - April 19th 2009, 10:21 PMCalculus26
Ideally you know the divergence thm --an ideal place yo use it

the flux in this case is equal to the volume since div(F) = 1

If not you have some work to do

You'll need 4 flux integrals

1. on the bottom but here z = 0 so the flux is 0

the parabaloid intersects the cylinder in the plane z =4

2. through the sides of the cylinder below z = 4 (split into right and left halves)

3. through the parabaloid above over the circle r = 2