August 9th, 2017, 12:29 AM  #1 
Member Joined: May 2017 From: Slovenia Posts: 87 Thanks: 0  Flux of vector field
I have F(x,y,z)=(z,0,2) and i need to find the flux through the upper side of the paraboloid z=2x^2y^2 1<z<2. When solving this with Gaussian theorem (divergence theorem) I'm not sure whether z will be = to 1 or 2? 
August 9th, 2017, 03:29 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,649 Thanks: 681 
The 'upper side' of the paraboloid is neither z= 1 nor z= 2, it is the paraboloid! The paraboloid has vertex at (0, 0, 2) and opens downward. In order to make it a closed surface, so that you can use the divergence theorem, you would add the plane z= 1.


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field, flux, vector 
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