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)
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)
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