suppose F(x,y,z)=(x,y,5z). Let W be the solid bounded by the paraboloid z=x^2+y^2 and the plane z=25. Let S be the closed boundary of W oriented outward. Find the flux of F out the bottom of S (the truncated paraboloid) and the top of S (the disk).

Question

suppose F(x,y,z)=(x,y,5z). Let W be the solid bounded by the paraboloid z=x^2+y^2 and the plane z=25. Let S be the closed boundary of W oriented outward.  Find the flux of F out the bottom of S (the truncated paraboloid) and the top of S (the disk).

anonymous · Answer

A bit rusty of multivariable but could you use stokes to relate the flux to the line integral around the circle formed by the intersection of the paraboloid and the plane.

anonymous · Answer

Or perhaps Divergence (Gauss) would be better seeing as this is reminiscent of those electrostatic problems