Discuss the below:
Flux
Consider the space region bounded below by the right angled cone z=sqrt(x^2+y^2), and above by the sphere
x^2+y^2+z^2=2.
These two surfaces intersect in a horizontal circle, let T be the horizontal disk having this circle as boundary, S the spherical cap forming the upper surface, and U the cone forming the lower surface.
Orient S,T,U "upwards", so the normal vector has a positive k-component.
Q1: For each of the three surfaces, determine geometrically (without calculation) whether the flux of the vector field F= -x*i-y*j is positive or negative.
Q2: Calculate the flux of F ACROSS EACH SURFACE (with the upwards orientation) .