Let S be a closed surface consisting of a paraboloid (z = x²+y²), with (0≤z≤1), and capped by the disc (x²+y² ≤1) on the plane (z=1).
Determine the flow of the vector field F (x,y,z) = zj − yk, in the direction that points out across the surface S.
I used the gauss theorem and found that the flow is zero, because the divergence of the vector function is zero. Since any definite integral of 0 is 0, the flow will be 0 too.
Is my logic correct or did I make a mistake? Thank you in advance.
Determine the flow of the vector field F (x,y,z) = zj − yk, in the direction that points out across the surface S.
I used the gauss theorem and found that the flow is zero, because the divergence of the vector function is zero. Since any definite integral of 0 is 0, the flow will be 0 too.
Is my logic correct or did I make a mistake? Thank you in advance.