1. Consider a cube with vertices at A=(0,0,0) B=(2,0,0) C=(2,2,0) D=(0,2,0) E=(0,0,2) F=(2,0,2) G=(2,2,2) H=(0,2,2)
A)Calculate the flux of the vector fieldF=xi through each face of the cube by taking the normal vectors pointing outwards.
B)Verify Gauss's divergence theorem for the cube and the vector field F by computing each side of the formula.
C)Using Gauss's divergence theorem evaluate the flux \(\displaystyle \int \int F.dS \) of the vector field F=xi+yj+\(\displaystyle z^2\)k where S is a closed surface consisting of the cylinder\(\displaystyle x^2 + y^2 = a^2\), 0<z<b and the circular disks \(\displaystyle x^2 + y^2 , a^2\) at z=0 and \(\displaystyle x^2 + y^2 = a^2\) at z=b.
I have the basics but dont know how to get an answer. My workings are attatched.
Gauss's divergence theorem
The Attempt at a Solution
My workings are attatched.
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