(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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 [MATH]\int \int F.dS [/MATH] of the vector fieldF=xi+yj+[MATH]z^2[/MATH]kwhere S is a closed surface consisting of the cylinder[MATH]x^2 + y^2 = a^2[/MATH], 0<z<b and the circular disks [MATH]x^2 + y^2 , a^2[/MATH] at z=0 and [MATH]x^2 + y^2 = a^2[/MATH] at z=b.

I have the basics but dont know how to get an answer. My workings are attatched.

2. Relevant equations

Gauss's divergence theorem

3. The attempt at a solution

My workings are attatched.

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# Homework Help: Vector Calculus - Divergence theorem

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