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

I take the divergence of the function:

[tex]V=x^2 \boldsymbol{\hat {x}}+3xz^2\boldsymbol{\hat {y}}-2xz\boldsymbol{\hat {z}}[/tex]

And get zero. the answer doesn't make sense, since i expect to get a zero divergence only for a function that looks like the one in the drawing attached.

3. The attempt at a solution

[tex]\nabla \cdot V=2x+0-2x=0[/tex]

I test to see whether the function V behaves like in the drawing.

The function V at an arbitrary point, (1,1,1) is:

[tex]V_(1,1,1)=1\boldsymbol{\hat {x}}+3\boldsymbol{\hat {y}}-2\boldsymbol{\hat {z}}[/tex]

And, on another arbitrary point, lets say (2,2,2):

[tex]V_(2,2,2)=4\boldsymbol{\hat {x}}+6\boldsymbol{\hat {y}}-6\boldsymbol{\hat {z}}[/tex]

The vectors are different, not the same like i expected.

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# Homework Help: Problem interpreting the divergence result

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