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

Show divergence theorem works

For the vector field [tex] E = \hat{r}10e^{-r}-\hat{z}3z[/tex]

2. Relevant equations

[tex]\int_{v}\nabla \cdot E dv = \oint_{s} E \cdot ds [/tex]

3. The attempt at a solution

[tex] \nabla \cdot E = 1/r \frac{d}{dr}(rAr)+1/r\frac{dA\phi}{d\phi}+\frac{dAz}{dz} [/tex]

Ar=10e^(-r)

Aphi=0

Az=-3z

[tex] \nabla \cdot E = \frac{1}{r}(10e^{-r}-10re^{-r})+3 [/tex]

[tex] \int_{0}^{2\pi}\int_{0}^{4}\int_{0}^{2} (r)(\frac{1}{r}(10e^{-r}-10re^{-r})+3) dr dz d\phi = -82.77 [/tex]

[tex] \oint_{s} E \cdot ds= \int_{0}^{2} \int_{0}^{4} (\hat{r}10e^{-r}-\hat{z}3z)\cdot(16 \pi \hat{r}+4\pi\hat{z}) = 2341.7 [/tex]

wow that took awhile to type

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# Homework Help: Show Divergence theorem works

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