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freezer

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## Homework Statement

Determine the charge density due to the following electric flux density:

[tex]\overrightarrow{D} = \hat{r}4rsin(\phi ) + \hat{\phi}2rcos(\phi)+\hat{z}2z^{2}[/tex]

## Homework Equations

[tex]\rho _{v} = \triangledown \cdot \vec{D}[/tex]

[tex]\rho _{v} = \frac{\partial }{\partial r} + \frac{\partial }{\partial \phi}+ \frac{\partial }{\partial z}[/tex]

## The Attempt at a Solution

[tex]\rho _{v} = \frac{\partial }{\partial r} 4rsin(\phi) + \frac{1}{r}\frac{\partial }{\partial \phi}2rcos(\phi)+ \frac{\partial }{\partial z}2z^{2}[/tex]

[tex]\rho _{v} = 4sin(\phi)- 2sin(\phi) + 4z[/tex]

[tex]\rho _{v} = 2sin(\phi) + 4z[/tex]

does this look correct?

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