Charge density from electric flux density

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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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Answers and Replies

  • #2
rude man
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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]

does this look correct?

There is a term missing here.
 
  • #3
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There is a term missing here.

I am not seeing it. For cylindrical I am only seeing the 1/r on the phihat term
 
  • #4
rude man
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I am not seeing it. For cylindrical I am only seeing the 1/r on the phihat term

Stick a term 4sinø in there somewhere, anywhere. No partial derivative. Just that term. (It's part of the rhat coefficient: 4rsinø/r).
 

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