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Charge density from electric flux density

  1. Apr 19, 2014 #1
    1. The problem statement, all variables and given/known data

    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]


    2. Relevant 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]

    3. 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?
     
    Last edited: Apr 19, 2014
  2. jcsd
  3. Apr 20, 2014 #2

    rude man

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    There is a term missing here.
     
  4. Apr 20, 2014 #3
    I am not seeing it. For cylindrical I am only seeing the 1/r on the phihat term
     
  5. Apr 20, 2014 #4

    rude man

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    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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