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Homework Help: Electric field help needed

  1. Sep 14, 2005 #1
    I apologise for any spelling errors or terms missnamed since I am swedish and this course Im reading is only swedish books and terms. But I think I have gotten the translations right. Also my first try with latex.


    I have a non conducting sphere with the radius R and the volume charge density

    [tex] \rho (r) = \rho_o (1- \frac{r}{R} [/tex] when 0<r<R
    and [tex] \rho(r) = 0 [/tex] when r>R
    where [tex] \rho_0 [/tex] is a positive constant.


    I want to calculate the field E(r) for 0<r<R and R<r and I want to use this forumla

    [tex]
    E = \int \frac{dQ \hat{r}}{4 \pi \epsilon r^2}
    [/tex]

    This is how I do it

    [tex]
    E = \frac{\rho}{4 \pi \epsilon_0 } \int_{0}^{r} (1-\frac{r}{R}) sin\theta d\theta dr d\phi
    [/tex]

    I get that to [tex]\bar{E}= \frac{\rho_o}{\epsilon_0} (r- \frac{r^2}{2R}) \hat{r} [/tex]

    is that a correct answere for 0<r<R??

    gonna post this now and se if I got the latex right
     
    Last edited: Sep 14, 2005
  2. jcsd
  3. Sep 14, 2005 #2
    if I use gauss

    [tex]
    \oint Eds = \frac{{Q_e_n_c_l}}{{\epsilon_o}}
    [/tex]

    with [tex] Q_e_n_c_l = \int_{0}^{r} \rho_0(1 - \frac{r}{R}) r^2 \sin \Theta dr d \Theta d \Phi = \rho_0 4\Pi (\frac{r^3}{3} - \frac{r^4}{4R}) [/tex]

    I get as answere
    [tex] \overline{E} = \frac{\rho_o}{\epsilon_0} ( \frac{r}{3} - \frac{r^2}{4R}) \hat{r} [/tex]

    why do I get different answeres. What equation do I implement wrong(or do I do them both wrong)?

    seems like the latex wont work :confused:
     
    Last edited: Sep 14, 2005
  4. Sep 14, 2005 #3
    might want to fix your tex tags. put the tags on the same line as the code
     
  5. Sep 14, 2005 #4
    found my error. I used capitals by misstake in the [ /tex ] :blushing:
     
    Last edited: Sep 14, 2005
  6. Sep 15, 2005 #5
    I solved it today fortunaly :)
     
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