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Electric field help needed

  • Thread starter Azael
  • Start date
  • #1
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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:

Answers and Replies

  • #2
253
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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:
  • #3
2,209
1
might want to fix your tex tags. put the tags on the same line as the code
 
  • #4
253
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found my error. I used capitals by misstake in the [ /tex ] :blushing:
 
Last edited:
  • #5
253
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I solved it today fortunaly :)
 

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