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Homework Help: Electrodynamics problem

  1. Jul 20, 2010 #1
    1. The problem statement, all variables and given/known data
    Circular plate radius R is uniformly charged and the charge of plate is Q. Find the electric field in arbitrary point perpendicular to the plate that passes through the center. Case [tex]R\rightarrow \infty[/tex] compared with a score of Gaussian theorem.


    2. Relevant equations

    Gauss theorem

    [tex]\int_S \vec{E}\cdot\vec{dS}=\frac{q}{\epsilon_0}[/tex]



    3. The attempt at a solution

    I calculate first part of assignment.

    [tex]\vec{E}_A=\frac{1}{4\pi\epsilon_0}\int_S\frac{\sigma dS}{r^3}\vec{r}[/tex]

    [tex]dS=\rho d\rho d\varphi[/tex]

    [tex]r=\sqrt{\rho^2+z^2}[/tex]

    [tex]\vec{r}=z\vec{e}_z-\rho\vec{e}_{\rho}[/tex]

    and get

    [tex]\vec{E}_A=\frac{\sigma}{2\epsilon_0}\frac{z}{|z|}(1-cos\alpha_0)[/tex]

    When [tex]R\rightarrow \infty[/tex] [tex]\alpha_0\rightarrow \frac{\pi}{2}[/tex]

    So when [tex]R\rightarrow \infty[/tex]

    [tex]\vec{E}_A=\frac{\sigma}{2\epsilon_0}sgnz \vec{e}_z[/tex]

    I don't know how can I do the second part with Gauss theorem? Thanks for your help!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 20, 2010 #2
    When R -> infinity, the plate -> something. What is it?
     
  4. Jul 20, 2010 #3
    infinite plane?
     
  5. Jul 20, 2010 #4
    Correct :wink:
    And what does the Gauss theorem give for E of an uniformly charged infinite plane?
     
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