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Homework Help: Electrical field outside spherical shell

  1. Jun 8, 2008 #1
    1. The problem statement, all variables and given/known data
    An insulated spherical shell with its center in the origin and radius R has a surface charge density of [tex]\sigma(\theta)=\sigma_0\sin(\theta)[/tex] when [tex]\theta[/tex] is the angle from the z axis. Calculate the electrical field outside the shell at point z=R.


    2. Relevant equations

    Gauss's Law
    [tex]\int\int{\vec{E}\cdot\vec{dS}}=4\pi{Q_{in}}[/tex]


    3. The attempt at a solution

    I tried first calculating the overall charge of the spherical shell:
    [tex]Q=R^2\int_0^{2\pi}\sigma_0\sin^2\theta{d\theta}\int_0^\pi{d\phi}=\frac{R^2\sigma_0}{2}\int_0^{2\pi}(1-\cos{2\theta})d\theta\cdot\pi=\frac{1}{2}\pi{R^2}\sigma_0\cdot{2\pi}=\pi^2R^2\sigma_0[/tex]
    However, I don't see how Gauss's Law can help me find the electrical field at that specific point.

    Please help!
     
  2. jcsd
  3. Jun 9, 2008 #2
    anyone?

    Can someone please help??

    Perhaps I should somehow calculate [tex]\int{\frac{dq}{r^2}}[/tex] ?
     
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