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Gauss Law Problem With A Spherical Conductive Shell

  1. Oct 2, 2011 #1
    You are a hollow metallic sphere of inner radius r1, and outer radius r2. Inside is a charge of magnitude Q and a distance d<r1 from the centre.

    First I need to draw the electric field lines for regions r<r1, r1<r<r2, and r2<r

    Since the sphere is a conductor the only place where there is not an electric field is inside the shell. The point charge induces a charge on the conducting sphere, making it in turn create an electric field outside the sphere.

    I then need to use Gauss's law to find the electric field where possible. I think this is correct:

    [tex]\int \vec{E}\cdot d\vec{A}=\frac{Q_{enclosed}}{\epsilon_{0}}[/tex]
    [tex]E\int d\vec{A}=\frac{Q}{\epsilon_{0}}[/tex]
    [tex]E(4\pi r^{2})=\frac{Q}{\epsilon_{0}}[/tex]
    [tex]E=\frac{Q}{4\pi r^{2}\epsilon_{0}}[/tex]

    For all locations that are not inside the shell. Am I correct?
     
    Last edited: Oct 2, 2011
  2. jcsd
  3. Oct 2, 2011 #2

    G01

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    Looks fine to me.
     
  4. Oct 2, 2011 #3
    Thanks for the confirmation.
     
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