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Dielectric Sphere with Free Volume Charge

  1. Oct 6, 2011 #1
    1. The problem statement, all variables and given/known data

    See figure attached.

    2. Relevant equations



    3. The attempt at a solution

    I'm confused as to how they got their D(r)

    Using Gauss' Law,

    For r < or = a

    [tex]\oint_{S} \vec{D} \cdot \hat{n} dS = \int_{v} \rho dv [/tex]

    [tex]D(4 \pi r^{2}) = \frac{\rho 4 \pi r^{3}}{3}[/tex]

    [tex]\Rightarrow D = \frac{P_{0}r^{2}}{3a}[/tex]

    What am I doing wrong?
     

    Attached Files:

  2. jcsd
  3. Oct 8, 2011 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    You have ρ = constant. It's not.
     
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