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Homework Help: Gauss's Law and a conducting sphere

  1. Mar 23, 2005 #1
    "A solid conducting sphere with radius [tex]R[/tex] carries a posative total charge [tex]Q[/tex]. The sphere is surrounded by an insulating shell with inner radius [tex]R[/tex] and outer radius [tex]2R[/tex]. The insulating shell has a uniform charge density [tex]\rho[/tex] a) find the value of [tex]\rho[/tex] so that the net charge of the entire system is zero b) if [tex]\rho[/tex] has the value found in part (a), fnd the electric field (magnitude and direction) in each of the regions
    [tex]0<r<R[/tex] [tex]R<r<2R[/tex] and [tex]r>2R[/tex]"

    Calculating charge in terms of [tex]\rho[/tex] i got
    [tex]\sum Q=\frac{-28\pi\rho R^3}{3}[/tex]

    now my problem is trying to fine the [tex]\vec{E}[/tex] below is my work
    [tex]\oint\vec{E}d\vec{A}=\frac{Q_inc}{\epsilon_0}[/tex]
    there is an electric field only between
    [tex]R<r<2R[/tex]
    [tex]\vec{E}=\frac{Q}{4\pi R^2 \epsilon_0}[/tex]
    and after solving my above value for
    [tex]\rho[/tex] in terms of [tex]Q[/tex]
    I got

    [tex]\vec{E}=\frac{7R\rho}{3}[/tex]

    which is soo wrong, im sure I did some of this problem correctly..the part I dont understand is how I would find the electric field? Can anyone please help?
     
    Last edited: Mar 23, 2005
  2. jcsd
  3. Mar 23, 2005 #2

    Dr Transport

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    Science Advisor
    Gold Member

    You had the charge density in the shell correct but forgot that

    [tex] Q_{inc} = Q - 4\pi \int_{R} ^{R'} \rho r^{2} dr [/tex]

    not just the charge of the spherical shell.....
     
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