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Gaussian sphere problem

  1. Feb 28, 2013 #1
    1. The problem statement, all variables and given/known data

    The problem states that you have a spherical shell with inner radius Ri=1 cm and outer radius R0=2 cm. The shell also has uniform charge density of ρ=10-3 N/m3. I found the first few answers of the question already. First was to get the charge of the shell, which is simply ρVshell, or Q=ρ(4∏/3)(R03-Ri3). This ends up being 2.93(10-8)C.
    Next I found that the electric field magnitude everywhere inside the shell could be expressed in terms of r by just setting EA=ρ(4∏/3)(r3-Ri3)/ε0, where the 4∏ cancels. the answer ends up being ((1/3)ρ/ε0)(r-(Ri3/r2), or 3.76(107) N/Cm.
    Now the part I'm having trouble with is finding an equation in terms of r for the electric field magnitude outside of the spherical shell.

    2. Relevant equations

    Gauss's Law. Surface area and volume of a sphere.

    3. The attempt at a solution

    I tried using Gauss's law in a similar way to the last part of the problem by having EA=Q/ε0, but I don't understand how you are supposed to solve for this if you don't know what the uniform charge density is outside of the shell. I don't feel like using that same value would make sense. Could somebody explain this to me?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 28, 2013 #2

    haruspex

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    How did you get that? There should not be a field inside an empty uniformly charged spherical shell.
     
  4. Mar 1, 2013 #3
    I said that is the E field inside the shell, as in like in the volume of the shell. Thats why I used the gaussian radius as arbitrary r minus the inner radius of the sphere.
     
  5. Mar 1, 2013 #4

    haruspex

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    OK - that's often a tricky distinction to make verbally.
    The field outside a uniformly charged spherical shell happens to be exactly as though all the charge were concentrated at the sphere's centre.
    Can you explain that some more? What same value?
     
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