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Homework Help: Gauss's Law and nonconducting spherical shell

  1. Oct 12, 2012 #1
    1. The problem statement, all variables and given/known data

    A nonconducting spherical shell of inner radius R1 and outer radius R2 contains a uniform volume charge density ρ throughout the shell. Use Gauss's law to derive an equation for the magnitude of the electric field at the following radial distances r from the center of the sphere. Your answers should be in terms of ρ, R_1, R_2, r, ε_0, and π.

    a) R_1 < r < R_2
    b) r > R_2

    2. Relevant equations
    ∫E dA = Q_enc/ε_0

    3. The attempt at a solution

    For a), I tried using Gauss's law to find it and I arrived at:

    E = [ρ(R_1)^3]/[3(ε_0)(r^2)]

    For b), I also used Gauss's law to find:

    [ρ(R_1)^3 + ρ(R_2)^3]/[3(ε_0)(r^2)]

    I'm not quite sure what I'm doing wrong...
  2. jcsd
  3. Oct 13, 2012 #2


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    Staff Emeritus
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    It's difficult to say what you are doing wrong, without having you give more detail regarding your steps in arriving at those solutions.
  4. Nov 20, 2013 #3
    A non-conducting spherical shell carries a non-uniform charge density ρ=ρ0r1/r. Determine the electric field in the regions:
    A) 0<r<r1

    r1 is radius to inside of shell. r0 is radius to outside of shell.
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