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Spherical Shell using Gauss' Law

  1. Jun 21, 2016 #1
    1. The problem statement, all variables and given/known data
    An insulator is in the shape of a spherical shell. The insulator is defined by an inner radius a = 4 cm and an outer radius b = 6 cm and carries a total charge of Q = + 9 mu.gif C (1 mu.gif C = 10-6 C). You may assume that the charge is distributed uniformly throughout the volume of the insulator.

    What is Ey, the y-component of the electric field at point P which is located at (x,y) = (0, -5 cm)?

    2. Relevant equations
    Φnet = Qenclosed / ∈0 = E × ∫surface dA


    3. The attempt at a solution
    I found the charge density ρ:
    Total charge 9e-6 C / ( 4/3 π (0.062 - 0.042)) = ρ

    Then, with my Gaussian surface a sphere with radius 5 cm, I found Qenclosed
    Qenclosed = ρV = ρ * 4/3 π (0.052 - 0.042)

    I know that
    Φnet = Qenclosed / ∈0 = E × ∫surface dA
    which I can rearrange such that
    E (this is what I need to find - the electric field on the surface) = Qenclosed / (ε0 * ∫surface dA)
    And since ∫surface dA = 4 π r2
    I can find E:
    E = 1/4πε0 * Qenclosed / r2 = 1/4πε0 * 4.05e-6 / 0.052 = 14563800

    This isn't correct, though. Where did I go wrong? I think it is in those last few equations - do I have the wrong area?

    The units do work out: k has units N*m2/C2, Qenc has units C, and r2 is in m2, which works out to N/C
     
  2. jcsd
  3. Jun 21, 2016 #2

    TSny

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    Homework Helper
    Gold Member

    Hello! Welcome to PF!

    Your expression for the volume of a sphere is not correct. The power of r is not right.

    Otherwise, your method looks good to me :smile:
     
  4. Jun 21, 2016 #3
    Oops! Thank you.
     
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