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Homework Help: Gauss' Law: Cylindrical sheath

  1. Apr 5, 2010 #1
    1. The problem statement, all variables and given/known data
    A non-conducting, infinitely long, cylindrical sheath has inner radius r=10 m, outer radius r=15 m and a uniform charge density of 9 nC/m^3 spread throughout the sheath. Magnitude of electric field at r=5, r=12, r=17?


    2. Relevant equations
    Q=rho(Volume) and phi=EA therefore phi=E(2pi(R)length)
    phi=Q/epsilon_0


    3. The attempt at a solution
    At r=5, Electric field=0
    At r=12, phi=Q/epsilon_0, so E(2pi(R)length)=Q/epsilon_0
    I just don't know what Q will be.
    The same for r=17, I don't know how to find Q.
     
  2. jcsd
  3. Apr 5, 2010 #2

    Doc Al

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    Staff: Mentor

    You are given the charge density. Figure out the volume of sheath enclosed in each case.
     
  4. Apr 5, 2010 #3
    Thank you Doc Al!

    So for r=17, if R is the outer radius of the sheath, then
    Q=rho(length)piR^2, so E=(rho(length)piR^2)/(2pi(length)r(epsilon_o), thus
    E=(rhoR^2)/(2r(epsilon_o))
    is that correct, where i would use r=17 and R=15???????
    I still don't know how I would figure out E for r=12, the area IN the sheath.

    Please help! :)
     
  5. Apr 5, 2010 #4

    Doc Al

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    Staff: Mentor

    The sheath only starts at r = 10m and extends to r = 15m. So to find the charge contained in a Gaussian surface with radius 12m, you need the volume of the sheath from r = 10 to 12 m. Similarly, for r = 17 you'd use the entire sheath, so from r = 10 to 15 m.

    Hint: To find the volume between r1 and r2, find the volume of each full cylinder and subtract.
     
  6. Apr 5, 2010 #5
    Thank you very very much Doc Al! This makes so much sense!
     
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