1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar

    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

    User Avatar

    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Gauss' Law: Cylindrical sheath
Loading...