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Finding the E field due to an infinitely long cylinder (Given volume charge density)

  1. Oct 13, 2011 #1
    1. The problem statement, all variables and given/known data
    An infinitely long cylinder of radius 4.0 cm carries a uniform volume charge density
    ρ = 200 nC/m^3 What is the electric field at r = 8.0 cm


    2. Relevant equations
    I'm confused as to how to do this problem, I've tried converting from volume charge density to simply charge density λ and then solving with the equation for the E field due to an infiinite line charge, but this doesnt give me the right answer.


    3. The attempt at a solution
    (200 x10 ^-9)((4/3)(pi)(.04^3)) = Q

    λ = Q / L so λ = Q (as we're taking L to be 1 meter in the above equation)

    Efield due to infinite line charge= 2kλ/(.08)

    the correct answer is supposed to be .23kN/c
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 13, 2011 #2

    SammyS

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    Re: Finding the E field due to an infinitely long cylinder (Given volume charge densi

    It looks like there is enough symmetry to use Gauss's Law.
     
  4. Oct 13, 2011 #3
    Re: Finding the E field due to an infinitely long cylinder (Given volume charge densi

    I know but I tried finding Q as I showed above, by taking ρ = 200nC/m^3 and multiplying it by the volume (4/3 pi (.04)^3) to get Q = 5.36E-11

    I then use Gauss's law: E(4pi(.08)^2) = 5.36E-11/ε0

    this however gives me E = 75.306

    What am I doing wrong?
     
  5. Oct 13, 2011 #4

    SammyS

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    Re: Finding the E field due to an infinitely long cylinder (Given volume charge densi

    (4/3)πR3 is the volume of a sphere of radius, R.

    You should be working with a cylinder.
     
  6. Oct 13, 2011 #5
    Re: Finding the E field due to an infinitely long cylinder (Given volume charge densi

    Edit: never mind I found the answer, Thanks again for the help.
     
    Last edited: Oct 13, 2011
  7. Oct 13, 2011 #6

    SammyS

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    Re: Finding the E field due to an infinitely long cylinder (Given volume charge densi

    A cylinder of height 1 m is OK. A radius of 4 cm will give you the charge enclosed by a cylinder of height 1 m and radius of 8 cm, which is your Gaussian surface.
     
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