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Electric field of a cylinder?

  1. Jan 22, 2012 #1
    1. The problem statement, all variables and given/known data

    Consider a long cylindrical charge distribution of radius R = 13 cm with a uniform charge density of ρ = 18 C/m3. Find the electric field at a distance r = 32 cm from the axis.



    2. Relevant equations
    ΦE = EA = qin/ε0



    3. The attempt at a solution
    My problem here is that I don't know how to solve it given uniform charge density. I can solve Gauss's law for a cylinder down to E = 2K(λ/r), but as I don't have a length, linear charge density doesn't help me much. So I'm stuck here, and any help would be great.

    Thanks!
    Ian
     
  2. jcsd
  3. Jan 22, 2012 #2

    Simon Bridge

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    Apply Gauss' law: when you are a long way from the collection of charge, the field is the same as if all the charge were concentrated.

    Do you know how to do it for a line of charge?

    Q=ρV = ρAh
    That help?
     
  4. Jan 22, 2012 #3
    Φ = EA = Qin / ε

    Qin = ρV = ρAh

    EA = ρAh / ε

    E = ρh / ε

    Then I get stuck with h...
     
  5. Jan 22, 2012 #4

    Simon Bridge

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    The electric field due to a short length dz of the cylinder will be the proportional amount of charge between z and z+dz and inversly proportional to the distance to the length. Use symmetry to cancel the z components and sum all the contributions along the entire cylinder.

    You will have an example of an infinite line of charge someplace in your course notes.

    Also see:
    http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html
     
    Last edited: Jan 22, 2012
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