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Electric field everywhere for a hollow cylindrical conductor?

  1. Dec 2, 2016 #1
    1. The problem statement, all variables and given/known data
    An infinitely long, hollow, conducting cylinder has a inner radius a and outer radius b and carries a linear charge density λ along its length. What is the electric field everywhere?

    2. Relevant equations
    ∫E⋅dA = Qenc/∈

    Variables
    ∈ = permittivity constant
    a = inner radius
    b = outer radius
    λ = linear charge density
    E = electric field
    r = distance to point of E field
    Qenc = enclosed charge

    3. The attempt at a solution
    For inside (r∠a) and in the shell (a∠r∠b) the electric field is zero. I don't know what to do for outside the shell. I think the charge is concentrated on the outer shell just as for a spherical conductor, is this true? Here is my attempt for outside.
     

    Attached Files:

  2. jcsd
  3. Dec 2, 2016 #2
    Use Gauss's law:
    ∫E⋅dA = Q / ∈

    E ⋅ (2πrL) = λ * L / ∈ where L denotes the imaginary Gaussian surface's length.

    Therefore,

    E = λ / (2π∈r)

    I hope this was helpful.
     
  4. Dec 2, 2016 #3
    That is exactly what I did in the picture. Great - thank you!
     
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