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Homework Help: Gauss's Law Problem: long, cylindrical charge distribution

  1. Apr 30, 2016 #1
    1. The problem statement, all variables and given/known data
    Consider a long, cylindrical charge distribution of radius R with uniform charge density ρ.

    a) Using Gauss’s law, find the electric field at distance r from the axis, where r < R

    b) Using Gauss’s law, find the electric field at distance r from the axis, where r > R

    2. Relevant equations
    ∫EdA = Qinside/ε0
    q = ρV
    V = πr2L
    A = 2πrL
    3. The attempt at a solution
    I've successfully solved the first part which is E = ρr/2ε0.

    However for the second part I am confused as to whether or not I would need to use big R for the area, because we are now going at a distance out of the surface or to use little r.
  2. jcsd
  3. Apr 30, 2016 #2
    i think you are going out to a point r where r >R ,
    so your Gaussian surface will be a cylinder of radius r (r>R) enveloping the charged cylinder and you have to calculate the total normal outward flux through this imaginary /constructed Gaussian surface-
  4. Apr 30, 2016 #3
    What I got from this method so far is ρr2/2Rε0
  5. Apr 30, 2016 #4
    R is the radius of your cylindrical charge distribtion of volume charge density rho-
    so in the gaussian surface you have charges inside which will be = rho x volume of the charged cylinder ;
    the flux will be passing through cylindrical surface constructed of radius r
    so there will be correction in your result
  6. Apr 30, 2016 #5
    I see exactly what you mean now, thank you!
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