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Homework Help: Charge density in cylinder with uniform charge

  1. Feb 28, 2015 #1
    1. A charge density ρ (charge per unit volume) is distributed uniformly throughout a non-conducting cylinder of radius R. What is the magnitude of the electric field a distance r = R/2 from the cylinder's axis?

    2. Relevant equations

    E ∫dA = q(interior)/ε0


    So I tried doing EA = (ρA)(v/V)/ε0 where v is the volume of the Gaussian surface and V is the volume of the cylinder

    E = (ρ*(πR^2L/4πR^2L))/ε0
    E = ρ/4ε0

    However the answer is supposed to be E = ρR/4ε0

    I'm not sure where I'm going wrong
  2. jcsd
  3. Feb 28, 2015 #2


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    Check Gauss law once more: one is a volume (to determine q(interior) ) and the other is an area (of the surface).
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