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Homework Help: Electric Field/Gauss' law of cylinder and shell

  1. Jan 30, 2009 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations
    Gauss' Law

    3. The attempt at a solution
    It may be that I'm sick with a cold and can't think straight, but I"m not seeing any way to approach this problem using Gauss' law. I tried using a few prederived formulas, but like for the first part of this 5 part problem, I need the charge/length in order to find out E. I don't have that value, and I did try using rho as lambda, and got it wrong. I also have to find the charge at values inbetween the cylinder and the shell, outside the shell, and on the inner shell.

    Some help would be nice, as I can't see how to do this by hand right now.
  2. jcsd
  3. Jan 30, 2009 #2
    Consider a Gaussian cylinder with radius of 2 cm. This cylinder is within the green cylindrical charge distribution. Gauss's Law is

    [tex]\oint_{S}\vec{E}\cdot\vec{dA}=\frac{1}{\epsilon_{0}}\int_{V}\rho dV[/tex]

    Use cylindrical coordinates, the given charge density, and the fact that the electric field is parallel to your Gaussian surface's normal vector to solve this.

    Note that S is the surface area of your Gaussian cylinder and V is the volume within it.
  4. Jan 30, 2009 #3
    Using a cylindrical Gaussian surface will give E in terms of charge/unit length. So, let the Gaussian surface be


    where l is a unit length. Then the charged enclosed per unit length within this surface is the volume within the surface times the charge density for r less than the radius of the inner conductor.
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