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Homework Help: Uniformly charged cylinder

  1. Sep 7, 2005 #1
    ok for one of my problem sets i have come across a problem im a little unsure of:

    a uniformly charged cylinder of radius R, length L, and volume charge density rho is aligned along the z-axis from z=0 to z=-L. Find the electric field a distance D above the top of the cylinder(ie at z=D).[ Hint consider the cylinder as a stack of disks of thickness dz.]

    ok now i already computed the charge for a flat disk and obtained

    E= [tex]\frac{ \sigma*z}{2*\epsilon}*(\frac{1}{z} - \frac{1}{\sqrt{z^2+R^2}})
    [/tex]

    so now i was thinking that all a cylinder is is many of these disks with a thickness dz i can simply take the integral


    [tex]\frac{\rho}{2*\epsilon}\int_{-L}^{D}(1- \frac{z}{\sqrt{z^2+R^2}})dz[/tex]

    which produces the answer


    [tex]\frac{\rho}{2*\epsilon}*(L+\sqrt{L^2+R^2}+D-\sqrt{D^2+R^2})[/tex]


    does this seem right? if not it would be great if someone could point me to my error

    thanks
     
  2. jcsd
  3. Sep 7, 2005 #2

    Dr Transport

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    You only have to integrate over the cylinder height fom -L to 0.
     
  4. Sep 7, 2005 #3
    even if the electic field at point D is well above the cylinder?
     
  5. Sep 8, 2005 #4

    mukundpa

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    Homework Helper

    ya the charge is only on the cylincer.
     
  6. Sep 8, 2005 #5

    mukundpa

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    Charge density above the cylinder is zero.
     
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