Uniformly charged cylinder

  • Thread starter matpo39
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  • #1
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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
 

Answers and Replies

  • #2
Dr Transport
Science Advisor
Gold Member
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You only have to integrate over the cylinder height fom -L to 0.
 
  • #3
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even if the electic field at point D is well above the cylinder?
 
  • #4
mukundpa
Homework Helper
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ya the charge is only on the cylincer.
 
  • #5
mukundpa
Homework Helper
524
3
Charge density above the cylinder is zero.
 

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