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Uniformly charged cylinder

  • Thread starter matpo39
  • Start date
43
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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

Dr Transport
Science Advisor
Gold Member
2,247
401
You only have to integrate over the cylinder height fom -L to 0.
 
43
0
even if the electic field at point D is well above the cylinder?
 
mukundpa
Homework Helper
524
3
ya the charge is only on the cylincer.
 
mukundpa
Homework Helper
524
3
Charge density above the cylinder is zero.
 

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