What is the electric field above a uniformly charged cylinder?

[matpo39]

ok for one of my problem sets i have come across a problem I am 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= $$\frac{ \sigma*z}{2*\epsilon}*(\frac{1}{z} - \frac{1}{\sqrt{z^2+R^2}})$$

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


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

which produces the answer


$$\frac{\rho}{2*\epsilon}*(L+\sqrt{L^2+R^2}+D-\sqrt{D^2+R^2})$$


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

thanks

 

[Dr Transport]

You only have to integrate over the cylinder height fom -L to 0.

 

[matpo39]

even if the electic field at point D is well above the cylinder?

 

[mukundpa]

ya the charge is only on the cylincer.

 

[mukundpa]

Charge density above the cylinder is zero.