# 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

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

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

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

thanks

Gold Member
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?

Homework Helper
ya the charge is only on the cylincer.

Homework Helper
Charge density above the cylinder is zero.