# Conic charge distribution need help setting up integral

1. Feb 24, 2008

### electrifice

1. The problem statement, all variables and given/known data
A uniform charge (with density D) is distributed over a cone of radius R and height z. The axis of the cone is coincident with the x-axis. Find the total electric field due to the cone along the x axis.

2. Relevant equations
E = kqq/r^2

3. The attempt at a solution
This is really just a hypothetical problem to help study for my midterm so I need to make sure that I have the right idea.
For the first part...

...../2(pi)..../ z......./(-R/z)x + R
.....|..........|.........|
kD |da.......|dz......| (1/r^2)r(dr)
.....|..........|.........|
..../ 0......../ 0......./ 0

(Sorry for the messy-looking integral)
All of that will be multiplied by the cosine of the angle that the cone's laterals make with the x-axis. Does that look reasonably correct? Now for the second part... I am not able to set up a proper integral to be able to describe a hollow cone. Would dQ just be D*2(pi)r*(dr)? I think the second part should be easier than the first, but I just can't figure out the integral.

Last edited: Feb 24, 2008