Calculating the Electric Field generated by a rod with charge

[jmarzouq]

Homework Statement

A rod of length 2L has a charge -Q uniformly distributed over its left half and +Q uniformly distributed over its right half. Find E at point p a distance z above the center of the rod.

Homework Equations

E= 1/(4pi$\epsilon$$_{0}$)∫dq/r($\hat{r}$)
dq=λdl

where $\epsilon$$_{0}$= 8.854 x 10^-12 C²/Nm²
and λ=charge per unit length

The Attempt at a Solution

I'm not even sure where to start exactly. I know the length from the rod to p at any given point will be √(L²+z²) but I'm really not sure where to go from here. I missed a couple of class periods due to being sick and I've been trying to play catch up ever since so any help would be greatly appreciated!

 

[rl.bhat]

Find the field dE at the point p due to symmetrically placed charged element with opposite charge. Resolve dE into two components and find the resultant field dE. To find the field due to whole rod, find the integration.

 

[jmarzouq]

That's the thing. I'm at a loss as to how to do that exactly. The only thing I've been able to calculate the electric field for is point charges. Like I said, I've missed a couple of days and really have no idea what to do. I'd imagine you'd use Gauss's law, I just don't know how to go about doing it exactly.