How Do You Calculate the Electric Field at a Point Near a Uniformly Charged Rod?

[deadpenguins]

Homework Statement

A nonconducting rod of length L = 8.15cm has charge -q = -4.23 fC uniformly distributed along its length. What are the magnitude and direction [relative to the positive direction of the x axis] of the electric field produced at point P, a distance a = 12.0cm from the rod?

NOTE: In the illustration, the rod and P are along the x axis, and P is to the right of the rod (assumed to be the positive end).

Homework Equations

dE = dq/(4*pi*E₀*r²)
dq = Lambda*dx
E₀ = permeativity of free space = 8.85x10^-12
Lambda = linear charge density = q/L

The Attempt at a Solution

I am not sure how 'L' and 'a' are to replace 'r' in the equation above. I have tried r = L + a, but it seems this method does not correctly describe the situation. I then tried to integrate the equation along the limits from 0 to L, but am not sure how to include the additional distance of 'a' into the equation. This seems like a fairly simple question, but my text does not extensively pursue this topic.

 

[willem2]

what you have to compute is $$\int_0^L \frac {dq} { 4 \pi \epsilon_0 r^2}$$

where r = the distance from the charge element dq to the point P