What Is the x Component of the Electric Field at a Point on the x-Axis?

[Broem]

Homework Statement

A charged rod of length L = 1.00 m lies centered on the x-axis as shown. The rod has a linear charge density which varies according to λ = ax where a = −90.0 μC/m.
What is the x component of the electric field at a point on the x-axis a distance of D = 2.00 m from the end of the rod?

Homework Equations

E=kQ/r^2
charge density = Q/A

The Attempt at a Solution

I really do not understand...Where do I get the r from? Since its not uniformly distributed how can there be any field outside?
Would my r = (D-(half of L))?
I'm assuming lambda is just regular charge density at a location of x?

 

[tiny-tim]

Hi Broem!

Would my r = (D-(half of L))?
I'm assuming lambda is just regular charge density at a location of x?

Yes.

(and of course it's a linear charge density, ie coulombs per metre, not per metre³ )

Since its not uniformly distributed how can there be any field outside?

Not following you.

 

[Broem]

Thanks for the quick response!
Ok so here's where I am:

I now know that lambda = Q/L so Q = L * (lambda)

So I'm left with
9e9(-9e-6)/(2-.5)^2

This however is not the correct answer...Where can I go from here?

 

[tiny-tim]

oh, no, you'll have to integrate …

use coulomb's law to find the electric field from a tiny section [x,x+dx] (whose charge will be λdx, and which you can assume is concentrated entirely at x), and integrate from -L/2 to L/2

 

[Broem]

I got it!
Thank you so much for your help!