Need help with Proper integral of a uniformly charged rod

[db2dz]

Homework Statement

A uniformly charged rod is places along the x-axis from x=0 to x= L. carefully set up, but do not solve the proper integral to determine the x component of the electric field at the point (L,a)

Homework Equations

E=u[tex]
\int \frac{dq}{(r^2)}
[/tex]

for a line dq=λdl

The Attempt at a Solution

i know for a line dq=λdl
i think its something along the lines of
Ey=Kλy=[tex]
\int \frac{dx}{(x^2y^2)^(3/2)}
[/tex] from 0 to L

I have no idea if this is right. I am using my notes to guide me.

 

[gabbagabbahey]

Coulomb's law for a linear charge distribution is:

[tex]\textbf{E}(\textbf{r})=\frac{1}{4\pi\epsilon_0}\int \lambda(\textbf{r}')\frac{\textbf{r}-\textbf{r}'}{|\textbf{r}-\textbf{r}'|^3}dl'[/tex]

Where [itex]dl'[/itex] is an infinitesimal length of the source, located at [itex]\textbf{r}'[/itex], and the integration is over the entire line of charge.

Use [itex]\textbf{r}=x\mathbf{\hat{x}}+y\mathbf{\hat{y}}+z\mathbf{\hat{z}}[/itex] and [itex]\textbf{r}'=x'\mathbf{\hat{x}}+y'\mathbf{\hat{y}}+z'\mathbf{\hat{z}}[/itex] to find the x-component.