Electric Field at the End of a Line of Charge

[bhdmia]

Field at End of Line of Charge 2

A charged rod of length L=7.10 m lies centered on the x axis as shown. The rod has a charge density which varies according to λ=ax^2 where a=−20.2 μC/m^3 .

What is the x component of the electric field at a point on the x-axis a distance of D=3.70 m from the end of the rod?

Relevant equations: Coulomb's Law - E=kQ/r^2The attempt at a solution: Ok, so part I of this problem was to calculate the total charge of the rod, which I figured out easily enough. Part II, as stated above, is to find the electric field at some point P along the axis of the line of charge. Here's my attempted solution:

E = ∫ (kdQ/r^2)*<i> where dQ=ax^2dx where r=x. The x^2 on top and x^2 on bottom cancel out so you just end up integrating dx with bounds (D+L) and (L) and multiply by k and a. That didn't work, so I tried the equation with <xi> for the r vector and that didn't work either. I can't figure out what I'm doing wrong. Help!

 

[gneill]

You need to integrate over the charge, from -L/2 to L/2. But the distance from the dq's to the point P is not the same as the x that "scans" the rod.