Finding magnitude of x-component Electric Field due to a Line Charge

[Arrhenius7991]

Homework Statement

A rod lies on the x-axis with one end at the origin and another at x=2. The linear charge density is given by λ(x)=C(x^(3) + 3x^(2)). Find the x-component of the electric field Ex at the origin in terms of q.

Homework Equations

Ex = ƩdEx
||dE||= (k|dq|/r^(2)) (z/r)
dq = λ dx

The Attempt at a Solution

I took z = 0 since there is no z dimension. r to be 2 since the rod is 2m long. So Ex = (1/4)kq. But the answer solution says (-2/3)kq.

 

[tms]

Since you only want the x component, this is just a simple one-dimensional integration from one end of the rod to another.

 

[Arrhenius7991]

I'm not seeing this integral then.

 

[tms]

You want to add up the contribution to the field from each infinitesimal charge element on the rod.