Electric field by infinite line of charge

[Sam99]

Homework Statement

Given an infinitely long line of charge density λ extended along the x-axis, what is the electric field at a point X = x(x')+y(y')+z(z') (in space)?

Homework Equations

E = kq / r^2, dq = (lamda)dx

The Attempt at a Solution

dE = kλ ∫ [x(x')+y(y')+z(z')- x(x')] dx / [(y^2) +(z^2)]^(3/2) (integral from -∞ to +∞)

I end up getting 0 because -∞ + ∞ equals 0?

 

[tiny-tim]

Welcome to PF!

Hi Sam99! Welcome to PF!

(try using the X² button just above the Reply box )

dE = kλ ∫ [x(x')+y(y')+z(z')- x(x')] dx / [(y²) +(z²)]^3/2 (integral from -∞ to +∞)

shouldn't there be an x² on the bottom also?

 

[Sam99]

Thanks!
I don't think so because I'm using (x-x')/ |x-x'|^3.
would that be right?

 

[tiny-tim]

yes, but there's still a difference in x, which has to go on the bottom