Electric field above one end of a straight line segment?

[aftershock]

Homework Statement

Find the electric field a distance z above one end of a straight line segment of length L, which carries a uniform line charge λ. Check that your formula is consistent with what you would expect for the case z>>L

Homework Equations

KQ/r²

The Attempt at a Solution

I first considered the x component of the field and integrated

Kλx*dx/(x²+z²)^3/2 from 0 to L

I then considered the y component of the field and integrated

Kλz*dx/(x²+z²)^3/2

Finally I used pythagorean theorem on both these terms to find the total field.

The problem became pretty cumbersome (which is why I didn't follow all the calculations through in this post). Is my method correct, or am I way off here?

 

[krome]

Looks good to me. So, when you combine the x and y components of the field using the Pythagorean theorem, you are effectively calculating the magnitude of the electric field. I don't think you need to do that, although you certainly can do. I would think it sufficient to say the x and y components separately. The point is that the x component should vanish in the $x>>L$ limit and the y component should become $k \lambda L / z^2$.