Calculating electric field due to charge distribution

[henry3369]

Homework Statement

http://imgur.com/EiCFIDe

Homework Equations

E = kq/r²
λ = dq/dx
Q = λa

The Attempt at a Solution

Here is the book solution:
http://imgur.com/aKSeKo0

I need help with part (a). I understand everything in the solution except for the distance they used for between (r² in the equation above). It seems they used (a+r-x) and they say that is the distance between a segment at x and the charge q. What does q have to do with the problem at all? Part (a) asks for the electric field due to the charge distribution Q where x > a. So shouldn't the distance be between dx(a segment on the charge distribution) and x?

 

[TSny]

You are right, it should not have mentioned q in the solution for (a). But the derivation is OK if you think of r as the distance from the right end of the rod to some arbitrary point P located to the right of the rod.