Electric field due to uniform charged line

[muaymike]

Homework Statement

Find the electric field at point p 5cm away from a 10cm line with a uniform charge of 2x10^-4C.
so its uniformly charged from 0 - 10cm and then point p is at 15cm



This question is broken down into 4 step by step parts:

first is to consider 100 individual charges equally spaced apart and determine what the charge of each would be to get a total of 2x10^-4C

Next one asks what is the distance from the first charge to our point p, and distance from last charge to point p

The third one is where I'm stuck, it asks what is the distance between the neighboring charges. write an expression for distance r_n from the nth charge to point p.

Homework Equations

The Attempt at a Solution

For the first part, the charges would have 2/100 x 10^-4 C each. The second part, the distance from the first to point p is 15cm and from the last to p is 5cm. The third part, I can't find a way to express this distance. I believe it should have a dr but it could be just 15-x_n. I am really drawing a blank right now

 

[mfb]

If you label the first one with n=1 and the last one with n=100, you need a function f(n) such that f(1)=5cm and f(100)=15cm.
As the distance between all points is the same, this function is linear...

(a different, easier problem: what would you with just three points, if the first point is at 5cm and the third point at 15cm?)