Understanding Point Charges Along a Uniformly Charged Line

[tripsynth]

Hi, I'm trying to understand point charges along a uniformly charged line with a charge per unit length. This is a screenshot of what I'm trying to understand. http://i.imgur.com/s1vX7.jpg

I am not sure where the term r/R is coming from. I realize that the r term in sigma*dx/4pi*enot should change as you go down the x-axis but I don't get where the factor r/R comes from. I feel like I'm missing something. This is an example page from the book "Electromagnetism" by John C. Slater and Nathaniel Frank.

 

[Doc Al]

They are only considering the component of the field perpendicular to the line of charge (the parallel component will add to zero for an infinite line of charge). r/R is equivalent to the cosine of the angle.

 

[gsal]

No, you are not trying to "understand point charges along a uniformly charged line"...you are trying to "understand the electric field intensity at point P which is at a distance r from a charge line".

You see, you are trying to determine the influence of the entire line charge (which is discretized in a bunch of little dx's) on a given point P.

If the x-axis is vertical and the y-axis is horizonatl and the charge line pretty much lies on the x-axis and the point P is at a coordinate (x,y)=(0,r)

The field intensity at P due to a given dx (x not equal 0) will be along the line the joins that dx and the P point, and hence, it can be thought of having two components, one parallel to the x-axis and one parallel to the y-axis...since the charge line is infinite long, the point P "sees" the same thing above it (x>0) as below it (x<0) and hence all the x-components of the field at P cancel out and all the y-components add up.