The equation given by the OP is relevant when the point charge is along the axis of the rod, and the rod is finite. The equation given in the pdf, the more familiar form, is for a different physical situation as shown in the diagrams for the pdf.
To understand the validity of the OP's equation...
It's correct
λ = Q/L
dE = k λ(delta x)/(x^2)
Integrate from d to d+l (with an added bit of algebra) to obtain the expression given.
The continuous charge distribution for a uniformly charged rod is usually given as follows, and is maybe the more familiar one, but used in a different...
Here is what I do not understand:
If you claim the radius of the disc is negligible in comparison to the distance z away from the point charge, the expression for flux seems to go to zero? Does it not?
The numerator in this equation is simply the charge related to the charge density.
where λ = delta Q / delta L -> delta Q = λ*delta L
The equation as a whole of course is simply the definition of the electric field from Coulomb's law.
I enrolled at the University of Wisconsin-Eau Claire with the intent of finishing their dual degree program with UW-Madison for physics and nuclear engineering (http://www.uwec.edu/admissions/facts/dualdegree.htm). Heading into my sophomore year, it has become apparent that such a program may...