still under construction
c(4) The binomial theorem approximation was supposed to be carried out to 3 terms, or else, as was stated in the hint given to us for this problem, the approximation would reduce to the equation for a point charge. Three terms are needed for a good approximation, but the person who wrote this solution only carried out the binomial theorem to two terms (see c(4), where the person specifies only two terms were used). Therefore, the approximation found in c(4) is incorrect.
When the person wrote the labels "Electric field density" and "Calculating the value of electric field" on lines b(12) and b(13), I think the person may have forgotten to back up to the first page when writing these labels on the electronic pad. These labels do not match the steps listed on lines b(12) and b(13).
On lines b(9) and b(10), I think it was good to replace (a + L - x) with u because this substitution makes it easier to see how to take the integral of 1/((a + L - x)^2).
Although the person who wrote this solution did not carry out the binomial approximation to three terms, the person did get an answer that seems more correct than mine. I found that E = kq/(L^2), and the person found that E = kq/(a^2). The definition of E is kq/(r^2), where r is the distance from the test charge at P to the charge producing the electric field (the rod). When P is at a great distance from the rod (so that a >> L), a is the distance between point P and the rod, not L. Therefore, my answer is wrong. I think the person writing this solution used good physics--the person knew how to set up the integral and choose accurate limits based on the information given in the problem. However, not taking the binomial theorem compromised the accuracy of the person's answer.