A nonconducting rod of length L has a nonuniform charge density at a total charg

Question

A nonconducting rod of length L has a nonuniform charge density at a total charge Q. Calculate the electrical field at a point P a distance d (d>L) to the right from the left end of the rod if the charge density is

a) cx (c=constant)

b) ax^2 (a=constant)

I have tried this so many times and can't seem to get it right. I was able to find the constant for part a but couldn't even figure out how to get the constant for part b. And I tried multiple different types of integrals to get the electrical fields of both but just cannot figure it out. Please help!

Explanation / Answer

So, the diagram goes like a rod along x axis, its left end at the origin, and we need to find the field at x=d where d>L.

a. (E=k int_{0}^{L}rac{c*x}{(d-x)^2}dx=[k*c*rac{x}{d-x}-log(d-x)]^{L}_{0}=k*c*(L/(d - L) - log(d) + log(d - L)))

b. (E=k int_{0}^{L}rac{a*x^2}{(d-x)^2}dx=[rac{x (2 d - x)}{(d - x)} + 2 d log(-d + x)]^{L}_{0}=rac{(2 d - L) L + 2 d (d - L) (-Log[-d] + Log[-d + L])}{(d - L)})

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