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## Homework Statement

A thin rod of length 2L has a linear charge density that isλ0 at the left end but decreases linearly with distance going from left to right in such a way that the charge on the entire rod is zero.

Given

E = −kλ

_{0}/L(d/(L−d)−ln(d−L)+d/(L+d)+ln(L+d))

for a point P that is distance d>l to the right of the center of the rod:

How does this expression simplify to a familiar result for the limiting case d≫L? (Hint: The dipole moment of the rod has magnitude p=2λ

_{0}L

^{2}/3.) Express your answer in terms of some or all of the variables p, d, and Coulomb's constant k.

## Homework Equations

p=q*d ?

E = −kλ

_{0}/L(d/(L−d)−ln(d−L)+d/(L+d)+ln(L+d))

p=2λ

_{0}L

^{2}/3

λ=λ

_{0}(1-x/L)

## The Attempt at a Solution

I don't have a clear idea of

*where*I'm going in this problem. I started with the limiting case, and narrowed down the E equation to

E= (−kλ

_{0}/L)(1-ln(d)+1+ln(d))

E= (−kλ

_{0}/L)(1+1)

E= (−kλ

_{0}/L)(2)

E= -2kλ

_{0}/L

I don't think this is correct, because the answer has to be defined by no other variable than p, d, and k. Because of that, I know I have to use their equation for p, but I don't know

*how*to use it. Frankly, I don't even know if my first step was correct.

I could definitely use some guidance in the right direction right now.

Thank you very much!