Non-Uniform Distribution of Charge on a Rod

[mouzis]

Homework Statement

A rod of length L lies along the x-axis with its left end at the origin. A total charge Q is distributed non-uniformly on the rod, so that ?=ax, where a is a positive constant. (a)Determine the constant a. (b) What is the potential due to this charged rod at a point along the positive x-axis, past the end of the rod? (c) A point charge +2Q is placed at 3L from the origin on the positive x-axis. What is the potential energy of this system?

Homework Equations

dq=λds
dV=(dq)/(4pi)(ε₀)r
dU=Vdq

The Attempt at a Solution

I completed part a and got a=(2Q)/(l²)

my attempt at part b:
V=∫dV=∫(ax dx)/(4pi)(ε₀)r

From there my question is more what is the value of r? is it x? From there I am sure i can figure out the rest.

 

[ehild]

r is the distance from the charge. A picture would help.

ehild