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Non-Uniform Distribution of Charge on a Rod

  1. Oct 16, 2012 #1
    1. The problem statement, all variables and given/known data

    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?

    2. Relevant equations
    dq=λds
    dV=(dq)/(4pi)(ε0)r
    dU=Vdq

    3. 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 im sure i can figure out the rest.
     
  2. jcsd
  3. Oct 16, 2012 #2

    ehild

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    Homework Helper
    Gold Member

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

    ehild
     
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