1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Calculating potential from a nonuniform linear charge distribution.

  1. Sep 13, 2012 #1
    1. The problem statement, all variables and given/known data
    The thin plastic rod has length L, and a nonuniform linear charge density λ = cx. With V = 0 at infinity, find the electric potential (in V) at point P1 on the axis, at distance d from one end.
    c = 28.9 pC/m^2
    L = 12.0cm
    d = 3.00 cm

    Now, from what I can tell the left side of the rod is placed at the origin, and p1 is a distance of d from the left end.
    2. Relevant equations

    V = (kq)/r (potential of the point charge).

    [itex]V = \int \frac{kcx}{x+d} dx [/itex].

    k is the Coulomb constant.

    3. The attempt at a solution

    Now I assumed using the above equation to integrate the potential over 0 to L would give the solution. However, when I checked the back of the book I was mistaken. Is it possible I missed something? I am treating cx dx as an point charge and summing over the potential each one produces at the point in question.

    I get using the equation 156Volts while the book claims the answer to be 18.6mV.
  2. jcsd
  3. Sep 13, 2012 #2
    Why is c C/m^2? It should be C/m.

    Apart from this, I think your approach is correct. Without seeing how you integrated the thing, I can't say more.
  4. Sep 13, 2012 #3
    Okay, yes disregard my question. I was using a computer algebra system (Microsoft Mathematics) to solve the integral. I tried it on my TI-84 Plus and I got .01863 Volts.

    (This is what I get for being lazy).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook