1. Not finding help here? Sign up for a free 30min 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!

Electric Field On A Point Charge Due To A Uniformly Charged Rod

  1. Feb 22, 2013 #1
    1. The problem statement, all variables and given/known data
    This is regarding setting up an integral to calculate the electric field on a point charge that is at a distance "a" from a uniformly charged rod of length "L". I have attached a picture of my work, which includes a diagram of the problem, and wanted to know if my thought process is correct.


    2. Relevant equations



    3. The attempt at a solution
    Finding a general expression for the electric field produced by an infinitely small "piece" of charge and then adding them all up. The charged rod is parallel to the y-axis and it's center is at the origin.

    We know that the linear charge density is

    λ=(Q/L).

    For an infinitely small piece of charge, we say λ=(dQ/dL), so dQ=λ*dL


    The formula for the Electric field on a point charge is E=q/((4∏ε)*r^2)

    To find an expression for the Electric field produced by the small piece of charge, we can replace q with dQ

    dE=dQ/((4∏ε)*r^2)

    (substitue λ*dL for dQ)

    dE=λ*dL / ((4∏ε)*r^2)


    The part that I am unsure about is finding an expression for the "r". Would it be reasonable to say that "r = (a+y)", where y is the variable that I am integrating, and my limits of integration would be [(-L/2),(L/2)]? The reason I am saying (a+y) is because if I plug "-L/2" in for y, then (a-(L/2)) is the distance from the point charge "a" to the end of the rod that is above the origin. If I plug in "L/2" for y, then (a+(L/2)) takes care of the distance from the point charge "a" to the end of the rod below the origin. If I plug in 0 for y, then I simply get "a" which makes sense, since that is the distance from the origin to the point charge.

    I hope my post was formatted correctly, please let me know if It is not, and I will be sure to make changes in the future
     

    Attached Files:

  2. jcsd
  3. Feb 22, 2013 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi Unix! :smile:

    (try using the X2 button just above the Reply box :wink:)

    Yes that all seems ok so far …

    what is worrying you about that?​

    (btw, are you sure the diagram is correct? these questions usually have the point charge perpendicular to the rod)
     
  4. Feb 22, 2013 #3

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    The distance from y=a to any arbitrary y on the charged rod is a - y .

    Therefore, r = (a - y) .
     
  5. Feb 22, 2013 #4
    Thank you for your quick responses! :)

    Tiny-tim: All of the examples in my physics book did in fact consist of charges that were perpendicular to the rod. I hadn't tried a problem where the charge was on the same axis as the rod so I thought I would give it a shot and make sure I could reason it out if I saw it on an exam (I mainly posted up here to get confirmation on my thought process :) ).

    SammyS:
    I plugged in a few numbers into (a-y) and it makes sense now. By having (a-y), then the negative sign accounts for points that are below the axis such as (a-(-L/2)) correct?
     
  6. Feb 22, 2013 #5

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Yes.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Electric Field On A Point Charge Due To A Uniformly Charged Rod
Loading...