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Need help with Proper integral of a uniformly charged rod

  1. Sep 13, 2009 #1
    1. The problem statement, all variables and given/known data

    A uniformly charged rod is places along the x-axis from x=0 to x= L. carefully set up, but do not solve the proper integral to determine the x component of the electric field at the point (L,a)

    2. Relevant equations
    E=u[tex]
    \int \frac{dq}{(r^2)}
    [/tex]

    for a line dq=λdl



    3. The attempt at a solution
    i know for a line dq=λdl
    i think its something along the lines of
    Ey=Kλy=[tex]
    \int \frac{dx}{(x^2y^2)^(3/2)}
    [/tex] from 0 to L

    I have no idea if this is right. I am using my notes to guide me.
     
  2. jcsd
  3. Sep 13, 2009 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Coulomb's law for a linear charge distribution is:

    [tex]\textbf{E}(\textbf{r})=\frac{1}{4\pi\epsilon_0}\int \lambda(\textbf{r}')\frac{\textbf{r}-\textbf{r}'}{|\textbf{r}-\textbf{r}'|^3}dl'[/tex]

    Where [itex]dl'[/itex] is an infinitesimal length of the source, located at [itex]\textbf{r}'[/itex], and the integration is over the entire line of charge.

    Use [itex]\textbf{r}=x\mathbf{\hat{x}}+y\mathbf{\hat{y}}+z\mathbf{\hat{z}}[/itex] and [itex]\textbf{r}'=x'\mathbf{\hat{x}}+y'\mathbf{\hat{y}}+z'\mathbf{\hat{z}}[/itex] to find the x-component.
     
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