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Homework Help: Electric field around a wire

  1. Sep 14, 2010 #1

    Uku

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    1. The problem statement, all variables and given/known data
    I know that around an infinitely long wire with even charge distribution the electric field is expressed as:

    [tex]E=\frac{1}{2\pi\epsilon_{0}}\frac{\lambda}{r}[/tex] (1)

    Where [tex]\lambda[/tex] can be expressed as [tex]\lambda=\frac{dq}{dl}[/tex]

    Right, but I want to know where I get this formula from, I mean the E field.

    3. The attempt at a solution

    So I know that in general:

    [tex]E=\frac{1}{4\pi\epsilon_{0}}\int\frac{\rho}{r^{2}}\widehat{r}dV[/tex]

    In my case I don't have volume, I have a thread. I can also forget about the unit vector, since the field is radially pointed outward. The charge is evenly distributed so I can write:

    [tex]E=\frac{1}{4\pi\epsilon_{0}}\lambda\int\frac{1}{r^{2}}dL[/tex]

    Okay, but now... I can integrate the expression from minus infinity to infinity, but how do I get to that formula (1)
     
  2. jcsd
  3. Sep 14, 2010 #2
    You can find a number of sites that work this out for you. A google search, or even a search here at PF will give you many looks at this problem. Here is one, for example.

    http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elelin.html
     
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