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Electric field of a ring

  1. May 27, 2009 #1
    This is about the electric field of a ring with radius r, at a distance z from center, along the axis of the ring. The ring carries a uniform line charge [tex]\lambda[/tex]. We always say that the radial component of the field cancels out due to symmetry. Can somebody tell how to prove it mathematically (using cylindrical coordinate system only)?

    [tex]dE_{rad}=-\frac{1}{4\pi\epsilon_0}\frac{r\lambda d\theta}{(r^2+z^2)}\hat{\textbf{r}}[/tex]
    [tex]E_{rad}=-\frac{1}{4\pi\epsilon_0}\frac{r\lambda}{(r^2+z^2)}\int_0^{2\pi} \hat{\textbf{r}} d\theta[/tex]

    ???
     
  2. jcsd
  3. May 27, 2009 #2

    Born2bwire

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    First thing you need to do is convert the directional vector that is local to the current element to a directional vector at the point of observation.

    So the electric field element points in the r-hat direction, convert that to cylindrical coordinates and then also provide the appropriate translation since you will be observing it at a point offset from the origin of the coordinate system of the electric field element.
     
  4. Nov 5, 2011 #3
    I don't get your answer
     
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