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Trying to get this

  1. Jul 18, 2011 #1
    Hi, I'm trying to understand point charges along a uniformly charged line with a charge per unit length. This is a screenshot of what i'm trying to understand. http://i.imgur.com/s1vX7.jpg

    I am not sure where the term r/R is coming from. I realise that the r term in sigma*dx/4pi*enot should change as you go down the x axis but I don't get where the factor r/R comes from. I feel like i'm missing something. This is an example page from the book "Electromagnetism" by John C. Slater and Nathaniel Frank.
  2. jcsd
  3. Jul 18, 2011 #2

    Doc Al

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    Staff: Mentor

    They are only considering the component of the field perpendicular to the line of charge (the parallel component will add to zero for an infinite line of charge). r/R is equivalent to the cosine of the angle.
  4. Jul 18, 2011 #3
    No, you are not trying to "understand point charges along a uniformly charged line"...you are trying to "understand the electric field intensity at point P which is at a distance r from a charge line".

    You see, you are trying to determine the influence of the entire line charge (which is discretized in a bunch of little dx's) on a given point P.

    If the x-axis is vertical and the y-axis is horizonatl and the charge line pretty much lies on the x-axis and the point P is at a coordinate (x,y)=(0,r)

    The field intensity at P due to a given dx (x not equal 0) will be along the line the joins that dx and the P point, and hence, it can be thought of having two components, one parallel to the x-axis and one parallel to the y-axis...since the charge line is infinite long, the point P "sees" the same thing above it (x>0) as below it (x<0) and hence all the x-components of the field at P cancel out and all the y-components add up.
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