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Finding E Field at Point from non uniform charge density

  1. Feb 22, 2015 #1
    1. Portion of z-axis for which |z| < 2 carries a non uniform charge density of 10|z| (nC/m). Using cylindrical coordinates, determine E in free space at P(0,0,4). Explicitly show your integration.


    2. Relevant equations
    E = (1/4πε0) ∫ dQ*aR/(R2)


    3. The attempt at a solution
    https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-xpf1/v/t34.0-12/11004892_945246908827650_417954135_n.jpg?oh=d538ef93ebc53d426c29d8a2f0116327&oe=54ECD699&__gda__=1424795396_496617364f01c6d9bac875a291ef70af
    I don't know what I'm doing wrong. the linear charge lies on the z axis and the point of interest lies on (0,0,4) so only the z unit vector applies right? As shown in the paper, the real answer is E = 34.20 az (V/m).
    I
     
  2. jcsd
  3. Feb 22, 2015 #2

    TSny

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    Welcome to PF!

    Everything looks good except for your expression for ##\vec{R}##. Try evaluating your expression for z = +2 and z = -2. Does it make sense?
     
  4. Feb 22, 2015 #3
    I would assume the R vector we can find as the difference in points between the source and destination. So our destination point is P(0,0,4), and our source charge point would have to be (0,0,|z|). Thus making our vector R = (4-|z|)az. Is this correct?
     
  5. Feb 22, 2015 #4

    TSny

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    No. Should R be the same for z = +2 and z = -2?
     
  6. Feb 22, 2015 #5
    Oh I see, it shouldn't. The absolute factor only applies to the charge density, the length of the position vector will still vary from top to bottom like always. So then just R = (4-z)?
     
  7. Feb 22, 2015 #6
    Never-mind, you were right. I got the answer. THANKS! :)
     
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