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Stuck on (proving) a linear charge problem

  1. Sep 29, 2014 #1
    1. The problem statement, all variables and given/known data

    Question:

    FmUcWz3.png

    ____________________________________________________________________________________

    And the answer in the solution manual:
    cbl0WP6.png


    2. Relevant equations
    Trig sub? [tex]a^2/x^2 = tan(θ) [/tex]
    I'm thinking x>>a would affect this majorly and I'm not seeing how.

    3. The attempt at a solution
    I understand the concept behind this (I think), but part c is killing me right now. I have no idea how the inverse square root turns into the final equation. Maybe I should have posted this in Calculus, but I have no recollection of learning this in calc I/II, nor physics I/II so I didn't know where to post.

    The [tex]a^2/x^2[/tex] looks eerily similar to a trig sub problem, but I don't see how that would work because there's no integral.

    For [tex]E_x,[/tex] I was able to set the limit of a to 0 to get the point charge equation. The solution manual didn't do it this way but it worked for me to get the point charge equation.

    BTW I already have a) and b), which were pretty straightforward.
    Could someone point me in the right direction please? Thank you!
     
  2. jcsd
  3. Sep 29, 2014 #2

    tms

    User Avatar

    You should double-check that with the definition of the tangent.

    Assuming you have the first two parts, you might want to take a look at the Taylor expansion of those answers.
     
  4. Sep 29, 2014 #3

    vanhees71

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    Science Advisor
    2016 Award

    How do you come to the conclusion that your equation is relevant for the problem? You should rather think about the question, how to calculate the force between two point charges and then how you can generalize this to many point charges and finally to a continuous charge distribution!
     
  5. Sep 29, 2014 #4
    Ah, okay. The format change to (1+x)^(n) is making more sense now... I'm very rusty on infinite series so I'll have to take some time to review. From a brief look at my calc book it looks like it matches the binomial series. Will spend more time to see if it is right. Thanks!

    They just looked similar, like [tex]y^2/x^2[/tex]
    No other reason.
    I actually did use that for part a, solving for [tex]E_x[/tex], but I've already solved parts a and b :) Sorry if I wasn't clear.
     
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