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Limit Problem - Electric field strength of an infinite line of charge

  1. Feb 4, 2010 #1

    JJBladester

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    Limit Problem --- Electric field strength of an infinite line of charge

    1. The problem statement, all variables and given/known data

    What is the limit of the following equation?

    2. Relevant equations

    [tex]\stackrel{lim}{L\rightarrow\infty} \frac{K|Q|}{r\sqrt{r^{2}+(L/2)^{2}}}[/tex]

    3. The attempt at a solution

    The book gives an answer of [tex]\frac{K|Q|}{rL/2}[/tex] but it doesn't explain the intermediate steps.

    K is a constant, Q represents charge, L represents length, and r represents distance from a wire to a point in space. The whole exercise is to see what happens to the electric field strength of the wire if its length is allowed to grow infinitely.
     
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  3. Feb 4, 2010 #2

    Dick

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    Re: Limit Problem --- Electric field strength of an infinite line of charge

    Factor the L^2 out of the expression in the square root. So sqrt(r^2+(L/2)^2)=sqrt(L^2(r^2/L^2+1/4)=sqrt(L^2)*sqrt((r/L)^2+1/4)=L*sqrt((r/L)^2+1/4). Now as L->infinity, r/L goes to zero.
     
  4. Feb 5, 2010 #3

    JJBladester

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    Re: Limit Problem --- Electric field strength of an infinite line of charge

    Dick,

    Thanks for your response. The first sentence you made helped me get through it!

    Factor the L^2 out of the expression in the square root... I guess the more problems I do, the more my math intuition will increase. On that note, I found a site www.betterexplained.com that has really helped me conceptualize things like "what is a limit" without a cheesy explanation like "the area under the curve". Check it out :)
     
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