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Homework Help: Capacitance of infinite cylinders

  1. Mar 4, 2010 #1
    1. The problem statement, all variables and given/known data

    I have two coaxial infinite cylinders and I must find their capacitance, where [tex]r_{1} < r_{2}[/tex]



    2. Relevant equations



    3. The attempt at a solution

    I got an answer (for finite cylinders) that is inversely proportional to [tex]Ln (r_{1}/r_{2})[/tex].

    Assuming this answer is correct (if someone can check it), in order to make it infinite the two radii have to become infinitesimally small (0) correct? If I do this though, I get an indeterminate in the argument of log.

    Have I done this wrong or must I rewrite my expression in terms of some approximate expansion?
     
  2. jcsd
  3. Mar 4, 2010 #2

    vela

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    Re: Capacitance

    Are you sure the problem isn't asking you for the capacitance per unit length?
     
  4. Mar 4, 2010 #3
    Re: Capacitance

    I am sure. I don't see how significant that is either, since I would just divide my expression by [tex]l[/tex]. But, the road block at the moment is trying to infinitesimally minimize the radii so as to give me a finite solution.
     
  5. Mar 5, 2010 #4

    vela

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    Re: Capacitance

    It's significant because the reason you get an infinite answer is because [itex]l[/itex] is infinite. Typically, this type of question asks you for the capacitance per unit length, which is a finite number.
     
  6. Mar 5, 2010 #5

    gabbagabbahey

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    Re: Capacitance

    No, in order two make the two cylinders infinitely long, you just make them longer.
     
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