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Capacitance of infinite cylinders

  • Thread starter Void123
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  • #1
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Homework Statement



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



Homework Equations





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?
 

Answers and Replies

  • #2
vela
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Are you sure the problem isn't asking you for the capacitance per unit length?
 
  • #3
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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.
 
  • #4
vela
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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.
 
  • #5
gabbagabbahey
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in order to make it infinite the two radii have to become infinitesimally small (0) correct?
No, in order two make the two cylinders infinitely long, you just make them longer.
 

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