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Magnetic Field due to a current

  1. Jul 30, 2006 #1

    app

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    INTRODUCTION: I had been doing some problems on "Magnetic field due to a current." Now i have one in which one has to find the field at the centre of a regular n-sided polygon. I dont know why i'm not getting it.
    THE EXACT PROBLEM: "A regular polygon of n sides is formed by bending a wire of total length 2Πr which carries a current i.(a)Find the magnetic field at the centre of the polygon.(b)By letting n -> infinity, deduce the expression for the magnetic field at the centre of a circular current."
    WHAT MY BRAIN SUGGESTED: The first part is allright.The length of each side is (2Πr)/n. Now using B=(mew)i (cosθ-cosθ)/(4Πd), i got the magnetic field at the centre of the polygon as {(mew)i (n^2) sin(Π/n)tan(Π/n)}/2(Π^2)r. But i have no idea how to get part (b).
    WHAT I ALSO KNOW:The magnetic field at the centre of a circular current is (mew)i/2a, where a is the radius of the circle. How do we deduce this from the earlier expression?
    CONCLUSION:I really dont know how to deduce part (b).Please help. Thanks a lot.
     
  2. jcsd
  3. Jul 30, 2006 #2

    Andrew Mason

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    For a) express the two angles as a function of the number of sides, n.

    Then take the limit as [itex]n\rightarrow\infty[/itex]

    AM
     
    Last edited: Jul 30, 2006
  4. Jul 31, 2006 #3

    app

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    Thanks...

    THANKS: Thanks a lot, i got it now.I didn't remember to take the limits.:smile: :smile: :smile:
     
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