Magnetic Field due to a current

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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 don't 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 don't know how to deduce part (b).Please help. Thanks a lot.

 

[Andrew Mason]

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 don't 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 don't know how to deduce part (b).Please help. Thanks a lot.

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

Then take the limit as $n\rightarrow\infty$

AM

 

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Thanks...

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