Magnetic field B...?

Question

(a) A wire in the form of a regular polygon of n sides is just enclosed by a circle of radius a. If the current in this wire is i, show that the magnetic field B at the center of the circle is given in magnitude by

B=(μni/2πa)*tan(π/n)

(b) Show that as n--->∞, this result approaches that of a circular lopp.

If you can help, thank you!

Answer 1

Part b is fairly easy, tan x ~= x when x << 1 (much less than), and π/n as n -> ∞ is very small (approaches zero).

B=(μni/2πa)*tan(π/n)~=(μni/2πa)*(π/n)

the n's and π's cancel out

B=(μi/2a) which is the magnetic field due to a single circular loop.