Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 55

A thin conducting wire is bent into the shape of a regular polygon of N sides. A current I flows in the wire. Show that the magnetic flux density at the center is

where b is the radius of the circle circumscribing the polygon and a n. is a unit vector normal to the plane of the polygon. Show also that, as N becomes very large, this result reduces to that given in Eq. (6- 38) with z = 0.