Prob. $5(10$ pts$)$ 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

$B=$hat$(z)\frac{{}_{0}NI}{2b}tan(\frac{}{N})$

where $b$ is the radius of the circle circumscribing the polygon and hat$(z)$ is the unit vector normal to the polygon.