Problem 3.220

A current $I$ flows along a thin wire shaped as a regular polygon with $n$ sides which can be inscribed into a circle of radius $R$ . Find the magnetic induction at the centre of the polygon. Analyse the obtained expression at $n \rightarrow \infty$ .

B=n \mu_{0} I \tan (\pi / n) / 2 \pi R, \text { for } n \rightarrow \infty \quad B=\mu_{0} I / 2 R

Constant Magnetic Field, Magnetics