All Problems

Constant Magnetic Field, Magnetics

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 \(n \rightarrow \infty\).

Reveal Answer
B=nμ0Itan⁡(π/n)/2πR, for n→∞B=μ0I/2RB=n \mu_{0} I \tan (\pi / n) / 2 \pi R, \text { for } n \rightarrow \infty \quad B=\mu_{0} I / 2 R
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