Biot-Savart law on a polygon

A current I flows along a thin wire, shaped as a regular polygon with N sides, which can be inscribed intro a circle of radius R. Find the magnetic field at the center of the polygon. What happens if N is made very large?


The polygon described in the problem is illustrated in the figure below, for N=8. The magnetic field created by this structure is the superposition of fields from N straight current carrying wires of length 2 R \sin (\pi/N). Therefore, we will need to find the magnetic field due to a wire of finite length first.

Rendered by

The Biot-Savart law gives the magnetic field …

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