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

Solution:

The polygon described in the problem is illustrated in the figure below, for . The magnetic field created by this structure is the superposition of fields from straight current carrying wires of length . Therefore, we will need to find the magnetic field due to a wire of finite length first.

The Biot-Savart law gives the magnetic field …