Approximation of the magnetic field of a circular loop of wire.

Abstract

For a current-carrying, circular loop of wire, there is no known method of solving the Biot-Savart law for the exact magnetic field at all points in space. By using a many-sided, regular, polygonal loop to approximate a circular loop, it is possible to solve the Biot-Savart law for the polygon and find an approximate value of the magnetic field for a circular loop. This method is checked for validity against the exact solution for the axial field of a circular loop and two known approximate solutions. The results from the polygonal approximation are found to be within acceptable elTor limits.