A comparative study of the magnetic field homogeneity for circular, square and equilateral triangular helmholtz coils

This paper presents a comparative study of the magnetic field homogeneity for circular, square and equilateral triangular Helmholtz coils that includes a power consumption analysis. The magnetic field distribution is obtained using the Biot-Savart law, furthermore a Taylor series approximation is performed in order to obtain simple mathematical expressions that relate the area, with uniform magnetic field, to the length of the different coils. For the analysis of magnetic field homogeneity and power consumption, two scenarios were considered: by taking the radius of the circular coil equal to half of the side length of the square and equilateral triangular coils and then equating the perimeters of all of them. Therefore, computational models are constructed and simulated using finite element software in order to validate the calculated results of the magnetic field distribution and the experimental tests of each geometry considering equal perimeters. The results show that the circular geometry has the highest magnetic field homogeneity compared to other Helmholtz coil geometries with the same perimeter.