This paper presents a mathematical analysis of the magnetic field homogeneity for an Equilateral Triangular Helmholtz (ETH) coil. The magnetic field analysis is based on the Biot-Savart law in which a Taylor series approximation is performed to obtain the analytical distance that complies with the Helmholtz condition between the pair of coils. This is done to compare the magnetic field distributions of the ETH and the Circular Helmholtz (CH) coils for the parameters side length (2a, 3a) and radius (a) respectively. Furthermore, an approximate expression of the magnetic field homogeneity with regard to the side length parameter is obtained and finally a computational model of the ETH coil using COMSOL® is performed in order to validate the calculated and experimental results. The results show that the ETH coils have a lower magnetic field homogeneity than the CH coils for the described parameters, and the implementation of either one basically depends on the application specifications.
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