Analysis of the Magnetic Field Homogeneity of Two Different Geometric Configurations of the Helmholtz Coils by Simulation

In order to make a more direct and profound comparison of the magnetic fields generated in the central region of the circular Helmholtz coils and the square Helmholtz coils, simulation was conducted regarding the magnetic fields generated in these two situations respectively. The basic theory of magnetic fields generated by square and circular coils along their longitudinal axes is given in Sect. 1 of this chapter. Subsequently, the results of simulation adopting the finite element method (FEM) are compared with the theoretical value, which shows that the simulated result is well consistent with the theoretical data. A mean error of as low as 0.78 % in the range of |y| < 20 mm along the longitudinal axis of the circular Helmholtz coil is obtained while the corresponding result of square Helmholtz coil is merely under 1.03 %. Finally, it is concluded that the square Helmholtz coils can generate a larger uniform magnetic field.