The Influence of Helmholtz Coil Geometry on the Magnitude and Homogeneity of the Magnetic Field

Creating installations capable of generating a stable and controllable homogeneous magnetic field is a complex and urgent technical task in the field of applied engineering. Controlling the magnetic field enables efficient manipulation of ferromagnetic micro- and nanoparticles, which opens up applications of homogeneous magnetic fields in magnetic separation, sensor calibration, and artificial compensation of the Earth's magnetic field. One of the new areas of application of such a homogeneous magnetic field is the magnetic separation of ferromagnetic micro- and nanoparticles. A Helmholtz coil is the most popular technology for creating and controlling a stable homogeneous magnetic field, consisting of two coaxial identical coils separated by a distance equal to their radius. Today, this technology is used in many areas of scientific research and technical applications. Geometrical configurations of the Helmholtz coil such as the shape, number of turns, and spacing between them, have a significant effect on both the magnitude of the magnetic field and its homogeneity. In this paper, theoretical calculations are performed comparing the effect of the geometry of round and square Helmholtz coils on the homogeneity and magnitude of the magnetic field. The calculations took into account the thickness of the coils and the arrangement of the turns. The results showed that the value of the homogeneity zone of the round coil is larger than that of the square coil, but the magnetic induction in this zone is larger for the square coil than for the round coil. When taking into account the thickness, the difference between the coils is smaller than without taking into account the thickness. In further studies, the obtained theoretical calculations of the distribution of the magnetic induction of the Helmholtz coil will be used to analyze the experimental data. Also, based on these calculations, a laboratory prototype for magnetic separation based on the Helmholtz coil will be developed.