Simulation of the magnetic field generated by square shape Helmholtz coils

Earth's magnetic field is used to determine and control the attitude of small satellites such as CubeSats with Low Earth Orbit (LEO). During the development of satellites it is necessary to calibrate the magnetic field sensors because a magnetic dipole could be created once the satellite is assembled. This dipole can affect the measurements of the sensors and thus, the satellite attitude. By using simulation and experimental measurement, we study the magnetic field generated by a Helmholtz square shape coil with the aim of understanding how to calibrate magnetic field sensors like those used in CubeSat. This paper describes the procedure to determine the magnitude and the direction of the magnetic field at any point around a set of conductors forming a Helmholtz square shape coil utilizing the Biot-Savart law. The results show simulation and experimental measurements of the magnetic field using the volume sample of a 10 cm cube with the magnetic field up to 200 µT. The simulation agrees with the experimental measurements with maximum error of 6%. In addition, the best distance between the coils is a half the length of one square coil side. The results also show the comparisons of the magnetic field generated by the Helmholtz square shape coil and the traditional circular coil enhancing knowledge about both configurations. The traditional coil achieved a larger magnetic field magnitude than the Helmholtz square shape coil. However, the Helmholtz square shape coil generated the required magnitude and so the decision to choose this coil must consider both the sample volume under study and the ease of manufacturing them. These results will facilitate the design of calibration tests for magnetic field sensors in LEO satellites as the Libertad 2 CubeSat, currently under development.