Interaction between two magnetic dipoles in a uniform magnetic field

A new formula for the interaction force between two magnetic dipoles in a uniform magnetic field is derived taking their mutual magnetic interaction into consideration and used to simulate their relative motion. Results show that when the angle β between the direction of external magnetic field and the centerline of two magnetic dipoles is 0 ° or 90 °, magnetic dipoles approach each other or move away from each other in a straight line, respectively. And the time required for them to contact each other from the initial position is related to the specific susceptibility and the diameter of magnetic particles, medium viscosity and magnetic field strength. When β is between 0 ° and 90 °, magnetic dipole pair performs approximate elliptical motion, and the motion trajectory is affected by the specific susceptibility, diameter and medium viscosity but not magnetic field strength. However, time required for magnetic dipoles to complete the same motion trajectory is shorter when adopting stronger magnetic field. Moreover, the subsequent motion trajectory of magnetic dipoles is ascertained once the initial position is set in a predetermined motion trajectory. Additionally, magnetic potential energy of magnetic dipole pairs is transformed into kinetic energy and friction energy during the motion.