The developments in the analytical expressions of the interaction force between cuboidal permanent magnets

Analytical models, of the surface charge or the current sheet type, are considered very suitable to obtain the magnetic field components of permanent magnets in free space. These methods provide fully 3D analytical field expressions, in principle without a need for meshing or numerical integration, which yields extremely accurate and time inexpensive results, especially compared to numerical methods. Although their basic principles were already discussed in the first half of the twentieth century, fully analytical field and interaction expressions were only proposed during the last decades. A number of authors have successfully obtained these fully analytical calculations of the interaction force, stiffness and torque between permanent magnets. This paper focuses on the achievements in the analytical force calculation between cuboidal permanent magnets in free space.