Coulombian Model for 3D Analytical Calculation of the Torque Exerted on Cuboidal Permanent Magnets with Arbitrary Oriented Polarizations

This paper proposes improved analytical expressions of the torque on cuboidal permanent magnets. Expressions are valid for any relative magnet position and for any polarization direction. The analytical calculation is made by replacing polarizations by distributions of magnetic charges on the magnet poles (coulombian approach). The torque exerted on the second magnet is calculated by Lorentz force formulas for any arbitrary position. The three components of the torque are written with functions based on logarithm and arc-tangent. Results have been verified and validated by comparison with finiteelement calculation. Further, the torque can be obtained with respect to any reference point. Although these equations seem rather complicated, they enable an extremely fast and accurate calculation of the torque exerted between two permanent magnets.