Mutual Inductance and Interaction Calculation Between Conductor or Coil of Rectangular Cross Section and Parallelepiped Permanent Magnet

Modeling and computing of mutual inductance between solid conductors or coils of rectangular cross section carrying uniform current and parallelepiped magnets of rigid polarization have been made. For this purpose, the integral approach using a quasi-static Green's functions is used. The inductance is calculated between the total volume of a conductor and the equivalent current surfaces densities described by the Amperian model of permanent magnets. The analytical results are obtained after five integrations. It is to be noted that the formulas developed in this paper are more general that the ones established in the literature and can be used for optimization purposes. In addition, this paper is carried out without using any simplifying assumptions. Consequently, these expressions are accurate whatever the magnet dimensions are. This analytical formulation compared with finite element method one is suitable for the design of unconventional magnetic couplings, magnetically planar actuator, electric machines, wigglers, and so on.