Analytic and Experimental Analysis of Magnetic Force Equations

The design of magnetic devices requires a precise estimation of magnetic forces. In previous works, we presented a general approach to estimate these forces based upon thermodynamically closed systems, resulting in four different forms of the force equations. This paper presents a complete theoretical model analysis tested by experiments, using arrangements of permanent magnets and a device for measuring the force induced on a soft magnetic material according to its position with respect to the permanent magnets. The results of analytical formulation, Finite Element Method numerical analysis, and experiments are compared with each other. This enabled the identification of two forms of the force equations that most precisely describe the magnetic forces. A follow-up experiment is then proposed and executed, identifying the correct form of the magnetic force equations. The resulting equation can be used to analytically estimate the magnetic force in many practical problems.