Electromagnetic body force calculation based on virtual air gap

Up to this date, the conventional electromagnetic force calculation methods such as Maxwell stress, virtual work, Kelvin's formula, equivalent magnetic charge, and equivalent magnetizing current produce results where the surface component takes up a major portion of the total force, with the portion of the body force being very small or even none. As the formulation of the above mentioned methods starts from the concept of body or volume force, there has been controversy over the true concept of electromagnetic force identity. In this paper, it is shown that electromagnetic body force, which is also called volume force, can be calculated using virtual air-gap scheme that is derived from the generalized equivalent source methods. For the body force calculation, the application of virtual air gap is extended to calculate the force of each finite element as if an element is an independent body surrounded by virtual air gap. The force calculation methods adopted in this paper include Maxwell stress, magnetic charge, and magnetizing current. The examination of the calculated force distribution shows that the force can be expressed only as body force distribution. The total force calculated by the volume integration of the body force on the magnetized body agrees well with the total force calculated by conventional approaches.