A new model of a micropolar continuum and some electromagnetic analogies

Abstract

A new model of micropolar continuum composed of two-spin particles is considered. In fact, this continuum represents a two-component continuum. The first component possesses the translational and rotational degrees of freedom, whereas the second component has only the rotational degrees of freedom. The main characteristic feature of the suggested model is that both the components are not infinitesimal rigid bodies. They are the body-points of a general type, which differ from infinitesimal rigid bodies by additional inertia parameters. A continuum, composed of such particles, has some additional properties compared with a conventional material. We suggest to use the continuum of two-spin particles as a mechanical model (or, in other words, a mechanical analogy) of the electromagnetic field in matter. This model does not pretend to be an explanation of the physical nature of electromagnetic phenomena. The interpretations of the electric charge, the electric field vector, the magnetic induction vector, and other physical quantities, which are given in accordance with the suggested model, are no more than the mechanical analogies. We show that the mathematical description of our model contains two special cases. Under one simplifying assumption, the suggested equations are reduced to the equations similar to Maxwell’s equations. Under another simplifying assumption, an analogue of the Lorentz force is obtained. We believe that in some cases the exact equations describing our mechanical model can be of interest for applications in electrodynamics.