Abstract:

The purpose of this article is to provide, from the perspective of deformable solid mechanics, a correct justification for the expressions of all forces acting on the surface of a ferromagnetic material in a magnetic field, initiated only by this field. It is shown that the moment of force applied to any closed body surface S, corresponding to the asymmetric part T_{\text{A}} of the stress tensor T (denoted as the force p_{\text{A}}), balances the mass magnetic moment L_{\text{mag}} acting in the volume V bounded by the surface S. The emergence of the asymmetric part T_{\text{A}} of the stress tensor arises as a consequence of a special case within the moment theory of elasticity, the use of which is necessary for accurately describing the behavior of a ferromagnetic material in a magnetic field. The force p_{\text{A}} acts in a plane tangential to the surface S at any point, while, in addition to this force, the normal force p_n also acts on the body surface. It is shown in the article that the latter force arises as a result of a jump in the normal component of the magnetic field strength appearing at the body surface, and its expression is defined by the mass's (ponderomotive) magnetic forces F_{\text{mag}}. Usually, this force is introduced based on the Maxwell stress tensor, which is used in the classical electromagnetism to represent the interaction between electromagnetic forces and mechanical momentum. However, as we believe and justify this in the article, such an approach is unacceptable in deformable solid mechanics.

Key words: magnetic field, deformable solid mechanics, tangential surface force, normal surface force