Discrete-to-continuum limit of magnetic forces: Dependence on the distance between bodies
The paper revisits a classical problem of the interaction between two solid magnetic bodies brought in the contact, in the case when the remaining distance between the bodies may be counted in terms of spacings of the intrinsic lattices which account for the magnetic properties of the bodies. It is relevant to mention that the first classical results concerning magnetic forces acting between macroscopic bodies were published by Augustin Cauchy in 1828. In the present paper, the authors present a rigorous analysis of the problem. In addition to the previously known long-range and short-range forces of the interaction between the two bodies, they derive an extra force, which is contributed to by the microscopic interactions between atomistic dipoles forming the magnetic lattices in the two bodies. This additional force exponentially decays as a function of the distance between the bodies, measured in units of the lattice period.
scientific article; zbMATH DE number 5598871