TWO FERROMAGNETIC SPHERES IN HOMOGENEOUS MAGNETIC FIELD

• Main Author: Y. A. Krasnitsky
• Format: Article
• Language: Russian
• Published: Moscow State Technical University of Civil Aviation 2018-04-01
• Series: Naučnyj Vestnik MGTU GA
• Subjects: bispherical coordinates; the solution of laplace's equation; magnetic field between spheres
• Online Access: https://avia.mstuca.ru/jour/article/view/1231
• ISSN: 2079-0619; 2542-0119

The problem of two spherical conductors is studied quite in detail with bispherical coordinates usage and has numerous appendices in an electrostatics. The boundary-value problem about two ferromagnetic spheres enclosed on homogeneous and infinite environment in which the lack of spheres exists like homogeneous magnetic field is considered. The solution of Laplace's equation in the bispherical system of coordinates allows us to find the potential and field distribution in all spaces, including area between spheres. The boundary conditions in potential continuity and in ordinary density constituent of spheres surfaces induction flux are used. It is supposed that spheres are identical, and magnetic permeability of their material is expressed in  >> 0. The problem about falling of electromagnetic plane wave on the system of two spheres, which possesses electrically small sizes, can be considered as quasistationary. The scalar potentials received as a result of Laplace's equation solution are represented by the series containing Legendre polynomials. The concept of two spheres system effective permeability is introduced. It is equal to the advantage in magnitude of magnetic induction flux vector through a certain system’s section arising due to its magnetic properties. Necessary ratios for the effective permeability referred to the central system’s section are obtained. Particularly, the results can be used during the analysis of ferroxcube core clearance, which influences on the magnetic antenna properties.