Mathematical model to investigate the behaviour of the systems of ferromagnetic particles under the magnetic fields

In this work, a comprehensive mathematical analysis is presented to explore the behaviour of multi-sphere system of ferromagnetic particles in a homogeneous medium under the uniform magnetic fields. We assume that the geometrical shapes of the particles are spheres. The magnetic field intensity due to all particles and the external field is obtained by the superposition of the magnetic potentials in the system. For that, the translational addition theorems were used to express the functions in the coordinates system attached to a specific particle. Further, by imposing the exact boundary conditions, the field quantities outside the particles are solved. Then, these known quantities and the boundary conditions are used to obtain the field quantities inside the particles in the system. Finally, from the derived expressions, we generate benchmark accurate numerical results for various values of the characteristic parameters such as the radii of the particles and the relative distance between the particles, at the points outside as well as inside of a system of three ferromagnetic particles in the presence of an uniform magnetic field. The generated numerical results are analysed qualitatively and quantitatively, and are validated by using theoretical concepts related to the magnetic field on ferromagnetic spheres with some specific geometric configurations involved.