Magnetization of Linear Arrays of Two Ferromagnetic Spheres in a Uniform Magnetic Field

The main objective of this paper is to explore the exact analytical solutions of the magnetization of linear arrays of two ideal ferromagnetic spheres in the presence of external magnetic fields. First, the total scalar magnetic potential outside the spheres, related to the magnetic field intensity, which satisfies the Laplace equation, is obtained by the superposition of the potentials due to all spheres and the potential corresponding to the external field. The translational addition theorems for scalar Laplacian functions in spherical coordinates are then used to translate the two coordinates systems into one coordinates system. Then, the exact boundary conditions were used to solve the magnetic field quantities outside the system. On the other hand, the scalar magnetic potential inside each sphere, related to the magnetic flux density, also satisfies the Laplace equation, which is solved by imposing the boundary conditions known from the solution of the outside quantities. Finally, the expressions derived are used to generate numerical results of controllable accuracy for various field quantities.