The magnetisation of two ferromagnetic spheres placed randomly in a magnetic field

The main objective of this research is to study the uniform magnetic field both inside and outside of two randomly placed ideal ferromagnetic spheres. The expressions are given for the scalar magnetic potentials both inside and outside the spheres. In addition, the expressions for the magnetic field intensity outside and the magnetic flux density inside are also derived. The magnetic potential outside the spheres is obtained by the superposition of the potentials due to the two spheres and the potential corresponding to the external magnetic field, while the scalar magnetic potential inside each sphere is solved by imposing the exact boundary conditions known from the solution of the outside field. Finally, the numerical results with the given accuracy are generated from the expressions derived.