“…In §3, we focus attention to the three-dimensional case. An expression in terms of the elliptic integrals is given for the coefficients of P. Owing to its physical relevance, particular attention is paid to the eigenvalues of P. Indeed, when N = 3, the matrix P and its eigenvalues, known in the theory of ferromagnetism, respectively, as the demagnetization tensor and the demagnetizing factors, are one of the most important and well-studied quantities of ferromagnetism [20,21,23,28,29,33]. In fact, the following magnetostatic counterpart of the homogeneous ellipsoid problem holds: given a uniformly magnetized ellipsoid, the induced magnetic field is also uniform inside the ellipsoid.…”