A study is made of the behaviour of ellipsoidal bodies, with no free currents and charges, under uniform applied electrostatic and magnetostatic fields. The method is valid for all sorts of solid homogenous isotropic or anisotropic materials: dielectric, ferroelectric, diamagnetic, paramagnetic, ferromagnetic, conducting, superconducting... Expressions are given, in all cases, for the fields internal and external to the body, as well as the free energy and the torques experienced by it. Apart from the body's volume and the electromagnetic properties of the material, these expressions depend only on the depolarization tensor '''''n''''' determined by the two shape ratios of the ellipsoid. Explicit expressions are given for '''''n''''' —both in field points internal and external to the body— in terms of elementary functions except for the triaxial ellipsoid where they are Legendre’s elliptic functions. In the non-linear range the electric or magnetic polarization is an implicit function of the applied field and the anisotropy of the material, while the external field is an explicit function of the polarization. In the linear range both the polarization and the internal field are explicit functions of the constant internal value of n inside the body and the isotropic or anisotropic susceptibility tensor '''''χ''''', and the external field is an explicit function of the polarization and '''''n'''''. In the isotropic case the limit values χ = ∞ and χ = -1 (SI units) fully describe the behaviour of conductor and superconductor ellipsoids. A discussion is made of some common errors in the treatment of electromagnetic singularities and of the behaviour of bodies of infinite extension and ellipsoidal cavities.
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==Sobre el autor / los autores====El libro en Véase la editorial==* biografía del [[ Electrostatics and Magnetostatics of Polarized Ellipsoidal Bodies: The Depolarization Tensor MethodEditor ECyT-ar]] en Free Scientific Information.