Abstract Here we report definite results on the mathematical metabolization of Maxwell’s equations in one of the building units, most commonly met in practice. We investigate the static/quasi-static case of a linear, homogeneous and isotropic magnetic and dielectric cylinder of intrinsic susceptibility, xint, subjected to an external potential/field, Uext/Fext, of any form on the plane normal to the directional axis, produced by a primary source that resides at the outside space. Specifically, here we address analytically a magnetic and dielectric cylinder of seemingly infinite length along the z axis, subjected to an external potential/field, Uext/Fext, that does not vary along the z axis, as well. An expansion-based mathematical approach is employed, enabling direct access to universal expressions of the response of the magnetic and dielectric cylinder, i.e., the internal potential/field, Uint/Fint, produced by the secondary source of bound charges that is originally induced by the external potential/field, Uext/Fext. Accordingly, ready-to-use expressions of the total potential/field, U=Uext+Uint/F=Fext+Fint, and of the polarization, P, of the magnetic and dielectric cylinder are directly obtained. These universal expressions are applicable to every distinct problem of different Uext/Fext, without the need to tackle it mathematically, every time, from the beginning. Interestingly, the depolarization factor, N, and extrinsic susceptibility, xext, are degenerate, obtaining a constant value irrespectively of the mode of the external potential/field, Uext/Fext. These universal expressions between Uint-Uext, U-Uext, Fint-Fext, F-Fint and P-Fext provide effective means to understand, design and realize cylindrical building units with specific characteristics.
Moraitis et al. (Tue,) studied this question.