The response of a magnetic and dielectric cylinder subjected to an external magnetic and electric field of any form on the plane normal to the directional axis

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.