We develop a general multilayer dielectric sphere model in the toroidal coordinates and give the analytical electrostatic solution when it is excited by a uniform field. The special case of the electrostatic result of an incomplete conducting sphere can be obtained simply. It is in agreement with the published result. We have also found that the coating dielectric film on the conducting sphere surface can remarkably reduce distortion on the external homogeneous field when the normalized dielectric constant is from 1–5.
The uniaxial bianisotropic-ferrite medium is a generalization of the well-studied magnetically biased ferrite and uniaxial material. It can be manufactured either by immersing randomly oriented short helices and Ω-shaped particles in a magnetically biased ferrite, or by arranging short conductive helices in a magnetized ferrite in a certain manner. It has potential applications in microwave technology, antenna design, and antireflection shielding. In the present consideration, based on the concept of characteristic waves and the method of angular spectral expansion, field representations in uniaxial bianisotropic-ferrite medium are developed. The analysis reveals the solutions of source-free Maxwell’s equations for uniaxial bianisotropic-ferrite medium can be represented in sum-integral forms of the circular cylindrical vector wave functions. The addition theorem of vector wave functions for uniaxial bianisotropic-ferrite medium can be straightforwardly derived from that of vector wave functions for isotropic medium. An application of the proposed theory in scattering is presented to show how to use these formulations in a practical way.
An analysis of the electromagnetic response of a cylindrical conductor of infinite length which has a uniform coating of bi-isotropic medium is rigorously formulated by constructing cylindrical vector wavefunctions. Subject to the radius and thickness of the coating, an anisotropic impedance boundary condition in the spectral domain is developed which holds in a general context.
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