Abstract
The current research involves an analytical method of electromagnetic wave scattering by an impenetrable spherical object, which is immerged in an otherwise lossless environment. The highly conducting body is excited by an arbitrarily orientated time-harmonic magnetic dipole that is located at a reasonable remote distance from the sphere and operates at low frequencies for the physical situation under consideration, wherein the wavelength is much bigger than the size of the object. Upon this assumption, the scattering problem is formulated according to expansions of the implicated magnetic and electric fields in terms of positive integer powers of the wave number of the medium, which is linearly associated to the implied frequency. The static Rayleigh zeroth-order case and the initial three dynamic terms provide an excellent approximation for the obtained solution, while terms of higher orders are of minor significance and are neglected, since we work at the low-frequency regime. To this end, Maxwell’s equations reduce to a finite set of interrelated elliptic partial differential equations, each one accompanied by the perfectly electrically conducting boundary conditions on the metal sphere and the necessary limiting behavior as we move towards theoretical infinity, which is in practice very far from the observation domain. The presented analytical technique is based on the introduction of a suitable spherical coordinated system and yields compact fashioned three-dimensional solutions for the scattered components in view of infinite series expansions of spherical harmonic modes. In order to secure the validity and demonstrate the efficiency of this analytical approach, we invoke an example of reducing already known results from the literature to our complete isotropic case.
Highlights
Real-life physical applications of practical interest in science and engineering are promptly associated with the fundamental principles of advanced electromagnetism [1]and the related information concerning analytical, semi-analytical and numerical techniques towards the solution of important problems
Demonstration of the utility of such solutions, given in an analytical compact fashion, to the construction of a fast and accurate inverse scheme was accomplished in [13], wherein the low-frequency on-site identification of a highly conductive body buried in Earth from a model ellipsoid was presented. In view of this aspect, cases that involve more complicated geometries for the metallic bodies have been introduced; one can refer, for instance, to [14], in which the authors study the low-frequency interaction with the conductive environment of a ring torus, which scatters off incident waves that are produced by a magnetic dipole source
In order to comply with the spherical geometry of the solid body, we introduce the spherical coordinate system (r, θ, φ) in view of the radial r ∈ [0, +∞), the polar θ ∈ [0, π ] and the azimuthal φ ∈ [0, 2π )
Summary
Real-life physical applications of practical interest in science and engineering are promptly associated with the fundamental principles of advanced electromagnetism [1]. A demonstration of the utility of such solutions, given in an analytical compact fashion, to the construction of a fast and accurate inverse scheme was accomplished in [13], wherein the low-frequency on-site identification of a highly conductive body buried in Earth from a model ellipsoid was presented In view of this aspect, cases that involve more complicated geometries for the metallic bodies have been introduced; one can refer, for instance, to [14], in which the authors study the low-frequency interaction with the conductive environment of a ring torus, which scatters off incident waves that are produced by a magnetic dipole source. The present work is focused on the application of low-frequency diffusive scattering theory in handling the problem of retrieving an impenetrable spherical metallic body in a lossless, i.e., perfect dielectric medium Such investigation, even concerning highly symmetric geometry, sets the basis of studying the problem for complete spatial isotropy and deepens the understanding of more complicated anisotropic geometries that are introduced in previous models. After, we discuss our results and conclude, while we end this article with an updated reference list
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