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A note on differential equations for Hertz potentials in inhomogeneous media

✍ Scribed by S.N. Samaddar

Publisher
Elsevier Science
Year
1963
Tongue
English
Weight
242 KB
Volume
276
Category
Article
ISSN
0016-0032

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✦ Synopsis

Differential equations for Hertz potentials in hlhomogeneous media in three coordinate systems (namely, rectangular, circular cylindrical, and spherical) have been derived. Suitable assumptions have been made so that a typical differential equation for a Hertz potential, Β’, reduces to a simple form, (V a -t-K% +f)Β’ = 0, where K 2 = ~0~0~o, and f is a known function of a single coordinate with respect to which the relative dielectric constant of the medium, e, varies. The results are summarized in a table which also enables one to formulate various problems of wave propagation in inhomogeneous media, including electromagnetic sources.

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Fundamental solutions to Helmholtz's equ
Fundamental solutions to Helmholtz's equation for inhomogeneous media by a first-order differential equation system
✍ George D. Manolis; Richard P. Shaw πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 973 KB

Helraholtz's equation with a variable wavenumber is solved for a point force through use of a first-order differential equation system approach. Since the system matrix in this formulation is non-constant, an eigensolution is no longer valid and recourse has to be made to approximate techniques such