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An Analysis of the Vector Kirchhoff Equations and the Associated Boundary‐Line Charge
Author(s) -
Sancer Maurice I.
Publication year - 1968
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1002/rds196832141
Subject(s) - mathematical analysis , boundary value problem , boundary (topology) , kirchhoff integral theorem , mathematics , line (geometry) , infinity , charge (physics) , maxwell's equations , physics , function (biology) , integral equation , geometry , quantum mechanics , summation equation , evolutionary biology , biology
The vector Kirchhoff equations are derived by the systematic use of the free‐space dyadic Green's function and the appropriate Green's theorem. As is generally the case, the derivation is valid only if the surfaces over which the integrations are to be performed are closed surfaces or infinite surfaces that can be closed at infinity. The approximations used in conjunction with Kirchhoff's equations can lead to integrations over portions of the closed surfaces and these portions are open surfaces. When the approximations are discontinuous and the resulting integrations are over open surfaces, the Kirchhoff equations derived in this paper intrinsically include the boundary‐line charge contributions. It is not necessary to addend integrals to equations resulting from a mathematical analysis of Maxwell's equations in order to include the boundary‐line charge contributions.