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Formulae for second‐ and third‐order electric field induced by uniform ELF magnetic field in eccentric two‐sphere conductor configuration
Author(s) -
Masutani Keigo,
Hamada Shoji,
Kobayashi Tetsuo
Publication year - 2011
Publication title -
electronics and communications in japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.131
H-Index - 13
eISSN - 1942-9541
pISSN - 1942-9533
DOI - 10.1002/ecj.10304
Subject(s) - multipole expansion , conductor , electric field , third order , mathematical analysis , electrical conductor , moment (physics) , field (mathematics) , mathematics , order (exchange) , perfect conductor , physics , magnetic field , method of moments (probability theory) , geometry , classical mechanics , quantum mechanics , pure mathematics , scattering , philosophy , statistics , theology , finance , estimator , economics
This paper describes analyses of the electric fields induced in two eccentrically arranged spherical conductors by a uniform ELF magnetic field, utilizing the equivalent multipolar‐moment method with re‐expansion (RE‐EMMM). Although an approximation formula has already been derived by Tarao for this situation, it is limited to a first‐order approximation. Here we mathematically derive a general form of the governing linear equations for unknown multipole and local coefficients. We also derive the first‐, second‐, and third‐order electric field formulae by manually solving the linear equations. We confirm that the accuracy of the first‐order formula is almost the same as that of Tarao's. The accuracies of the second‐ and third‐order formulae are confirmed to be more precise. © 2011 Wiley Periodicals, Inc. Electron Comm Jpn, 94(3): 20–32, 2011; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/ecj.10304