Determination of Coefficients of Capacitance of Regions Bounded by Collinear Slits and of Related Regions (Classic Reprint) - Couverture souple

Epstein, Bernard

Couverture souple

ISBN 10 : 1333571836 ISBN 13 : 9781333571832

Editeur : Forgotten Books, 2018

Synopsis

This book delves into the intricate world of electromagnetism, providing formulas and techniques to determine the capacitance of regions bounded by collinear slits. The author explores a broad class of domains possessing a specific symmetry property, demonstrating their conformal equivalence to 'slit -domains'. This equivalence simplifies the problem of conformal mapping to that of mapping simply-connected domains, rather than the more complex multiply-connected ones. The book's significance lies in its provision of practical methods for calculating capacitance coefficients, a crucial aspect in the design of electrostatic devices and systems.

A propos du livre

Présentation de l'éditeur

Introduction In the study of electrostatic field problems the principal objective usually is to determine the potentisil and its gradient (the field strength) throughout a given domain boimded by a system of conductors. Frequently, however, it is necessary only to determine certain constants of capacitance. In this paper vre consider the latter problem for a certain class of plane domains. Let nbe a domain consisting of the entire x-y plane with any finite number of slits along a single line. Several formulas for the coefficients of capacitance of such a domain are derived, two of which appear to be well suited for nu nerical computations. One of these formulas is based on the explicit representation of the potential as the ieal part of an analytic function I- J-- while the other formula has the feature of requiring a knowledge of the potential only on the line containing the boundary components of Dj it does not involve any derivatives of the potential, A convenient method for determining the field along the line containing the boundary components has [2] been giv nby the author in a previous paper, -S ince the coefficients of capacitance of a domain are invariant under conformal mapping, the formulas which are derived may be employed to compute the coefficients of any domain which can be conformally mapped upon a domain Dof the type described above. This procedure can be applied to a certain class of domains which are of practical interest. In these cases the mapping problem involves essentially only simply-connected domains rather than multiply-connected domains. One particular case of interest, the bi-filar shielded cable is considered in some detail, and as an illustration of the procedure, the coefficients of capacitance are evaluated numerically for one such domain.
(Typographical errors above are due to OCR software and don't occur in the book.)

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Détails de l'édition

• Éditeur: Forgotten Books
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 1333571836
• ISBN 13: 9781333571832
• Reliure: Broché
• Nombre de pages: 28
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