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Domains of validity of quasistatic and quasistationary field approximations

Domains of validity of quasistatic and quasistationary field approximations Purpose – The paper aims at proposing a uniform and demonstrative description of two well‐known and widely used approximations of slowly time‐varying electromagnetic fields, i.e. the electro‐quasistatic and the magneto‐quasistationary approximation to Maxwell's equations. Design/methodology/approach – Under both approximations, the orders of magnitude of the relative errors of the dominant fields are analyzed by using three characteristic time constants. These time constants are determined by considering the material properties, the characteristic length scale and the characteristic time scale. Findings – Limiting curves which show the domains of applicability of the two approximations are retrieved from the estimation of their relative errors. The relation between the domains of validity of the electro‐quasistatic and magneto‐quasistationary approximations was found and depicted in a combined diagram. Research limitations/implications – The study is restricted to slowly time‐varying electromagnetic fields. Heuristic and local estimates based on local material properties were used for the analysis. Rigorous estimations of the errors (e.g. also considering the field problem's topology) of the magneto‐quasistationary approximation are already known in the literature. A rigorous estimation of the error of the electro‐quasistatic approximation is, therefore, suggested for future research. Originality/value – The combined diagram showing the domains of validity of both approximations considered here in a uniform way is novel. It gives rise to an intuitive and easily accessible understanding of their applicability. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

Domains of validity of quasistatic and quasistationary field approximations

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References (7)

Publisher
Emerald Publishing
Copyright
Copyright © 2011 Emerald Group Publishing Limited. All rights reserved.
ISSN
0332-1649
DOI
10.1108/03321641111133154
Publisher site
See Article on Publisher Site

Abstract

Purpose – The paper aims at proposing a uniform and demonstrative description of two well‐known and widely used approximations of slowly time‐varying electromagnetic fields, i.e. the electro‐quasistatic and the magneto‐quasistationary approximation to Maxwell's equations. Design/methodology/approach – Under both approximations, the orders of magnitude of the relative errors of the dominant fields are analyzed by using three characteristic time constants. These time constants are determined by considering the material properties, the characteristic length scale and the characteristic time scale. Findings – Limiting curves which show the domains of applicability of the two approximations are retrieved from the estimation of their relative errors. The relation between the domains of validity of the electro‐quasistatic and magneto‐quasistationary approximations was found and depicted in a combined diagram. Research limitations/implications – The study is restricted to slowly time‐varying electromagnetic fields. Heuristic and local estimates based on local material properties were used for the analysis. Rigorous estimations of the errors (e.g. also considering the field problem's topology) of the magneto‐quasistationary approximation are already known in the literature. A rigorous estimation of the error of the electro‐quasistatic approximation is, therefore, suggested for future research. Originality/value – The combined diagram showing the domains of validity of both approximations considered here in a uniform way is novel. It gives rise to an intuitive and easily accessible understanding of their applicability.

Journal

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering – Emerald Publishing

Published: Jul 12, 2011

Keywords: Electromagnetic fields; High voltage; Electronic engineering

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