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Domains of validity of quasistatic and quasistationary field approximations

Thorsten Steinmetz (ABB Schweiz AG, Baden‐Dättwil, Switzerland)
Stefan Kurz (Tampere University of Technology, Tampere, Finland)
Markus Clemens (Bergische Universität Wuppertal, Wuppertal, Germany)



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.


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.


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.


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.



Steinmetz, T., Kurz, S. and Clemens, M. (2011), "Domains of validity of quasistatic and quasistationary field approximations", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 30 No. 4, pp. 1237-1247.



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