On quasi-static models hidden in Maxwell's equations

In this paper we introduce the electromagnetic quasi-static models in a simple but meaningful way, relying on the dimensional analysis of Maxwell's equations. This analysis puts in evidence the three characteristic times of an electromagnetic phenomenon. It allows to define the range of validity of well-known models, such as the eddy-current (MQS) or the electroquasistatic (EQS) ones, and thus their pertinence to describe a given phenomenon. The role of the so-called “small parameters” of a model is explained in detail for two classical examples, namely a capacitor and a solenoid. We show how the MQS and EQS models result from having replaced fields by their first order truncations of Taylor expansions with respect to these small parameters. We finally investigate the connection between quasi-static models and circuit theory, clarifying the role of the fields with respect to classical circuit elements, and provide an example of application to study the electromagnetic fields in a simple case.