3.3 CONDITIONS FOR FIELDS TO BE QUASISTATIC An appreciation for the quasistatic approximations will come with a consideration

An appreciation for the quasistatic approximations will come with a consideration of many case studies. Justification of one or the other of the approximations hinges on using the quasistatic fields to estimate the “error” fields, which are then hopefully found to be small compared to the original quasistatic fields. In developing any mathematical “theory” for the description of some part of the physical world, approximations are made. Conclusions based on this “theory” should indeed be made with a concern for implicit approximations made out of ignorance or through oversight. But in making quasistatic approximations, we are fortunate in having available the “exact” laws. These can always be used to test the validity of a tentative approximation. Provided that the system of interest has dimensions that are all within a factor of two or so of each other, order of magnitude arguments easily illustrate how the error fields are related to the quasistatic fields. The examples shown in Fig. 3.3.1 are not to be considered in detail, but rather should be regarded as prototypes. The candidate for the EQS approximation in part (a) consists of metal spheres that are insulated from each other and driven by a source of EMF. In the case of part (b), which is proposed for the MQS approximation, a current source drives a current around a one­turn loop. The dimensions are “on the same order” if the diameter of one of the spheres, is within a factor of two or so of the spacing between spheres