4.1: Objectives

The representation of total forces and torques in terms of Maxwell stresses is developed in Sec. 4.2,followed in Sec. 4.3 by a classification of common types of energy converters, based on the fundamental field interactions. An extension of the transfer relations found in Secs. 2.16 and 2.19 to describe regions occupied by specified distributions of charge and current is made in Secs. 4.5 and 4.8.. Although this chapter is concerned with modeling specific interactions, it is the technique for representing these systems that is the message. Section 4.4 exemplifies the notation and strategy underlying the methodical formulation of complex systems in not only this chapter, but those to follow. Of the remaining sections, only one does not pertain to a specific class of devices. Section 4.12 lends some formality to the philosophy underlying quasi-one-dimensional models. Such approximations retain nonlinear interactions and are illustrated in Secs. 4.13 and 4.14. By contrast, Secs. 4.4, 4.6 -4.9 and 4.11are concerned with field models that are naturally linear, or are linearized. Formally, the linearized model, in which products of amplitudes are ignored compared to terms that are linear in the amplitudes,is the zero-order approximation in an amplitude-parameter expansion for the exact solution. Similarly,the quasi-one-dimensional model is a zero-order approximation to an expansion in a space-rate parameter.

The analogies that exist between electric and magnetic field interactions is a theme throughout the chapter. This is clear in Sec. 4.3. But a thoughtful comparison of the characteristics of the d-c magnetic machine, considered in more detail in Sec. 4.10, with those of the Van de Graaff machine in Sec. 4.14 is worth while.

An overview of the chapter is given in Sec. 4.15.