In Part 3, the principles developed in the preceding parts are illustrated by applying them to the problem of a sphere, with arbitrary material properties, immersed in a fluid with linear dielectric properties, in an applied electric field that is symmetric about an axis but is otherwise arbitrary. The long-range electric force and the short-range force due to fluid pressure are calculated separately; the sum of these is what is usually calculated by the maxwell stress method, and the resolution into two terms is admittedly not unique. In Part 4, some general work and energy relations are developed; these are put into a form such that elementary thermodynamic principles can be applied directly, without resort to physical interpretations of the macroscopic field vectors. The application to magnetoelastic and piezoelectric phenomena is indicated. The standard formulas of piezoelectricity, as developed by Voigt, are shown to be correct only if the “stresses” occurring in them are given a particular one of several possible interpretations.
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William Fuller Brown (1951) studied this question.