Abstract
The present chapter is intended as a discussion of various electromagnetic phenomena occurring in rigid continuous bodies. In reality, all bodies are, of course, deformable. However, when the effect of strains are negligible compared with electromagnetic effects, gross mathematical simplifications are achieved. After a summary of basic equations in Section 6.2, we present an account of the potential theory in Section 6.3, including the uniqueness theorem and various methods of solution (e.g., Green’s function technique, eigenfunction expansions, mixed boundary-value problems).
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References
For the obsolete notion of luminiferous aether, the ad hoc substratum of electromagnetic vibrations, see Whittaker [1951].
See Whittaker [1951] and Tonnélat [1971, pp. 82–84].
See Eringen [1967, p. 463].
For an alternative approach, see Bloembergen [1965]. A full discussion of nonlinear optics involves both memory effects and spatial nonlocality. In this generality, D is considered to be a nonlinear functional of E(x′, t − τ′), where x′ covers the entire volume of the body, and 0 ≤ τ′ < ∞ (see Chapter 14). Usually, for D, a Volterra series involving multiple space—time integrals, is written in terms of E(x′, t − τ′) (see Shen [1984] and Schubert and Wilhelmi [1986]). We return to this question later in Chapters 13 and 14.
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© 1990 Springer-Verlag New York Inc.
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Eringen, A.C., Maugin, G.A. (1990). Rigid Dielectrics. In: Electrodynamics of Continua I. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3226-1_6
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DOI: https://doi.org/10.1007/978-1-4612-3226-1_6
Publisher Name: Springer, New York, NY
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