Electrical Equations

  • Antonio Castellanos
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 380)


In this chapter we study the governing electrical equations in Electrohydrodynamics as a particular case of Electroquasistatics for fluids in nonrelativistic motion. First, we present in a very succint way Maxwell’s equations. Secondly, we show how these equations may be simplified after choosing suitable scales to make them dimensionless, and the electroquasistatic and magnetoquasistatic limits to the Maxwell’s equations are obtained. In these limits a nonrelativistic approach suffices, and using the Galilean principle of relativity the equations of Electroquasistatics and Magnetoquasistatics will be obtained for slowly moving fluids. Here slow means slow compared to the velocity of light, though the fluids could be moving at high speeds by ordinary standards. Galilean invariance imposes a transformation of the field quantities that is specific to this limits; it is important to note that, contrary to Mechanics, these limits are not obtained simply taken the factor γ = [1 - (u/c)2]−1/2 = 1 in the relativistic transformations of the fields [1]. For an alternative approach see [2]. The boundary and jump conditions are considered. Finally, a discussion of the concept of electrical energy is done in order to place this concept in the appropriate thermodynamic context [3],[4].


Jump Condition Displacement Current Galilean Invariance Lossy Medium Electrical Equation 
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    Landau L. M. and Lifshitz E. M.: Théorie des Champs, MIR, Moscow 1989.Google Scholar
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    Melcher J. R.: Continuum Electromechanics, The MIT Press, Cambridge, Massachusetts, 1981.Google Scholar
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    Landau L. M. and Lifshitz E. M.: Electrodynamique des Milieux Continus, MIR, Moscow 1989.Google Scholar
  4. 4.
    Panofsky W. K. H. and Phillips M.: Classical Electricity and Magnetism, Addison-Wesley, Reading, USA, 1962.zbMATHGoogle Scholar
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    Van Vleck J. H.: The Theory of Electric and Magnetic Susceptibilities. Oxford University Press, London, 1932.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 1998

Authors and Affiliations

  • Antonio Castellanos
    • 1
  1. 1.University of SevillaSpain

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