caa a22 4500 46790670X CHVBK 20180406152836.0 cr unu---uuuuu 170328e20061101xx s 000 0 eng 10.1007/s10701-006-9075-7 doi (NATIONALLICENCE)springer-10.1007/s10701-006-9075-7 Christov Christo Department of Mathematics, University of Louisiana at Lafayette, 70504, Lafayette, LA, USA aut On the Material Invariant Formulation of Maxwell's Displacement Current [Elektronische Daten] [Christo Christov] Maxwell accounted for the apparent elastic behavior of the electromagnetic field by augmenting Ampere's law with the so-called displacement current, in much the same way that he treated the viscoelasticity of gases. Maxwell's original constitutive relations for both electrodynamics and fluid dynamics were not material invariant. In the theory of viscoelastic fluids, the situation was later corrected by Oldroyd, who introduced the upper-convective derivative. Assuming that the electromagnetic field should follow the general requirements for a material field, we show that if the upper convected derivative is used in place of the partial time derivative in the displacement current term, Maxwell's electrodynamics becomes material invariant. Note, that the material invariance of Faraday's law is automatically established if the Lorentz force is admitted as an integral part of the model. The new formulation ensures that the equation for conservation of charge is also material invariant in vacuo. The viscoelastic medium whose apparent manifestation are the known phenomena of electrodynamics is called here the metacontinuum. Springer Science+Business Media, LLC, 2006 Maxwell's electrodynamics nationallicence Hertz's equations nationallicence material invariance nationallicence Oldroyd's upper-convected derivative nationallicence Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/11(2006-11-01), 1701-1717 0015-9018 36:11<1701 2006 36 10701 https://doi.org/10.1007/s10701-006-9075-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10701-006-9075-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Christov Christo Department of Mathematics, University of Louisiana at Lafayette, 70504, Lafayette, LA, USA aut NATIONALLICENCE 773 0- Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/11(2006-11-01), 1701-1717 0015-9018 36:11<1701 2006 36 10701 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer