Several energy-momentum-stress balance equations deduced from Maxwell's equations in material media. Non-covariant and explicitly covariant formulation

Balance Equations of Electromagnetic Angular Momentum

“…We find then a need to derive carefully balance equations of angular momentum of radiation directly from the macroscopic Maxwell equations, as we have done for the linear momentum of radiation [12] [13]. We hope in this way to establish a unified and general view of the balance of electromagnetic angular momentum that permits us to asses torques that have been proposed by some authors.…”

“…This produces a strange mixture of external fields and total fields. We have found [13], however, that several momentum balance equations can also be obtained directly from the macroscopic Maxwell equations by means of vector and tensor identities. These different balance equations result from different ways of expressing the macroscopic Maxwell equations in terms of fields E, D, B, H, and polarizations P and M. This approach has led to a possible settlement of the old Abraham-Minkowski controversy, since these proposals for the electromagnetic momentum appear in different balance equations [13].…”

“…We have found [13], however, that several momentum balance equations can also be obtained directly from the macroscopic Maxwell equations by means of vector and tensor identities. These different balance equations result from different ways of expressing the macroscopic Maxwell equations in terms of fields E, D, B, H, and polarizations P and M. This approach has led to a possible settlement of the old Abraham-Minkowski controversy, since these proposals for the electromagnetic momentum appear in different balance equations [13]. In the present work we use the same approach to derive balance equations of electromagnetic angular momentum, subject that has occupied theorists and experimentalists since long ago, for example Poynting in 1909 [14].…”

Induced Dipoles in Electromagnetic Media in Motion

“…The relevance of choosing a particular and convenient expression of the Maxwell equations can be better appreciated considering different momentum balance equations that can be derived from these different expressions [2]. It must be emphasized that these different forms of the macroscopic Maxwell equations are all equivalent.…”

“…It must be emphasized that these different forms of the macroscopic Maxwell equations are all equivalent. With one of these forms of expressing Maxwell's equations [2] equations we can get for the motion of a current circuit, which is a typical magnetic dipole moment, the results obtained by Hnizdo [3] and later by Griffiths [4] using relativity. These authors conclude that it is necessary to introduce a new electromagnetic momentum density, the so-called hidden momentum.…”