Energy-momentum Tensor Of Electromagnetic Field Research Articles

Energy-Momentum Density’s Conservation Law of Electromagnetic Field in Rindler Space-time

We find the energy-momentum density of electromagnetic field by energy-momentum tensor of electromagnetic field in Rindler space-time. We find the energy-momentum density’s conservation law of electromagnetic field in Rindler spacetime.

Ponderomotive forces in electrodynamics of moving media: The Minkowski and Abraham approaches

In the general setting of the problem, the explicit compact formulae are derived for the ponderomotive forces in the macroscopic electrodynamics of moving media in the Minkowski and Abraham approaches. Taking account of the Minkowski constitutive relations and making use of a special representation for the Abraham energy-momentum tensor enable one to obtain a compact expression for the Abraham force in the case of arbitrary dependence of the medium velocity on spatial coordinates and the time and for nonstationary external electromagnetic field. We term the difference between the ponderomotive forces in the Abraham and Minkowski approaches as the Abraham force not only under consideration of media at rest but also in the case of moving media. The Lorentz force is found which is exerted by external electromagnetic field on the conduction current in a medium, the covariant Ohm law, and the constitutive Minkowski relations being taken into account. The physical argumentation is traced for the definition of the 4-vector of the ponderomotive force as the 4-divergence of the energy-momentum tensor of electromagnetic field in a medium.

Symmetric energy-momentum tensor: The Abraham form and the explicitly covariant formula

We compare the known in literature, explicitly covariant 4-dimensional formula for the symmetric energy-momentum tensor of electromagnetic field in a medium and the energy-momentum tensor derived by Abraham in the 3-dimensional vector form. It is shown that these two objects coincide only on the physical configuration space Γ¯, formed by the field vectors and the velocity of the medium, which satisfy the Minkowski constitutive relations. It should be emphasized that the 3-dimensional vector formulae for the components of the energy-momentum tensor were obtained by Abraham only on Γ¯, and the task of their extension to the whole unconditional configuration space Γ was not posed. In order to accomplish the comparison noted above, we derive the covariant formula a new by another method, namely, by generalizing the Abraham reasoning. The comparison conducted enables one to treat the explicitly covariant formula as a unique consistent extension of the Abraham formulae to the whole configuration space Γ. Thus the question concerning the relativistic covariance of the original 3-dimensional Abraham formulae defined on Γ¯ is solved positively. We discuss in detail the relativistic covariance of the 3-dimensional vector formulae for individual components of the 4-dimensional tensors in electrodynamics which is manifested in the form-invariance of these formulae under Lorentz transformations.

Mechanical equation of motion for energy and energy-momentum tensor of electromagnetic field in transparent medium

With reference to one of K. F. Novobatzky’s papers we deduce a mechanical equation of motion for energy of a non-isolated classical field. By way of application we consider the stress tensor of an electromagnetic plane-wave propagating in a transparent medium. It turns out from this consideration that Abraham’s energy-momentum tensor describes the energy and momentum of electromagnetic field in an isotropic transparent medium correctly.

Use of the variational equation in the study of polarizable and magnetizable continuous media: PMM vol. 37, n≗5, 1973, pp. 803–812

A model of a continuum is constructed, using the variational equation suggested in [1, 2] which makes it possible to obtain models of continua using a minimum number of unified physical hypotheses. In the present paper the variational equation is used to obtain a system of equations defining the macroscopic motion of a continuum with polarization and magnetization effects taken into account, within the framework of the special relativity theory. Use of the four-dimensional space-time and special relativity theory is required in order to match theories of electromagnetism and mechanics. We investigate some of the consequences of two possible decompositions of the total energy-momentum tensor of the electromagnetic field and the continuum into the continuum energy-momentum tensor and the electromagnetic field energy-momentum tensor according to Minkowski and to Abraham, respectively. When moment stresses and external mass moments are absent in the medium, we assume the symmetry of the total energy-momentum tensor of electromagnetic field and medium (this is equivalent to the absence or constancy of the combined electromagnetic field and medium, intrinsic internal moments of momenta along the world lines) and on this assumption consider certain models of continua.

Energy-Momentum Tensor of Electromagnetic Field in Moving Dispersive Media and Instability: Relativistic Formulation

Based on the Lagrangian principle, the energy-momentum tensor of the electromagnetic field is obtained for general linear anisotropic dispersive media whose components are moving with different uniform velocities. The field is assumed to change in space and time with a center wave-number 4-vector ${\ensuremath{\omega}}_{\ensuremath{\nu}}$. The energy-momentum tensor obtained can be classified into three parts of the pure electromagnetic field, the medium and the interaction with the external system, and the explicit expression for each part is given in terms of the two 4-forces acting on unit electric and magnetic charges. When $\ensuremath{\omega}_{\ensuremath{\nu}}^{}{}_{}{}^{2}>0$, the energy density is not positive definite, depending upon the frame of reference, while the "rest" energy of the field is nonvanishing (in contrast with the case of nondispersive media) and has a positive sign at least in isotropic media with no external source; thus the energy density is positive definite in the rest frame of the wave itself. The direction of the power flow 4-vector agrees with that of the wave packet. The instability of the wave is discussed from a general point of view based on the energy-momentum tensor and the covariance of equations, and the wave is found to become unstable when the group velocity reaches the velocity of light in vacuum, over a finite range of the wave number; the two beam instability in a plasma belongs to this type of instability. The wave becomes unstable also when, in any frame of reference, the conductivities of one or more of the medium components become negative and the field energy is positive, so that the total energy increases in timelike direction.