Variational formulation of the electrodynamics of fluids and its application to the radiation pressure problem
Abstract
A covariant formulation of classical electrodynamics is given for nonviscous, compressible, nondispersive, polarizable, and magnetizable fluids. The part of the Lagrangian density accounting for the various interactions to be existent in such fluids under the influence of the electromagnetic fields is constructed rather intuitively by introducing two four-vector variables, one to describe the states of polarization and the other to describe those of magnetization. The energy-momentum conservation law can be derived separately for the material and the field subsystems. The energy-momentum tensor of the total system cannot be split in a unique way into the material and the field parts. However, physically reasonable ways of splitting can be found so as to give one and the same result as to the electromagnetic radiation pressure in electromagnetic fluids. This pressure is shown to be (D-->×E-->)4π(μν)12, in agreement with experiment. This indicates that the pressure observed in experiment consists almost entirely of the "true" electromagnetic radiation pressure. For the sake of consistency, the mechanical pressure arising both from the electro- and magnetostrictive forces and the forced motions of the fluid particles under the influence of the electromagnetic radiation fields is also estimated and found, in fact, to be negligible in ordinary experimental conditions.
- Publication:
-
Physical Review A
- Pub Date:
- June 1976
- DOI:
- 10.1103/PhysRevA.13.2265
- Bibcode:
- 1976PhRvA..13.2265M
- Keywords:
-
- Compressible Fluids;
- Electrohydrodynamics;
- Electromagnetic Radiation;
- Momentum Theory;
- Radiation Pressure;
- Variational Principles;
- Conservation Laws;
- Field Theory (Physics);
- Magnetohydrodynamics;
- Minkowski Space;
- Plasma-Electromagnetic Interaction;
- Tensor Analysis;
- Theoretical Physics;
- Physics (General)