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The connection between electromagnetic stress tensors and the dielectric constant in a medium

R. Dengler

Abstract

We perform explicit calculations for microscopic models to confirm that a single, unique electromagnetic stress tensor exists in a dielectric medium: the microscopic tensor $σ^{#}$. We demonstrate that the conventional macroscopic stress tensor of continuum electrodynamics, which contains the derivative of the dielectric coefficient, is merely a representation of $σ^{#}$'s spatial average. This result establishes that, contrary to claims in the literature, both this averaged electromagnetic stress and the hydrodynamic pressure always possess a unique physical meaning.

The connection between electromagnetic stress tensors and the dielectric constant in a medium

Abstract

We perform explicit calculations for microscopic models to confirm that a single, unique electromagnetic stress tensor exists in a dielectric medium: the microscopic tensor . We demonstrate that the conventional macroscopic stress tensor of continuum electrodynamics, which contains the derivative of the dielectric coefficient, is merely a representation of 's spatial average. This result establishes that, contrary to claims in the literature, both this averaged electromagnetic stress and the hydrodynamic pressure always possess a unique physical meaning.
Paper Structure (10 sections, 29 equations, 1 figure)

This paper contains 10 sections, 29 equations, 1 figure.

Table of Contents

  1. Stress tensor in a medium
  2. Conventional stress tensor
  3. Planar capacitor filled with a liquid
  4. Planar capacitor containing a solid
  5. Uniaxial microscopic model
  6. Point dipoles on an orthorhombic lattice
  7. Stress tensor perpendicular to electric field
  8. Stress tensor in direction of electric field
  9. Deformation of a cubic crystal
  10. Conclusion

Figures (1)

  • Figure 1: A dielectric medium consisting of polarizable rods. Microscopic and macroscopic electric field are identical.