Electromagnetic force density in dissipative isotropic media

TL;DR

This paper derives a macroscopic electromagnetic force density expression for dissipative isotropic media, enabling realistic force calculations in complex materials and clarifying the energy-momentum tensor in such contexts.

Contribution

It introduces a new averaged force density formula applicable to dissipative media, extending previous models and reconciling with known tensors in lossless cases.

Findings

The derived force density expression matches the Helmholtz tensor in lossless media.

The field's momentum density aligns with the Abraham expression in non-magnetic materials.

The formula allows for practical calculations in materials with complex permittivity and permeability.

Abstract

We derive an expression for the macroscopic force density that a narrow-band electromagnetic field imposes on a dissipative isotropic medium. The result is obtained by averaging the microscopic form for Lorentz force density. The derived expression allows us to calculate realistic electromagnetic forces in a wide range of materials that are described by complex-valued electric permittivity and magnetic permeability. The three-dimensional energy-momentum tensor in our expression reduces for lossless media to the so-called Helmholtz tensor that has not been contradicted in any experiment so far. The momentum density of the field does not coincide with any well-known expression, but for non-magnetic materials it matches the Abraham expression.