Electromagnetic force distribution inside matter

TL;DR

This paper uses numerical simulations to analyze electromagnetic force distributions inside materials, comparing two force-density formulations and highlighting their differences despite identical total forces, with implications for experimental measurement.

Contribution

It demonstrates that different electromagnetic force-density formulations can produce substantially different internal force distributions, despite identical total forces.

Findings

Force-density distributions differ between Lorentz and Einstein-Laub formulations.

Total force on objects remains the same regardless of the formulation.

Differences in force distributions could be experimentally measurable.

Abstract

Using the Finite Difference Time Domain method, we solve Maxwell's equations numerically and compute the distribution of electromagnetic fields and forces inside material media. The media are generally specified by their dielectric permittivity epsilon(w) and magnetic permeability mu(w), representing small, transparent dielectric and magnetic objects such as platelets and micro-beads. Using two formulations of the electromagnetic force-density, one due to H. A. Lorentz [Collected Papers 2, 164 (1892)], the other due to A. Einstein and J. Laub [Ann, Phys. 331, 541 (1908)], we show that the force-density distribution inside a given object can differ substantially between the two formulations. This is remarkable, considering that the total force experienced by the object is always the same, irrespective of whether the Lorentz or the Einstein-Laub formula is employed. The differences between the two formulations should be accessible to measurement in deformable objects.