Balance Equations of Electromagnetic Angular Momentum

Ignacio Campos-Flores,José Luis Jiménez-Ramírez,José Antonio Eduardo Roa-Neri

doi:10.4236/jemaa.2017.912017

Ignacio Campos-Flores, José Luis Jiménez-Ramírez + Show 1 more

Open Access

https://doi.org/10.4236/jemaa.2017.912017

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Abstract

We give theoretical foundation to torque densities proposed in the past, like the one used by Beth to study experimentally the action of circularly polarized radiation on a birefringent material, or that proposed by Mansuripur to resolve a seeming paradox concerning the Lorentz force law and relativity. Our results provide new insights into electromagnetic theory, since they provide a unified and general treatment of the balance of lineal and angular momentum that permits a better assessment of some torques. Thus in this work we extend the derivations we have made of balance equations for electromagnetic linear momentum to balance equations for electromagnetic angular momentum. These balance equations are derived from the macroscopic Maxwell equations by means of vector and tensor identities and from the different ways in which these equations are written in terms of fields E, D, B, and H, as well as polarizations P, and M. Therefore these balance equations are as sound as the macroscopic Maxwell equations, with the limitations of the constitutive relations.

Highlights

We find a need to derive carefully balance equations of angular momentum of radiation directly from the macroscopic Maxwell equations, as we have done for the linear momentum of radiation [12] [13]
There are other forms of expressing the Maxwell equations, but these five different ways of expressing these equations are sufficient to illustrate the method for deducing balance equations of electromagnetic angular momentum, and for the analysis of the torque used by Beth [15] and that considered by Mansuripur [10]
We can see that these torques are proposed with plausibility arguments founded on the Lorentz force law, while we offer a general and unified approach based on balance equations derived from the Maxwell equations

Summary

Introduction

The classical theory of electromagnetism is a well established theory; there are still some conceptual problems which deserve insightful reflections, in the theory of electromagnetic media. We have shown in past works [12] [13] how from the macroscopic Maxwell equations different momentum balance equations can be deduced by means of vector and tensor identities These balance equations arise from different forms of expressing the Maxwell equations and constitutive relations in terms of the electromagnetic fields E, D, B, and H, and the electric and magnetic polarizations P and M. We resume five different ways of expressing the Maxwell equations, with their corresponding momentum balance equations deduced from them From these balance equations we want to obtain angular momentum balance equations which will permit us to analyze the origin of the torque experimentally tested by Beth [15], and the torque which Mansuripur [10] interpreted as an inconsistency between the Lorentz force and the principle of relativity. There are other forms of expressing the Maxwell equations, but these five different ways of expressing these equations are sufficient to illustrate the method for deducing balance equations of electromagnetic angular momentum, and for the analysis of the torque used by Beth [15] and that considered by Mansuripur [10]

Balance Equations of Angular Momentum

Conclusion