Electromagnetic angular momentum in anisotropic media and Beth's torque

The interaction of radiation with material media is a very active area of research, in particular the interaction with new exotic materials. However, we find several controversies in this field, like the Abraham-Minkowski controversy, or the attribution of angular momentum to quasi-static fields.

In the present work we show that besides the electromagnetic momentum density proportional to Poynting's vector, whose time derivative is force and therefore can produce a torque, there are other momentum densities implied by the macroscopic Maxwell equations transformed into momentum balance equations. These momentum densities are also related to forces and torques. We show in this way that torques like D × E and B × H appear in these balance equations transformed into balance equations of angular momentum. The density D × E was used by Beth [Phys. Rev. 50 115–125 (1936)] to measure the angular momentum of radiation fields in interaction with anisotropic dielectrics. Our analysis show that also static or quasi-static fields carry angular momentum and produce torques when interacting with anisotropic materials.