Electromagnetic Momentum Conservation in media

TL;DR

This paper investigates electromagnetic momentum conservation in media, analyzing how momentum is transferred or appears to vanish in different scenarios, and discusses the implications for the Abraham-Minkowski debate.

Contribution

It provides detailed examples of momentum transfer in dielectric media, highlighting the role of infinite magnetic fields and comparing Minkowski and Abraham frameworks.

Findings

Momentum transfer occurs during magnetic field decay.

Some field momentum appears to vanish at infinity.

Conservation laws hold in both Minkowski and Abraham formalisms.

Abstract

That static electric and magnetic fields can store momentum may be perplexing, but is necessary to ensure total conservation of momentum. Simple situations in which such field momentum is transferred to nearby bodies and point charges have often been considered for pedagogical purposes, normally assuming vacuum surroundings. If dielectric media are involved, however, the analysis becomes more delicate, not least since one encounters the electromagnetic energy-momentum problem in matter, the `Abraham-Minkowski enigma', of what the momentum is of a photon in matter. We analyze the momentum balance in three nontrivial examples obeying azimuthal symmetry, showing how the momentum conservation is satisfied as the magnetic field decays and momentum is transferred to bodies present. In the last of the examples, that of point charge outside a dielectric sphere in an infinite magnetic field, we find that not all of the field momentum is transferred to the nearby bodies; a part of the momentum appears to vanish as momentum flux towards infinity. We discuss this and other surprising observations which can be attributed to the assumption of magnetic fields of infinite extent. We emphasize how formal arguments of conserved quantities cannot determine which energy-momentum tensor is more "correct", and each of our conservation checks may be performed equally well in the Minkowski or Abraham framework.