Four Expressions for Electromagnetic Field Momentum

in Gaussian units, where is the electric charge density, A is the magnetic vector potential (where ∇ ·A = 0 for static fields in both the Coulomb and Lorenz gauges), E is the electric field, B is the magnetic field, V is the electric scalar potential, and J is the electric current density. The first form is due to Faraday and Maxwell, the second form is due to Poynting Thomson and Poincaré, the third form was introduced by Furry, and the fourth form is due to Aharonov et al. Of these four forms, the second depends only on the electromagnetic fields, and so is the most “Maxwwellian.” As such, we consider the the volume density of electromagnetic field momentum to be