On the electromagnetic momentum of static charge and steady current distributions

Abstract

Faraday's and Furry's formulas for the electromagnetic momentum of static charge distributions combined with steady electric current distributions are generalised in order to obtain full agreement with Poynting's formula in the case where all fields are of class C^1, i.e., continuous and continuously differentiable, and the integration volume is of finite or infinite extent. These three formulas are further generalised to the case where singularities are allowed to exist at isolated points in the fields, and at surfaces separating domains in which the distributions are of class C^1. Applications are made to electric and magnetic, point-like and finite dipolar systems, with an emphasis on the impact of singularities on the magnitude and location of the electromagnetic momentum.