A catalogue of hidden momenta

Abstract

Electromagnetic fields carry momentum: . But if the centre of energy of a (localized) system is at rest, its total momentum must be zero. The compensating term has come to be called ‘hidden’ momentum: P h  =  −  P em . It is (typically) ordinary mechanical momentum, relativistic in nature, and is ‘hidden’ only in the sense that it is not associated with motion of the system as a whole—only with that of its constituent parts. This article develops a catalogue of field momenta and hidden momenta for ideal electric and magnetic dipoles—both the ‘standard’ variety made from electric charges and currents and the ‘anomalous’ variety made from hypothetical magnetic monopoles and their currents—in the presence of electric and magnetic fields (which themselves may be produced by ‘standard’ or ‘anomalous’ sources). This article is part of the theme issue ‘Celebrating 125 years of Oliver Heaviside's ‘Electromagnetic Theory’’.