Action-reaction forces between current-carrying conductors

The direction of the magnetic forces on currents, at right-angles to the conductor, leads to an apparent failure of the action-reaction force balance when applied to the component parts of a current-carrying circuit. The electromagnetic railgun provides an example showing the need for a force in the direction of current flow. These and other applications continue a long-standing debate, originating in Ampere´s analysis of the nature of the forces on current elements. The paper examines the consequences of Maxwell´s ´dynamical´ approach to currents in terms of ´electrical fluids´. The conductor surfaces transfer the transverse force on the conduction electrons to the crystal lattice but, since there are no similar constraints in the axial direction, a current element cannot be treated as a single entity. The implications of the separation into two groups of charge are examined. It is shown that the hydraulic fluid, or ´hosepipe´, analogue provides a useful insight in terms of momentum and pressure. The corresponding electromagnetic properties provide a ´dynamical´ alternative to the magnetostatic Maxwell stresses in the field. This also accounts for the reaction in a self-consistent way, but requires such high levels of energy and stress in empty space as to be widely regarded as ´unreal´.