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 Amp" ere’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 entitity. 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’.