Railgun recoil, ampere tension, and the laws of electrodynamics

There has recently been a revival of an old controversy over whether Ampere’s original law of force between current elements is to be preferred over the more familiar and universally used Biot–Savart–Lorentz law. Although it is agreed that the two laws give identical results when used to calculate the force between two circuits, it has been claimed that if Ampere’s law is applied to the action of a circuit upon part of itself it predicts internal longitudinal forces that are excluded by Biot–Savart–Lorentz. The existence of longitudinal forces has been inferred from observations of the buckling of the rails in a railgun, attributed to compressive stress, and the fracture of long wires subjected to pulsed currents, attributed to ‘‘Ampere tension.’’ An experiment has been performed that should provide an unambiguous demonstration of this longitudinal force, if it exists. The apparatus consisted of a rigid coaxial circuit in which an unsymmetrical section of the center conductor was free to move in the axial direction under the influence of the longitudinal force. Pulsed currents of up to 100 kA were passed through the circuit but no evidence of a longitudinal force was found. It is shown that this result is consistent with Ampere’s force law, and that claims that the law predicts longitudinal forces are based on the incomplete application of the law.