Net Magnetic Force Between Loops with Harmonic Out-of-Phase Currents: Analysis of Power to Force Ratio

In this paper, the electromagnetic interaction force between two straight current-carrying wires is examined using Maxwell’s equations and the Lorentz force law. It is shown that, due to far-field asymmetry, the interaction forces may not cancel out if an out-of-phase current–time profile is selected. This configuration can, in principle, produce a nonzero net force. However, quantitative analysis reveals that achieving a measurable net momentum gain requires a substantial energy input. Consequently, the overall efficiency of such a mechanism is significantly lower than that of conventional radiative thrusters