Thomson Jumping Ring
Explore induced ring current, phase lag and local lift force under AC drive.
About this tool
A sinusoidal prescribed coil current induces EMF in a closed RL ring. At a fixed position: R i + L di/dt = −M dI/dt and Fz=(dM/dz) I i, with upwards positive. Both currents use the same winding orientation. Ring current lags the EMF by δ=atan(ωL/R); the mean force is −(dM/dz) I₀² M ω²L/[2(R²+ω²L²)]. For M>0 and a negative gradient this gives mean repulsion. A pure resistor has zero mean force, although instantaneous force alternates and the ring heats. An open ring still has EMF but no current, heating or force. At f=0 this is steady DC: no induction or switching transient.
M and its height gradient are editable local coupling parameters, not derived from a number of turns. Defaults are illustrative, not a measured apparatus. Compare mean force with weight for a local free acceleration; this is not a jump-height or flight prediction. No changing coupling during motion, switching transient, core saturation, losses, thermal feedback or coil-current feedback. Blue: coil current / instantaneous force; orange: ring current / mean force; grey: weight. Currents are separately normalized to their amplitudes, never compared in absolute size. Probe values are quantitative. Phase playback deliberately slows one cycle to four seconds and does not move the ring. Saved drafts restore paused. Only the last entered phase is restored, paused; the playback cursor is temporary.