Let a magnet fall through a coil. Its changing flux induces an EMF pulse; if the coil is closed, the current pushes back on the magnet (Lenz) so it falls more slowly, and the lost potential energy shows up as heat in the wire and the load.
Each row is a full drop computed in the same model with the current magnet, coil and height.
The science
Faraday: EMF = −dΦ/dt. The magnet is a point dipole of moment m = BrV/μ₀ on the coil axis; the flux through one turn of radius a at axial distance d is Φ = μ₀ m a² / (2 (a² + d²)3/2). The coil's N turns are lumped into up to 120 layers along its length and summed.
One coupling coefficient: with G = dΦ/dz, the EMF is ε = −G v and the force on the magnet is F = I G. With circuit equation L dI/dt = ε − R I (R = wire + load) the brake force is about −(G²/R) v, so low resistance means strong braking (Lenz's law). The motion is integrated with RK4 at 20 µs.
Energy: m g Δh = ½ m v² + ∫ I² R dt. The page shows the balance. Two pulses appear because dΦ/dz changes sign at the coil centre; the second is larger because the magnet is faster.
Simplifications: point dipole (a 20 mm magnet is not small next to the coil), no iron, no eddy currents in the tube, no air drag, inductance approximated by a solenoid formula with an end correction, and when R/L is large the inductance is dropped (quasi-static current). Wire resistance uses copper at 20 °C. Remanence values are typical, not measured.