Drop a bar magnet through a coil and a voltage appears — even though nothing touches. Is the induced voltage set by how STRONG the magnet's flux is through the coil, or by how FAST that flux is changing?
▶ Launch the interactive simulationLet a magnet (axial dipole, flux Φ(z) = μ₀m·a²/2(a²+z²)^{3/2}) fall under gravity straight down the axis of an N-turn coil. The lab traces the flux Φ(t) — a single hump peaking when the magnet is centred — alongside the induced EMF = −N dΦ/dt, integrating the EMF to track ∮ EMF dt and the area of each lobe. A real NdFeB magnet is also dropped through a real 240-turn 13 mm coil with 3% reading noise.
Faraday's law EMF = −N dΦ/dt — the RATE, not the flux: the EMF is exactly ZERO when the magnet is centred (flux MAXIMUM) and peaks off-centre where the flux changes fastest, a BIPOLAR pulse whose two lobes carry equal & opposite impulse (∮ EMF dt = −N·ΔΦ = 0); because the magnet accelerates the exit lobe is taller & narrower yet equal in area, and ∫|EMF| dt = N·Φ_max = Nμ₀m/2a inverts to recover the magnet's dipole moment m ≈ 0.55 A·m² independent of fall speed