Quantum Levitation (2D)

Why the disc floats

A superconductor expels part of the magnetic field (Meissner effect) and traps the rest in thin flux tubes (flux pinning in a type-II material such as YBCO). The expelled field presses back on the track with a magnetic pressure B^2 / (2 mu0). This page models the lift as F(z) = eta(T) kappa A B0^2 / (2 mu0) exp(-2z/l), where A = pi R^2, kappa is a geometry/trapping factor (0.5 here) and the track field decays as B(z) = B0 exp(-z/l) with l = p / pi for pole width p. Because force goes with B squared, it decays twice as fast as the field.

Equilibrium and bobbing

Weight equals lift at z_eq = (l/2) ln(F0 / mg). For small vertical motion the force acts like a spring with stiffness k = mg / (l/2), so the disc bobs at f = (1/2 pi) sqrt(2 g / l), independent of its mass. Flux pinning also gives a sideways restoring force; here it is a spring k_x = s m g / delta with delta = 5 mm and s the pinning strength.

Temperature

The superconducting fraction follows the two-fluid form eta(T) = 1 - (T/Tc)^4 below Tc = 92 K and is zero above it. The disc warms after leaving the liquid nitrogen as T(t) = T_amb - (T_amb - T0) exp(-t / tau) (the time-lapse slider speeds this up). It drops when eta F_max = mg, the lift-off temperature in the readouts.

Honest simplifications

Real levitation force depends on cooling height, hysteresis and the field geometry; the exponential law, kappa and the two-fluid fraction are textbook-level stand-ins chosen to give realistic heights of a few millimetres. No hysteresis, no field-cooled versus zero-field-cooled difference and no eddy-current heating are included. The animation runs in slow motion.

• Press Re-cool, then watch the disc warm: the margin falls and it drops at the lift-off temperature.
• Pick Narrow poles: the field dies off faster, so the disc floats lower.
• Pick Heavy disc: equilibrium height shrinks but the bobbing frequency stays almost the same.
• Drag the disc sideways: weak pinning lets it wander, strong pinning pulls it back.