Magnetic Levitation — Meissner Effect & Superconductor Physics

Observe a permanent magnet levitating above a superconductor cooled below Tc. The Meissner effect expels magnetic flux, creating a repulsive force that defies gravity with zero drag.

Cross-section: magnet (top), field lines, superconductor (cold = blue)
Levitation force F(h) and gravitational load — stable if F(h) = mg

Controls

Meissner effect: Below Tc, a Type-I superconductor completely expels B (χ = −1). Induced surface currents maintain B = 0 inside. Levitation force F ≈ A·B²/(2μ₀), decaying as h².
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Force Analysis

Active (T < Tc)?— Surface B (T)— Levitation F (N)— Gravity mg (N)— Net force (N)— Stable equilib.?— Magnetic stiffness— Flux penetration λ—
Physics notes

Earnshaw's theorem: stable levitation is impossible with static fields alone — superconductors bypass this by active flux expulsion.

London penetration depth λ_L: B decays as e^(−z/λ_L) into surface; λ_L ~ 50–500 nm.

Type-II flux pinning: Above Hc1, flux tubes (Abrikosov vortices) are pinned by defects — this creates lateral stability.