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.

About this simulation

This simulation models superconducting levitation via the Meissner effect: below a critical temperature Tc, a superconductor expels an applied magnetic field from its interior (magnetic susceptibility χ = −1), inducing surface screening currents that create a repulsive force on a nearby permanent magnet. The levitation force is approximated as F ≈ A·B²/(2μ₀), decaying roughly with the square of the gap height, and is balanced against the load's weight mg to find the equilibrium levitation height.

🔬 What it shows

A permanent magnet levitating above a cooled superconducting disc. When temperature T drops below the critical temperature Tc, field lines are expelled from the superconductor's interior (Meissner effect) and bend around it, while the force plot traces the levitation force F(h) against the constant gravitational load mg, marking the stable equilibrium height where the two curves cross.

🎮 How to use

Choose a preset — YBCO (Tc = 93 K), Nb (Tc = 9.2 K), or an idealised Electromagnet with no thermal cutoff — then adjust the Temperature T, Magnet field B₀, Magnet height h and Load mass m sliders. Watch the Force Analysis panel update the surface field, levitation force, net force and magnetic stiffness live, and expand the Physics notes for Earnshaw's theorem, London penetration depth and flux pinning.

💡 Did you know?

Static magnetic fields alone can never produce stable levitation — this is Earnshaw's theorem. Superconductors sidestep it because they aren't passive magnets: their screening currents actively respond to any change in position, restoring equilibrium instead of just balancing it momentarily.

Frequently asked questions

What is the Meissner effect?

The Meissner effect is the expulsion of a magnetic field from the interior of a superconductor once it is cooled below its critical temperature Tc. Persistent surface currents form spontaneously to cancel the internal field, keeping B = 0 inside the bulk material and pushing field lines around the outside instead of through it.

How does the simulation calculate the levitation force?

It uses the approximation F ≈ A·B²/(2μ₀), where A is an effective interaction area set by the chosen preset, B is the magnetic field at the superconductor's surface, and μ₀ is the permeability of free space. Because the surface field falls off with distance, the force drops sharply as the magnet height h increases, which is why levitation only happens within a limited gap range.

What do the sliders and presets actually change?

The Temperature slider T determines whether the material is below its critical temperature Tc; the Magnet field B₀ slider sets the source magnet's strength; Magnet height h sets the gap between magnet and superconductor; and Load mass m sets the weight the levitation force must support. The YBCO, Nb and Electromagnet presets change Tc and the effective area A, reflecting real differences between high-Tc ceramic, low-Tc metallic, and actively driven electromagnetic levitation.

Why is stable levitation possible here when Earnshaw's theorem forbids it?

Earnshaw's theorem shows that a magnet cannot be held in stable equilibrium by static fields from fixed permanent magnets or currents alone, because such fields have no local minimum in potential energy. A superconductor is not a static source: its screening currents actively adjust in response to the magnet's position, and in type-II materials flux pinning locks vortices in place, both of which supply the restoring behaviour Earnshaw's theorem rules out for ordinary magnets.

What is the difference between the YBCO, Nb and Electromagnet presets?

YBCO is a high-temperature ceramic superconductor with Tc around 93 K, so it can be cooled cheaply with liquid nitrogen and is the material most often used in demonstration levitation setups. Niobium (Nb) is a conventional low-Tc superconductor with Tc near 9.2 K, needing liquid helium instead. The Electromagnet preset removes the temperature cutoff entirely to represent an actively driven coil, showing the same force law without any superconducting physics.