Meissner Effect Simulator: Magnetic Flux Expulsion in Superconductors

simulator intermediate ~10 min
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B_internal ≈ 0 — perfect diamagnetic shielding at 4.2 K

At 4.2 K in a 20 mT applied field, the superconductor expels virtually all magnetic flux. The field decays exponentially within ~39 nm of the surface.

Formula

B(x) = B₀ × exp(-x/λ)
λ(T) = λ₀ / √(1 - (T/Tc)⁴)
M = -B₀/μ₀ (χ = -1, perfect diamagnet)

Discovery of Perfect Diamagnetism

In 1933, Walther Meissner and Robert Ochsenfeld made a discovery that fundamentally changed the understanding of superconductivity. They found that a superconductor cooled below Tc in an applied magnetic field actively expels the field from its interior — not just preventing new flux from entering, but ejecting flux that was already there. This is qualitatively different from perfect conductivity and established superconductivity as a distinct thermodynamic phase.

London Equations

Fritz and Heinz London proposed two equations in 1935 that capture the electrodynamics of the Meissner effect. The second London equation relates the supercurrent density to the vector potential, predicting that magnetic fields decay exponentially inside the superconductor with a characteristic length λ — the London penetration depth. For most elemental superconductors, λ is tens of nanometers.

Temperature Dependence

The penetration depth increases with temperature as λ(T) = λ₀ / √(1 - (T/Tc)⁴). Near Tc, λ diverges — the screening currents weaken and flux begins to penetrate deeper. At exactly Tc, the shielding vanishes and the material transitions to the normal state. This simulation shows how the field profile inside the superconductor evolves as you sweep temperature.

Levitation and Applications

The Meissner effect is the physics behind dramatic levitation demonstrations with high-temperature superconductors. YBCO cooled in liquid nitrogen hovers stably above permanent magnets. Beyond demonstrations, Meissner screening is essential for superconducting RF cavities in particle accelerators, where surface currents must flow without loss at microwave frequencies, and for shielding sensitive quantum devices from stray fields.

FAQ

What is the Meissner effect?

The Meissner effect is the complete expulsion of magnetic flux from the interior of a superconductor when cooled below its critical temperature Tc. Discovered by Meissner and Ochsenfeld in 1933, it proves superconductivity is a true thermodynamic phase — not merely zero resistance, but perfect diamagnetism.

What is the London penetration depth?

The London penetration depth λ is the characteristic distance over which an external magnetic field decays exponentially inside a superconductor. For niobium, λ₀ ≈ 39 nm at T = 0. It diverges as T approaches Tc, signaling the collapse of superconducting screening.

How does the Meissner effect enable levitation?

A superconductor repels a magnet because it generates surface currents that create an opposing field. This produces a stable repulsive force — the basis of magnetic levitation demonstrations and proposed Maglev train technologies using high-Tc superconductors.

Is the Meissner effect the same as perfect conductivity?

No. A perfect conductor would trap whatever flux was present when resistance vanished. The Meissner effect actively expels flux, even if the field was applied before cooling. This distinction proves superconductivity is a new phase of matter, not just zero resistance.

Sources

Embed

<iframe src="https://homo-deus.com/lab/superconductivity/meissner-effect/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub