Meissner Effect

About this lab

The Meissner effect is the complete expulsion of magnetic flux from the interior of a material as it transitions into the superconducting state. Discovered by Walther Meissner and Robert Ochsenfeld in 1933, it demonstrates that a superconductor is not merely a perfect conductor (which would trap existing flux) but actively excludes magnetic fields. Below the critical temperature T_c, persistent surface currents arise spontaneously to generate a field that exactly cancels the applied field inside the material. The penetration depth—the thin surface layer where currents flow—is typically only tens of nanometers, described by the London equation: ∇²B = B/λ_L².

This flux expulsion is what causes levitation. A permanent magnet placed above a superconductor experiences a repulsive force because the superconductor’s surface currents create an image dipole of opposite polarity. The result is equivalent to the magnet being repelled by its own mirror image, producing stable levitation at an equilibrium height where the magnetic repulsion balances gravity. The London penetration depth λ_L = √(m/μ₀n_se²) determines how sharply the field decays inside the superconductor, where n_s is the superfluid electron density.

This simulation models the magnetic field of a dipole and computes field lines using numerical integration (fourth-order Runge-Kutta tracing of the B field). Below T_c, the superconductor is modeled using the method of images: an image dipole placed symmetrically below the superconductor surface generates the field-free interior and the characteristic bending of field lines around the material. The transition at T_c is shown as a smooth crossover where the image strength ramps from zero (normal state) to full (superconducting state), illustrating how the field is progressively expelled and the magnet rises to its levitation height.