London Equations

Superconductivity · 1935

Equation: ∂J/∂t = (n_s·e²/mₑ)·E · ∇×J = −(n_s·e²/mₑ)·B
Field: Superconductivity
Named After: Fritz London · Heinz London
Year: 1935

Symbols

J supercurrent density · n_s density of superconducting electrons · E, B electric and magnetic fields · fields penetrate only the London depth λ_L = √(mₑ/(μ₀·n_s·e²))

Significance

Two lines that capture superconductivity's twin miracles: current accelerates freely with no resistance, and magnetic fields are expelled from the interior — the Meissner effect, which is why superconductors levitate magnets. Written by refugee brothers two years after the expulsion was discovered.