\[\lambda_L=\sqrt{\frac{m}{\mu_0ne^2}}\]
Variables
lambdaL[λ_L]London penetration depth (m)
melectron mass (kg)
mu0[μ_0]vacuum permeability (H/m)
nsuperconducting carrier density (1/m³)
eelementary charge (C)
Description
What is this formula?
The London penetration depth formula calculates the characteristic distance over which an external magnetic field decays inside a superconductor.
When to use it
This formula is used in superconductivity theory, condensed matter physics, and electromagnetic analysis of superconducting materials.
Example
A superconductor has:
n = 5.0×10^28 1/m³
Using:
λ_L = √(m/(μ_0ne²))
Where:
m = 9.11×10^-31 kg
μ_0 = 4π×10^-7 H/m
e = 1.60×10^-19 C
Substitution:
λ_L = √((9.11×10^-31)/((4π×10^-7)×5.0×10^28×(1.60×10^-19)²))
Result:
λ_L ≈ 5.3×10^-8 m
Applications
- Superconductivity analysis
- Magnetic field shielding
- Quantum materials
- Cryogenic engineering
- Electromagnetic superconducting devices
- Condensed matter physics