London equations

The London equations, developed by brothers Fritz and Heinz London in 1935, relate current to electromagnetic fields in and around a superconductor. Arguably the simplest meaningful description of superconducting phenomena, they form the genesis of almost any modern introductory text on the subject. A major triumph of the equations is their ability to explain the Meissner effect, wherein a material exponentially expels all internal magnetic fields as it crosses the superconducting threshold.

There are two London equations when expressed in terms of measurable fields:

Here ${\displaystyle {\mathbf {j} }_{s}}$ is the superconducting current density, E and B are respectively the electric and magnetic fields within the superconductor, ${\displaystyle e\,}$ is the charge of an electron & proton, ${\displaystyle m\,}$ is electron mass, and ${\displaystyle n_{s}\,}$ is a phenomenological constant loosely associated with a number density of superconducting carriers. Throughout this article SI units are employed.

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