 If "x" leads perpendicular to the boundary then the solution inside the superconductor may be shown to be

From here the physical meaning of the London penetration depth can perhaps most easily be discerned.While it is important to note that the above equations cannot be formally derived,
the Londons did follow a certain intuitive logic in the formulation of their theory.Substances across a stunningly wide range of composition behave roughly according to Ohm's law, which states that current is proportional to electric field.