In 1935, F. London and H. London described Meissner effect and zero resistivity by adding two conditions E=0(absence of Resistivity) and B=0(Meissner effect) to Maxwells Electromagnetic equations.
According to them, the applied field does not suddenly drop to zero at the surface of super conductor, but decays exponentially according to equation
B(x) = Bₐexp(-x/ƛ)
B(x) - Magnetic field at depth 'x' of material
Bₐ - Applied field; ƛ - penetration depth
Penetration depth is the length or depth from surface of metal at which the magentic field falls to 1/e of its original value.
Generally the magnetic field is likely to penetrate a superconductor to a depth of 10 - 100 nm.
Penetration depth doesn't have a fixed value but varies with temperature.
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