In 1935, the brothers Fritz and Heinz London described superconductivity using a phenomenological constitutive equation where a length δ > 0 relates the current density to the Coulomb vector potential:

(a) Use the London constitutive equation to derive a differential equation for B(r).
(b) The London theory predicts that B is not strictly zero at every point inside a superconductor. To see this, consider a slab of superconductor which is infinite in the x- and y-directions and lies between z = −d and z = d. Compute B(z) inside the superconductor when the slab is placed in a static and uniform magnetic field B₀ = B₀ x̂.
(c) Find the current density inside the superconductor.

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j= 1 Hode A.