Critical field of thin films (a) Using the result of Problem lb, show that the free energy
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Critical field of thin films
(a) Using the result of Problem lb, show that the free energy density at T = 0 K within a superconducting film of thickness δ in an external magnetic field Ba is given by, for δ << A, (CGS) FS (x, Ba) = US (0) + (δ2 – 4x2) B2a/64πλ2. In SI the factor π is replaced by ¼μ0. We neglect a kinetic energy contribution to the problem.
(b) Show that the magnetic contribution to FS when averaged over the thickness of the film is B2a (δ /λ)2/96π.
(c) S how that the critical field of the thin film is proportional to (λ/δ) Hc, where Hc, is the bulk critical field, if we consider only the magnetic contribution to US.
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