7. Superconductivity - University of Liverpool

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Vector potential In order to use the vector potential, lets review its meaning. It is defined by ∇ × A = B, where B is the magnetic field. This a bit similar to relation between the electric field and electric potential. http://en.wikipedia.org/wiki/Magnetic_potential For a qualitative understanding, the integral form of this equation is sufficient: ∫C A.dl = ∫ S B.dS, where the left integral is along any loop C, and and the right integral is over any surface S enclosed by the loop. Superconductivity 17
Ampere’s law. The right side of this equation is the magnetic flux Φ, ∫C A.dl = ∫ S B.dS and the left side is the line integral for magnetic potential. If we make the following replacements: A → B and B → J, where J is the current density, we get Ampere’s law. In the more familiar Ampere’s law, the electric current is related to the integral of magnetic field over a loop round the current. In the same way, the equation ∫ C A.dl = Φ tells us that magnetic flux is equal to the integral of vector potential over a loop round the flux. Superconductivity 18
Page 1 and 2: Statistical and Low Temperature Phy
Page 3 and 4: Resistance, magnetic field and heat
Page 5 and 6: Examples of superconductors. http:/
Page 7 and 8: Measuring magnetic field. This grap
Page 9 and 10: Heat capacity. Recall the heat capa
Page 11 and 12: If we select the normal conducting
Page 13 and 14: Explanation using macroscopic wavef
Page 15 and 16: Lenz’s law. According to Lenz’s
Page 17: Macroscopic wavefunction. We shall
Page 21 and 22: ∫ ∆φ = m ∫L v.dl + q A.dl. L
Page 23 and 24: Meissner effect. According to Farad
Page 25 and 26: London’s penetration depth. Flux
Page 27 and 28: London penetration depth Assuming t
Page 29 and 30: Integrating the current along a cir
Page 31 and 32: Combining with the solenoid formula
Page 33 and 34: Vortices. In the lectures on superf
Page 35 and 36: Likewise, Essmann and Trauble sprin
Page 37 and 38: Type II superconductors. This shows
Page 39 and 40: Flux measurement. Deaver and Fairba
Page 41 and 42: In the case of the superfluid, no m
Page 43 and 44: So if we choose the loop L away fro
Page 45 and 46: Cooper pairs Superconductivity 44
Page 47 and 48: The Isotope Effect. If electrons re
Page 49 and 50: How electrons “attract” When a
Page 51 and 52: Cooper pair in real space The wavef
Page 53 and 54: Energy gap. As an example of a pred
Page 55 and 56: BCS superfluid. The most obvious pr
Page 57 and 58: Cooper pair The average charge in a
Page 59 and 60: When a lattice vibrates the maximum
Page 61 and 62: This is also the length, or extent,
Page 63 and 64: It has an energy 2E F − ∆, wher
Page 65 and 66: Applications of superconductors Sup
Page 67 and 68: Maglev train. A train can be levita
Page 69 and 70:
Particle accelerators Particle acce
Page 71 and 72:
High Temperature Superconductors In
Page 73:
Applications? Using these high temp
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7. Superconductivity - University of Liverpool

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