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By Taubes C.H.

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99)  We shall come back in length to this point in Chapter 9, which will be devoted to the effects of coherence. 2 - LONDON THEORY 45 Appendix 2A Total and partial derivatives with respect to time Let us consider the movement of a fluid such as water where each elementary particle moves with a velocity v(r, t) that depends on its position and the time. Let r0 be the position of a particle at time t0 and (r0  dr) its position at time (t0  dt). Clearly we have dr  v(r0, t0) dt. 100) Fm . dt This change in velocity dv can be divided into two terms: » as the fluid changes in time, the velocity of particles located at r0 at time t0  dt v  v  dt  that of particles located at r0 at time t0.

32 SUPERCONDUCTIVITY Such an increase in the field near the surface was proved by OCHSENFELD by inserting a magnetic flux-meter between two superconducting samples separated by a small gap and subject to a uniform B0 (Fig. 11). » When T  Tc: the metal is normal and the magnetic field uniform everywhere: the measured flux equals n  B0S. » When T  Tc: the metal becomes superconducting, the field lines “avoid” the samples and the magnetic field strengthens in the gap between them. The measured flux s becomes larger than n.

While the magnetic state of the “perfect conductor” depends on its history (compare Fig. 4a), the magnetic state of the superconductor does not (compare Fig. 4c). 4 - The LONDON equations As experimental results showed that MAXWELL’s equations were insufficient to describe the magnetic state of the superconductor, additional equations had to be added. These were originally written on intuitive grounds and are known as the LONDON equations. 1 - “Superconducting electrons” Up to now the electrons that we have considered are implicitly the mobile electrons of the metal, that is to say all its free electrons.

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