A Superconductor Analogue of the Thompson-Lampard Theorem of Electrostatics and its Possible Application to a New SI Standard of DC Resistance

The magnetostatics of cylindrical superconductors with parallel axes is formally analogous to the electrostatics of cylindrical normal conductors of the same geometry, provided that the London penetration depth can be neglected. This analogy when applied to the Thompson-Lampard theorem of electrostatics, which forms the basis of the calculable capacitor, leads to a method of deriving an SI standard of dc resistance, R 0 , given by R 0 = μ 0 c (π/log 4) ( f J / f opt ) ( n fr / n fq ), where μ 0 c is the impedance of vacuum, f J is the Josephson frequency of the voltage across the potential terminals of R 0 , f opt is the optical frequency of an interferometer light source, n fr is an optical interferometer fringe count and n fq is a SQUID flux-quantum count. This paper gives the theory of the method, and offers some further theoretical results that point to the practical feasibility of the standard.