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Four coplanar superconducting strips: flux-focusing effects and inductance

We present analytic solutions for the Meissner-state magnetic-field and current-density distributions for four long parallel coplanar superconducting strips carrying subcritical currents in a perpendicular magnetic field when there is no net magnetic flux through the two slots between the outermost strips. We make use of these solutions to investigate the flux-focusing effect; i.e., we calculate how much magnetic flux per unit length is focused into the central slot when the strips are in a perpendicular magnetic field Ha = Ba/μ0 and the outermost pairs of strips carry no net current. We also calculate the inductance per unit length of the system when the net current flowing in the two right strips is equal in magnitude and but opposite in direction to the net current flowing in the two left strips. We show that for narrow superconducting strips mutual-inductance calculations based on exact results for two strips provide good approximations to our exact results for four strips.