## Magnetic Torque on a Rotating Superconducting Sphere |

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0r cosh 0r sinh 3M A A angle arbitrary magnetic field boundary condition characteristic distance choose z parallel classical electrodynamics coherence length Cooper pair coordinate system cos0 cos0 cosft cos0 cosh 0r curl curl h current distribution current loop diamagnetic dipole electrons excess charge FL(r gyro hole Image method infinite superconducting plane integral j3r cosh j3r j3R sinh j3Rj j3Rsinhj3R Legendre polynomials London field London theory macroscopic magnetic induction Marshall Space Flight niobium order in X/R order X/R parallel to Bq penetration depth Pg(cos0 point dipole/infinite r x r x z radius readout loop result rotating sphere rotating superconducting sphere rotor scalar potential Section IIIB sin0 sin0 sinft cos0 sinft sin0 cos0 sinh 0(RQ sinh 0r sinh j3r solutions Space Flight Center spherical harmonics spin axis superconducting shield superconducting sphere rotating theorem uniform applied field uniform field X2 curl curl