Impossible Magnetic-Field Self-Patterning

Abstract

THE ‘self-sustaining’ Corbino disk recently proposed¹ is suspect. It was suggested that an axial magnetic field could Hall-deflect from an impressed radial current the azimuthal current just necessary for its existence. Inside, or axis side (outside, respectively), of an elemental current ring, its field contribution has indeed the sense of the field responsible for the ring, for inward (outward) motion of the dominant carriers. Outside (inside) the ring, however, its contribution is counter-sense to the field at the ring. This crucial embarrassment makes it difficult to imagine any finite, that is, physical, possibility for field self-patterning.