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electrically charged balls confined to a plane: a 2-d model system

Reference List

  1. J. A. Ewing, Proc. Roy. Soc. [London] 48, 342 (1890); Phil. Mag. 30, 205 (1890)] Ewing was the first to deduce the origin of hysteresis and magnetic remnance by analogy with a square array of gimbled magnets.
  2. L. Bragg, J. Sci. Instr. 19, 148 (1942); L. Bragg and J. F. Nye, Proc. Roy. Soc. A190, 474 (1947); L. Bragg and W. M. Lomer, Proc. Roy. Soc. A196, 171 (1949). Bragg and Nye's elegant experiments on bubble rafts, illustrated (among other effects) dislocation movement in solids
  3. A. C. Rose-Innes and E. A. Stangham, Cryogenics 9, 456 (1969)
  4. H. Meissner, Cryogenics 14, 36 (1974)
  5. Bragg (1947) refers to earlier, unnamed work on crystal model systems. These included magnets on corks floating on water, and floating disks attracted by capillary action
  6. see ref 5.
  7. Pawel Pieranski, Contemp. Phys. 24, 25 (1983)
  8. E.J. Yarmchuk, M.J.V. Gordon and R.E. Packard, Phys. Rev. Lett. 43, 215 (1979)
  9. L. J. Campbell and Robert Ziff, Los Alamos Scientific Lab Report LA-7384-MS, 1979

Professor McBride of Yale points out that "experiments described in J.J. Thomson, Chapter VI of "The Corpuscular Theory of Matter", (1907) with magnetized needles in floating corks discovered additional meta-stable states. His tables of "the various rings for corpuscles" is based on his previously published mathematical analysis (Philosophical Magazine, Series 6, Volume 7, Number 39 March 1904, p. 237-265) for a set of negatively charged corpuscles held within a sphere of equivalent uniform positive charge (related to what came to be called the "plum pudding" atom).  For solvability he assumed that the corpuscles were constrained to a plane within the sphere.

He then compared his analytical results with those from experiments with floating corks "a method introduced for a different purpose by an American physicist, Professor Mayer," and for iron spheres floating in mercury and induced by a large magnet placed above them (R. W. Wood).  He also refers to Monckman's electrostatic analogue using vertically floating needles "electrified by induction by a charged body held above the surface of the water."  He states that in all cases the two-dimensional patterns are "analogous", whatever that means. (He gives no specific literature references in the book) ".

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