Levitating a spinning magnetic top above an air coil

摘要

We study the levitation of a spinning magnetic top above an air coil carrying a DC current. On the theoretical side we carry out an optimizing process for the geometry of the coil that minimizes the power consumption for a given hovering height, h, and a given top. We find that for a rectangular cross-section coil, carrying a uniform current density the normalized dimensions of the optimum coil are: d/h=0.83, R/sub 1//h=1.85 and R/sub 2//h=4.2 where d, R/sub 1/ and R/sub 2/ are the thickness, inner radius and outer radius of the coil in [cm], respectively. For this specific coil the power itself is given in [Watts] by P=A/spl rho/g/sup 2/h/sup 3///spl sigma//sup 2/. Here, A=2720 [Amp/sup 2/ emu/sup 2//erg/sup 2/ cm/sup 2/], /spl rho/ is the coil's resistivity in [/spl Omega/ cm], g is the free fall acceleration in [cm/sec/sup 2/] and /spl sigma/ is the magnetization per unit mass of the top in [emu/gr]. A similar optimizing scheme is done for a semi-infinite coil. We look for the optimal distribution of the current density so as to minimize the power consumption. In this case we show that A=491[Amp/sup 2/ emu/sup 2//erg/sup 2/ cm/sup 2/]. On the experimental side we hovered the top above two different coils with measurements in reasonable agreement with the calculation.