Levitating a spinning magnetic top above an air coil

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 ₁/h=1.85 and R₂/h=4.2 where d, R₁ and R 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=Aρg²h³/σ² . Here, A=2720 [Amp² emu²/erg² cm ²], ρ is the coil´s resistivity in [Ω cm], g is the free fall acceleration in [cm/sec²] and σ 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[Amp² emu² /erg² cm²]. On the experimental side we hovered the top above two different coils with measurements in reasonable agreement with the calculation