FIG. 1: Bottom: Magnetogravitational potential U ( x, z ) of a water droplet levitated by the mag- netic field B ( x, z ) of a vertical-bore superconducting solenoid magnet (contours at Δ U/g = 0.05 mm intervals); x and z are radial and vertical cylindrical coordinates, respectively, with origin at the geometric center of the solenoid. The field at the center of the solenoid is B$_{0}$ = B (0 , 0) = 16 . 5 T. The field profile B ( x, z ), used to construct the plot, was computed by numerical integration of the Biot Savart integral. The stable levitation point at a local minimum in the potential is labeled L$_{0}$ . An unstable levitation point at a saddle-point in the potential is labeled L$_{1}$ . Top: schematic of the experimental set-up. The magnetic field lines are shown in gray. Rays are shown as bold lines. Fig. 1 shows a spatial map of the magnetogravitational potential of a unit mass of water in the potential trap, where x and z are radial and vertical cylindrical coordinates with origin at the geometric center of the solenoid coil, χ = − 9 × 10 − 6 and ρ = 1 × 10 3 kgm − 3 are the SI volume magnetic susceptibility and density of water respectively, 3 U ( x, z ) = gz − χB $^{2}$( x, z ) 2 ρµ$_{0}$ (2) −20 −15 −10 −5 0 5 10 15 20 55 60 65 70 75 80 85 90 95 100 x  (mm) z  (mm) L 1 L 0