The Simon et al . paper is particularly approachable for someone as mathematically challenged as I am. The papers are important souces for this poster and present most of the information with more rigor and detail. The poster intends to serve as a qualitative appetizer to the Berry and the Simon et al. papers by providing pictures to illustrate the conditions for vertical and horizontal stability. The force from an infinite base would be zero. As an inverted vertical top falls toward a disk-shaped base on axis, the force opposing gravity increases to a maximum then falls to zero , as the base begins to look effectively infinite.
Force is maximum at a height equal to half the base radius.
A top of small enough mass will float at an appropriate level above the height of maximum force where vertical repulsion balances gravity. If the top drifts left, its footprint loses a small crescent from the rim of the base magnet. But the top gains an equivalent crescent of the base magnet at the right, further from the top's axis and outside the original footprint. An inverted dipole interacts most favorably with base elements that are at a radius equal to twice the dipole's height Base elements near the top's axis raise the energy. Note that radial distance is measured in units of the height of the top.