= Diamagnetic levitation in an inverse-height field
{title2=$z_0^3=-\chi(B_0r_0)^2/(\mu_0\rho g)$}
A small weakly susceptible <sphere> has induced <magnetic energy> $-\chi VB^2/(2\mu_0)$ and vertical <force> $\chi VBB'/\mu_0$. In field magnitude $B=B_0r_0/z$, balancing <gravity> gives the title height for $\chi<0$. The vertical <force> varies as $z^{-3}$, giving a restoring derivative at that equilibrium. Three-dimensional trapping cannot be established from an axial field magnitude alone; lateral field geometry and Maxwell constraints also matter.
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