Dipole levitation force above a superconducting plane ($F_z$)

For a small fixed-current loop with moment $m=I\pi R^2$ and $R\ll h$, the image field gives upward force $3{\mu }_0{m}^2/(32\pi h^4)$. Differentiating the external field holds the image position fixed; moving both source and image in that derivative would double the force incorrectly.