Superconducting plane image dipole

A perpendicular magnetic dipole $m\hat{z}$ a height $h$ above an ideal flux-excluding plane has image $-m\hat{z}$ at $-h$. The exterior field has zero normal component at the plane. Images are a mathematical construction outside the physical solution domain.

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.