 Gravity-equivalent magnetic surface density

For an isolated razor-thin disk, rescale its exterior magnetic scalar potential to satisfy $\sqrt{4\pi G/{\mu }_0}\mathbf{B}=-\nabla {\Phi }_M$. Comparing the normal magnetic boundary derivative with ${\partial }_z\Phi =2\pi G\Sigma$ identifies the displayed equivalent signed surface density. Both exterior potentials satisfy Laplace's equation. The equivalent surface density is a representation of the magnetic boundary data, rather than physical negative mass.