Charge and size of a ring in an electrolyte with atomic force microscopy

We study the interaction force between a ring with a dipole density and the tip of an Atomic Force Microscope. Given the vector nature of a dipole we study the force for all possible dipole orientations. These results are applied to the practical problem of a charged ring electrically partially shielded by ions in an electrolyte. We provide theoretical tools to analyze experiments and extract parameters such as the charge and size of the ring, the screening, and the Debye length.