Theory for measuring electric charge density of a ring from scanning force microscopy

We consider a ring that carries an arbitrary electric charge density in the presence of a scanning force microscopy tip. We propose an algorithm that predicts this charge density from knowledge of the electrostatic ring-tip contribution to the total scanning force microscopy force–distance curves. We first solve the direct electrostatic problem of finding the electrostatic forces by the ring on a scanning force microscopy conducting probe. These forces are in the pN and nN range and, therefore, measurable with current technologies. Finally, we describe a method based on the least squares minimization method to measure the charge on the ring.