Determining electric charge from atomic force microscopy

The use of the method of images in electromagnetism is elegant but often perceived as a formal exercise. To motivate its relevance, we apply it to evaluate the force between a sensor and a charged sample in an Atomic Force Microscopy (AFM) configuration. The problem is motivated by work in AFM, where the measurement of charge is an ongoing research topic. While the problem of measuring charge involves substantial technical and theoretical difficulties, here we present a minimalist model that is amenable to a simple but nontrivial solution.