Stellar-mass objects orbiting massive black holes are an important source of waves for space-based gravitational wave detectors, such as LISA. Although there has been substantial progress in computing these waveforms, the methods used have required considerable technical machinery and the results are somewhat non-intuitive. Calculations in this area have also taken on a life of their own and often branch into a host of related questions, such as computing the forces acting on electric or scalar charges orbiting a black hole. Thinking of the orbiting particle as a charge offers a fresh way of visualizing the problem: How do the field lines emanate from the charge? Does the background curvature wrench the field lines and create a force on the charge. How do the field lines attach to the horizon? If the charged particle is infinitesimally small, how do we deal with the infinite fields near the particle? I will present a fundamentally new approach to this problem using the method of image charges. This approach makes the forces easier to visualize and restores an intuitive understanding of the origin of the forces. To make the talk accessible to non-specialists, I will make a clear connection between this new work in curved spacetime and the method of images we use in elementary electrostatics.