Introducing corrugated surfaces in electrostatic problems via a perturbative approach

In electromagnetism courses, students often solve Poisson's equation for a point charge in the presence of an infinitely large perfectly conducting planar surface, usually by the method of images. However, no surface is perfectly flat; so at some level, corrugations must be introduced to model the real world. Clinton et al. [Phys. Rev. B 31, 7540 (1985)] solved the problem, including corrugations, using a perturbative calculation of the corresponding Green's function. We provide a detailed pedagogical review of this calculation and extend it in order to solve for the electrostatic potential of a corrugated neutral conducting cylinder in the presence of a uniform electric field. These calculations can be used as pedagogical examples of this perturbative approach in electromagnetism courses.