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Problems involving boundary conditions on corrugated surfaces are relevant tounderstand nature, since, at some scale, surfaces manifest corrugations thathave to be taken into account. In introductory level electromagnetism courses,a very common and fundamental exercise is to solve Poisson's equation for apoint charge in the presence of an infinity perfectly conducting planarsurface, which is usually done by image method. Clinton, Esrick and Sacks[Phys. Rev. B 31, 7540 (1985)] added corrugation to this surface, and solvedthe problem by a perturbative analytical calculation of the correspondingGreen's function. In the present paper, we make a detailed pedagogical reviewof this calculation, aiming to popularize their results. We also present anoriginal contribution, extending this perturbative approach to solve theLaplace's equation for the electrostatic potential for a corrugated neutralconducting cylinder in the presence of a uniform electric field (withoutcorrugation, this is another very common model considered as an exercise inelectromagnetism courses). All these calculations can be used as pedagogicalexamples of the application of the present perturbative approach inelectromagnetism courses.

Introducing corrugated surfaces in electromagnetism problems via perturbative approach