  Problems involving boundary conditions on corrugated surfaces are relevant to
understand nature, since, at some scale, surfaces manifest corrugations that
have to be taken into account. In introductory level electromagnetism courses,
a very common and fundamental exercise is to solve Poisson's equation for a
point charge in the presence of an infinity perfectly conducting planar
surface, which is usually done by image method. Clinton, Esrick and Sacks
[Phys. Rev. B 31, 7540 (1985)] added corrugation to this surface, and solved
the problem by a perturbative analytical calculation of the corresponding
Green's function. In the present paper, we make a detailed pedagogical review
of this calculation, aiming to popularize their results. We also present an
original contribution, extending this perturbative approach to solve the
Laplace's equation for the electrostatic potential for a corrugated neutral
conducting cylinder in the presence of a uniform electric field (without
corrugation, this is another very common model considered as an exercise in
electromagnetism courses). All these calculations can be used as pedagogical
examples of the application of the present perturbative approach in
electromagnetism courses.
