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...

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Bibliographic Details
Published in:American journal of physics 2023-08, Vol.91 (8), p.629-636
Main Authors: Costa, Alexandre P., Queiroz, Lucas, Nogueira, Edson C. M., Alves, Danilo T.
Format: Article
Language:English
Subjects:
Electromagnetism
Electrostatics
Mathematical models
Poisson distribution
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Summary: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.
ISSN:0002-9505
1943-2909
DOI:10.1119/5.0099928