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Undergraduate students in upper levels of physics or engineering programs learn the theory of Fourier series and integral transform method from mathematics courses. Nevertheless, they rarely see the application of such a method to solving problems in calculus-based physics courses that deal with topics such as electrostatics or magnetism. In this work, we illustrate the utility of the Fourier transform method by considering and solving via such a technique a representative problem that arises in electrostatics. The chosen case study is that of a spherical surface with uniform surface charge density and the calculation of its electrostatic Coulomb self-energy. By solving this problem by using the Fourier transform technique we also draw attention to the pedagogical aspects of the treatment. In particular, we stress the point that the Fourier transform method should be treated at more depth in calculus-based physics courses for undergraduate students.
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Coulomb self-energy of a solid hemisphere with uniform volume charge density
Calculation of the Coulomb self-energy of a solid hemisphere with uniform volume charge density represents a very challenging task. This system is an interesting example of a body that lacks spherical symmetry though it can be conveniently dealt with in spherical coordinates. In this work, we explain how to calculate the Coulomb self-energy of a solid hemisphere with uniform volume charge density by using a method that relies on the expansion of the Coulomb potential as an infinite series in terms of Legendre polynomials. The final result for the Coulomb self-energy of a uniformly charged solid hemisphere turns out to be quite simple.
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- Award ID(s):
- 2001980
- PAR ID:
- 10480194
- Publisher / Repository:
- World Scientific
- Date Published:
- Journal Name:
- Modern Physics Letters B
- Volume:
- 37
- Issue:
- 14
- ISSN:
- 0217-9849
- Page Range / eLocation ID:
- 2350018
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1142/S0217984923500185
