Abstract
We study the interconnection between Physics and Mathematics in concrete instances, departing from the usual expression for the Coulomb electric field, produced by a point-like charge. It is scrutinized by means of six epistemology-intensive questions and radical answers are proposed, intended to widen one’s understanding of the subject. Our interventions act along two complementary directions. One of them regards ontology, since questions induce one to look closely at the electric charge, from different perspectives, promoting reflections about its nature and reinforcing the corresponding concept. Formal manipulations rely on the identification of concepts with symbols, and the other direction concerns the spatial extension of mathematical structures. Our questions and their somewhat unusual answers help disclosing information which is not present in many textbooks, and show that Mathematics can be used as an efficient epistemological tool in Physics teaching.
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Notes
Saci is pronounced Sah-see, the tonic syllable being the last one. The interested reader may find pictures and other information in the internet, under Saci Perere.
In a space with \(n\) dimensions, the surface of a sphere with radius \(r\) is given by \(S_n= r^{(n-1)}\; 2\, \pi ^{n/2}/\Gamma (n/2)\,\).
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Acknowledgments
We would like to thank Ricardo Karam for inducing this paper and for continuous encouragement during its preparation.
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Kneubil, F.B., Robilotta, M.R. Physics Teaching: Mathematics as an Epistemological Tool. Sci & Educ 24, 645–660 (2015). https://doi.org/10.1007/s11191-014-9727-5
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DOI: https://doi.org/10.1007/s11191-014-9727-5