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Equilibria of Point Charges on Nested Circles
| Content Provider | Semantic Scholar |
|---|---|
| Author | Giorgadze, Grigori Khimshiashvili, Giorgi |
| Copyright Year | 2015 |
| Abstract | We discuss a natural problem concerned with equilibrium configurations of Coulomb potential of three positive point charges constrained to a system of nested circles in the plane. After describing our approach in general setting, several concrete problems of such type are studied in detail. First, we consider a system of three concentric circles each of which contains exactly one charge, and give a complete description of configurations, which can serve as equilibria of three positive charges. Next, we give explicit formulae for the sought charges and obtain a geometric characterization of those configurations, which can serve as stable equilibria of three positive charges. Moreover, we obtain similar results in the case of three nested circles, which are not necessarily concentric and describe the topology of the set of equilibrium configurations. Several related problems and conjectures are also presented. © 2015 Bull. Georg. Natl. Acad. Sci. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://science.org.ge/newsite/bnas/t9-n3/06-Giorgadze.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
