Title

En Electrostatics Problem on the Sphere Arising from a Nearby Point Charge

Document Type

Book Chapter

Publication Date

Winter 12-2014

Publication Source

Constructive Theory of Functions (K. Ivanov, G. Nikolov, and R. Uluchev, Eds.)

Inclusive pages

11-55

Publisher

Prof. Marin Drinov Academic Publishing House

Place of Publication

Sofia, Bulgaria

Peer Reviewed

yes

Abstract

For a positively charged insulated d-dimensional sphere we investigate howthe distribution of this charge is affected by proximity to a nearby positive or negative point charge when the system is governed by a Riesz potential. Of particular interest are those distances from the point charge to the sphere for which the equilibrium charge distribution is no longer supported on the whole of the sphere (i.e. spherical caps of negative charge appear). Arising from this problem attributed to A. A. Gonchar are sequences of polynomials of a complex variable that have some fascinating properties regarding their zeros.

Keywords

Electrostatics problem; Golden ratio; Gonchar problem; Gonchar polynomial; Plastic Number; Riesz potential, Signed Equilibrium; Sphere

Disciplines

Mathematics