En Electrostatics Problem on the Sphere Arising from a Nearby Point Charge
Constructive Theory of Functions (K. Ivanov, G. Nikolov, and R. Uluchev, Eds.)
Prof. Marin Drinov Academic Publishing House
Place of Publication
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.
Electrostatics problem; Golden ratio; Gonchar problem; Gonchar polynomial; Plastic Number; Riesz potential, Signed Equilibrium; Sphere
Johann S. Brauchart, Peter D. Dragnev, and Edward B. Saff (2014).
En Electrostatics Problem on the Sphere Arising from a Nearby Point Charge. Constructive Theory of Functions (K. Ivanov, G. Nikolov, and R. Uluchev, Eds.). 11-55. Sofia, Bulgaria: Prof. Marin Drinov Academic Publishing House.