2016 | OriginalPaper | Buchkapitel
On Maxwell’s Conjecture for Coulomb Potential Generated by Point Charges
Autoren: Alexei Yu. Uteshev, Marina V. Yashina
Verlag: Springer Berlin Heidelberg
Erschienen in:
Transactions on Computational Science XXVII
Abstract
The problem discussed herein is the one of finding the set of stationary points for the Coulomb potential function \( F(P)=\sum _{j=1}^K m_j / |PP_j | \) for the cases of \( K=3 \) and \( K=4 \) positive charges \( \{m_j\}_{j=1}^K \) fixed at the positions \( \{P_j\}_{j=1}^K \subset \mathbb R^2 \). Our approach is based on reducing the problem to that of evaluation of the number of real solution of an appropriate algebraic system of equations. We also investigate the bifurcation picture in the parameter domains.
