Mystery of point charges after Gauss-Maxwell-Morse
Organizers
Vassily Manturov
, Shiquan Ren
,
Zhe Yan Wan
Speaker
Boris Shapiro
Time
Wednesday, July 3, 2024 3:30 PM - 5:00 PM
Venue
A3-2-301
Online
Zoom 831 5020 0580
(141592)
Abstract
In his 2 volume chef-d'oeuvre “Treatise of electricity and Magnetism” J.C.Maxwell (among thousands of much more important claims) formulated the following statement.
Given any configurations of N fixed point charges in R^3, the electrostatic field created by them has at most (N-1)^2 points of equilibrium.
Maxwell’s arguments are incomplete and this problem was considered much later by M.Morse and revitalised about two decades ago. However Maxwell’s original claim is still open already in case of N=3 charges. In my talk I will survey what is known in this direction and, in particular, formulate a calculus 1 problem which currently still remains unsolved.
Given any configurations of N fixed point charges in R^3, the electrostatic field created by them has at most (N-1)^2 points of equilibrium.
Maxwell’s arguments are incomplete and this problem was considered much later by M.Morse and revitalised about two decades ago. However Maxwell’s original claim is still open already in case of N=3 charges. In my talk I will survey what is known in this direction and, in particular, formulate a calculus 1 problem which currently still remains unsolved.