A Note on Three Collinear Point Charges

We review and complement some recent results concerned with the Maxwell’s conjecture for three point charges. In particular, we prove that any triple of collinear points can be endowed with non-zero charges such that the arising triple of point charges is an equilibrium configuration of saddle type in the ambient line. Next, we show that Maxwell’s conjecture holds true for certain configurations of three collinear point charges arising in this way, which complements an analogous result proven by Y.-L.Tsai for three charges of equal magnitudes. Several generalizations and open problems are also presented.