Graduation Year
2008
Document Type
Thesis
Degree
M.A.
Degree Granting Department
Mathematics and Statistics
Major Professor
Dmitry Khavinson, Ph.D.
Committee Member
Catherine Beneteau, Ph.D.
Committee Member
Yuncheng You, Ph.D.
Keywords
Potential theory, Electrostatics, Bezout's Theorem, Algebraic curves, Harmonic functions
Abstract
This paper deals with approximating an upper bound for the number of equilibrium points of a potential field produced by point charges in the plane. This is a simplified form of a problem posed by Maxwell [4], who considered spatial configurations of the point charges. Using algebraic techniques, we will give an upper bound for planar charges that is sharper than the bound given in [6] for most general configurations of charges. Then we will study an example of a configuration of charges that has exactly the number of equilibrium points that Maxwell's conjecture predicts, and we will look into the nature of the extremal points in this case. We will conclude with a solution to the twin problem for the logarithmic potential, followed by a discussion of the conditions necessary for a degenerate case in the plane.
Scholar Commons Citation
Killian, Kenneth, "Maxwell’s Problem on Point Charges in the Plane" (2008). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/333
