Abstract
In this article, we will approximate an upper bound for the number of critical points of a potential field produced by co-planar point charges. This is a simplified form of a problem posed by Maxwell [J.C. Maxwell, A Treatise on Electricity and Magnetism, Vol. 1 (Republication of the 3rd revised edition), Dover Publications, Inc., New York, 1954.], who conjectured an upper bound on the number of critical points of 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 [A. Gabrielov, D. Novikov, and B. Shapiro, Mystery of point charges. Proc. Lond. Math. Soc. (3) 95(2) (2007), pp. 443–472.], but in a much more restricted case.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
