Open AccessConstraints for electric charge from Maxwell’s equations and boundary conditions
Author(s) -
Robert P. Cameron
Publication year - 2022
Publication title -
physica scripta
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.415
H-Index - 83
eISSN - 1402-4896
pISSN - 0031-8949
DOI - 10.1088/1402-4896/ac50c7
Subject(s) - physics , maxwell's equations , boundary (topology) , charge (physics) , electric field , consistency (knowledge bases) , boundary value problem , electric charge , magnetic monopole , classical mechanics , electromagnetic field , quantum electrodynamics , universe , magnetic field , charge conservation , theoretical physics , mathematical analysis , quantum mechanics , mathematics , geometry
Certain boundary conditions constrain the forms that the electromagnetic field can take in a theory, in particular the boundary conditions inherent to closed spaces. According to Maxwell’s equations, this can give rise to constraints for the electric charge in the theory. We identify three such ‘boundary constraints’ for electric charge and highlight some of their myriad implications, touching upon a wealth of topics including the self-consistency of practical calculations, the nature of dark matter, the origin of electric-charge quantisation and the shape of the Universe. Furthermore, we explain that magnetic analogues of our boundary constraints offer new insights into the possible existence of magnetic monopoles and dyons.