Constraints for electric charge from Maxwell's equations and boundary conditions

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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.
Original languageEnglish
Article number035502
Number of pages16
JournalPhysica Scripta
Issue number3
Early online date1 Feb 2022
Publication statusPublished - 10 Feb 2022


  • electric charge
  • Maxwell's equations
  • boundary conditions
  • boundary constraints
  • electromagnetic field


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