What would have been the Maxwell's equations if there were magnetic monopoles?

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SUMMARY

The discussion centers on the implications of magnetic monopoles in the differential forms of Maxwell's equations. It asserts that the divergence of the magnetic field, traditionally zero, would instead relate to magnetic charge density divided by permeability of free space. Additionally, the participants question the validity of Faraday's law in the context of magnetic monopoles, suggesting a need for reevaluation of the equations. Heaviside's rendition of Maxwell's equations is referenced, highlighting the normalization of magnetic charge post-calculation.

PREREQUISITES
  • Understanding of Maxwell's equations in differential form
  • Familiarity with magnetic charge density concepts
  • Knowledge of Heaviside's modifications to Maxwell's equations
  • Basic principles of Dirac theory and magnetic monopoles
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  • Research the implications of magnetic monopoles on Maxwell's equations
  • Study Heaviside's original vector form of Maxwell's equations
  • Explore Dirac theory and the conditions for magnetic monopole creation
  • Investigate the relationship between magnetic charge density and permeability of free space
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Physicists, electrical engineers, and students of electromagnetism interested in advanced theoretical concepts related to magnetic monopoles and their effects on classical electromagnetism.

roshan2004
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I am specifically talking about differential forms of Maxwell's equations here-
I think ( Tell me if I am incorrect here...) since the divergence of the magnetic field is zero, we have to say it is incorrect for my above problem, so the equation should have been the divergence of magnetic field is magnetic charge density divided by what ? ( Is it the permeability of free space ?)
Also, I think ( not too sure) the faraday's law: \frac{-\partial B}{\partial t} is also incorerct here- but I am not sure why is it and what should have been the equation for the above condition ?
 
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Heaviside's original rendition of the "Maxwell Equations" in vector form is expressed where a magnetic charge may be present. In his usage, he would normalize away the charge after the bulk of the calculations for any particular problem were done.

A charge, in Maxwell's theory is a more general concept than monopole, if by monopole you mean point singularity. A charge is a discontinuity of polarization and may therefore be a point, line segment, line or surface.

In Dirac theory and in related theories such as the Harmuth ansatz, the magnetic monopole or charge is not necessarily a persistent object. It can be created and evaporated in a very short period of time under certain conditions.
 

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