Proving Symmetry of Modified Maxwell Equations

AI Thread Summary
The discussion centers on the modification of Maxwell's equations to include magnetic monopoles, specifically the equations for divergence and curl involving magnetic charge density and current. Participants express the need to prove the correctness of these modified equations, emphasizing the role of symmetry in deriving them. There is a consensus that theoretical derivation alone may not suffice without considering the experimental basis of Maxwell's equations. The divergence equation is identified as defining "magnetic charge," while the curl equation is linked to the continuity of magnetic charge. The conversation highlights the interplay between theoretical mathematics and empirical laws in physics.
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If there were magnetic monopole, the Maxwell equations should be modified as

<br /> \nabla\cdot\vec{B} = \mu_0\rho_m<br />

<br /> \nabla\times\vec{E} = - \frac{\partial \vec{B}}{\partial t} - \mu\vec{J}_m<br />

and plus the other two.

I wonder how to prove these two modified equations are of correct form? Someone told me they should be of those form because of symmetry. I would like to prove that mathematically but have no way to start ...
 
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Em,I think it's not possible by just derive theoretically and do not use the idea of symmetry,because Maxwell equations themselves are mathematical summaries of experimental laws,right?
 
The divB equation is the definition of "magnetic charge".
The curl E follows from the continuity equation for magnetic charge.
 
"magnetic charge density", to be exact.
 
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