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I have encountered a statement that upon existence of magnetic monopoles, the equation $$\nabla \times \textbf{E} = -\partial_t \textbf{B}$$ must be modified.

I only see that the last equation $$\nabla \cdot \textbf{B} =0$$ should be modified, but not the first equation. Can someone shed some light on it?

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  • $\begingroup$ Hint: The magnetic charges must satisfy a continuity equation. $\endgroup$
    – Qmechanic ♦
    Commented Oct 19, 2019 at 20:20

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The first equation needs a term to account for the magnetic current density, since the introduction of monopoles admits the possibility that they can move - producing a current.

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