# Reformulation of Maxwell's equations in the event of finding a magnetic monopole

If we ever obtain empirical confirmation of the existence of magnetic monopoles, how would Maxwell's classical equations be re-written? I'm assuming we'd only need to set the divergence of the magnetic field equal to some nonzero density as is the case with the electric field, but would there be something else we'd need to change? Would there be some sort of term we would be missing, such as was the case with the displacement current, which was initially missing in the equations?

The existence of magnetic monopoles and therefor magnetic charge density and magnetic current density would mean that Maxwell's equations would become more symmetric. If we use the standard $$\rho$$ and $$\vec{J}$$ for the electric charge and current density, and $$\eta$$ and $$\vec{K}$$ for the magnetic charge and current density, Maxwell's equations would be $$\nabla\cdot \vec{E}=4 \pi \rho$$ $$\nabla \cdot \vec{B}=4 \pi \eta$$ $$\nabla \times \vec{E}=-\frac{4 \pi}{c}\vec{K}-\frac{1}{c}\frac{\partial \vec{B}}{\partial t}$$ $$\nabla \times \vec{B}=+\frac{4 \pi}{c}\vec{J}+\frac{1}{c}\frac{\partial \vec{E}}{\partial t}$$