# The Generalized Symmetric Form of Maxwell's Equations

For a linear, homogeneous and isotropic medium, the time-harmonic, symmetric form of Maxwell's equations, i.e., the form in which both electric and fictitious magnetic charges and currents are taken into account, can be written as follows:

$\mathrm{\nabla}\times \overrightarrow{E}=-j\omega \mu \overrightarrow{H}-\overrightarrow{M},$

(A.1)

$\mathrm{\nabla}\times \overrightarrow{H}=j\omega \epsilon \overrightarrow{E}+\overrightarrow{J},$

(A.2)

$\mathrm{\nabla}\cdot \overrightarrow{E}=\frac{1}{\epsilon}{\rho}_{e},$

(A.3)

$\mathrm{\nabla}\cdot \overrightarrow{H}=\frac{1}{\mu}{\rho}_{m}.$

(A.4)

Note that $\overrightarrow{M}$ and ${\rho}_{m}$ are the fictitious magnetic surface current and charge density, ...

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