2. Wave equation
After introducing the constitutive relations, Maxwell's equations involve at least the sources and two field quantities. By performing relatively simple manipulations on the operators, it is possible to eliminate one of the fields and obtain a wave equation. However, when there are source distributions in the computational volume, it is not possible to reduce these equations in this form, without introducing the potentials.
Let's consider a linear, isotropic, homogeneous medium with no charge distributions (note that by virtue of the charge conservation law
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Wave equation