Question
Derive the wave equation for the electric field in anisotropic non-conducting medium starting from Maxwell's equations.
Answer :
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Starting from Maxwell’s equations in a non-conducting medium with no free charges or currents, we have: [ \nabla \cdot \vec{D} = 0, \quad \nabla \cdot \vec{B} = 0, \quad \nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}, \quad \nabla \times \vec{H} = \frac{\partial \vec{D}}{\partial t}. ] In an anisotropic medium, the displacement vector (\vec{D}) and electric field (\vec{E}) are related by a tensor: [ \vec{D} = \epsilon \cdot \vec{E}, ] where (\epsilon) is the permittivity tensor. Also, (\vec{B} = \mu \vec{H}), and for non-magnetic media, (\mu \approx
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