Consider the electromagnetic field in a linear medium with material properties [itex] \epsilon \ \ \text{and} \ \ \mu [/itex]. Calculate [itex] \nabla \cdot \mathbf{S} [/itex] for the energy flux [itex] \mathbf{S = E \times H} [/itex].(adsbygoogle = window.adsbygoogle || []).push({});

My work:

[tex] \nabla \cdot \mathbf{S} = \nabla \cdot \frac{1}{\mu}(\mathbf{E \times B }) [/tex]

[tex] = \frac{1}{\mu}[ \nabla \cdot(\mathbf{E \times B })] [/tex]

[tex] = \frac{1}{\mu}[\mathbf{B} \cdot(\nabla \times \mathbf{E} }) - \mathbf{E} \cdot(\nabla \times \mathbf{B} }) ] [/tex]

[tex] = \frac{1}{\mu}[\mathbf{B} \cdot(-\frac{\partial \mathbf{B}}{ \partial t}) - \mathbf{E} \cdot(\mu\epsilon\frac{\partial \mathbf{E}}{ \partial t})] [/tex]

I guess my question is: is this the result? I have no idea what this problem wants. Are there at least any more immediately obvious simplifications?

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# EM Problem

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