Monday, 23 May 2016

electromagnetism - Why does the divergence of the Poynting vector have energy flux density?


The poynting vector is defined as




$\vec{S}=\mu_{0}^{-1}\vec{E}\times \vec{B}$



Taking the divergence of the poynting vector, one arrives at



$\vec{\nabla} \cdot \vec{S}=-\frac{\partial u}{\partial t}=0$



after some algebraic manipulation.


Note $u$ is the electromagnetic energy density.


The claim is that the $\vec{\nabla} \cdot \vec{S}$ is an energy flux density.


How do I see this is true?



Thanks in advance.




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