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Are those two terms the same, or...? My book says that the Poynting vector is an energy flux density given by:

$$\mathbf{S} = \frac{1}{\mu_{0}}(\mathbf{E} \times \mathbf{B})$$

So that alone should indicate that it's not the same thing. But I've been looking through my book, and every time I look up energy density, not flux, it points me in the direction of the Poynting vector.

So, are they the same, and if not, what is the energy density given by?

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up vote 3 down vote accepted

The energy density (energy per unit volume) of electromagnetic fields in vacuum is given by $\frac{1}{2}(\varepsilon_0 E^2+B^2/\mu_0)$. The Poynting flux is different: it is the flux of that energy passing through some surface (energy per unit surface per unit time). You can see it as the rate at which the energy is displaced.

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So even though fields have direction, you just use the magnitude of the fields, and ignore the field direction ? –  Denver Dang May 26 '13 at 21:52
    
@DenverDang $E^2 = \vec{E} \cdot \vec{E}$ is a scalar. Likewise with $B^2$. The energy density does not have a direction. $\vec{E} \times \vec{B}$ on the other hand does have direction... –  dmckee May 26 '13 at 21:59
    
Yup, just saw that :) My mistake. And thank you :) –  Denver Dang May 26 '13 at 22:04
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