How Does Poynting's Theorem Explain Ohmic Loss?

[yungman]

Poynting Theorem:

$$\frac {dW}{dt} \;=\; \int _{v'} (\vec E \cdot \vec J) d \vec {v'} \;=\; -\frac 1 2 \frac {\partial}{\partial t} \int _{v'} ( \epsilon_0 E^2 +\frac 1 {\mu_0} B^2) d \vec {v'}\;-\;\frac 1 {\mu_0} \int _{s'} (\vec E X \vec B) d \vec {s'}$$

In Cheng's "Field and Wave Electromagnetics", it interpret this is ohmic loss because:

$$\vec E \cdot \vec J \;=\; \sigma E^2$$

Which is the ohmic loss.

I don't see it described like this in Griffiths. Can anyone comment what this term really means?

 

[yungman]

Anyone?

 

[kloptok]

What is your question, is it how to interpret the J.E-term (. denotes scalar product), or how you find out that the J.E-term is the Ohmic loss?