Poynting theory apply to both static and time varying fields?

[yungman]

Poynting vector is flow of energy per unit area. Dose it apply for both static field where E and B are decoupled, AND time varying EM field where E and B are coupled?

 

[yungman]

The reason I ask is referring to page 346-349 of Griffiths. The Poynting theorem was derived using time varying relation where

$$\nabla \times \vec B= \mu\vec J -\mu\frac {\partial \vec D}{\partial t} \;\hbox { and }\; \nabla \times \vec E=-\frac{\partial \vec B}{\partial t}$$

But then in Example 8.1 on page 348, it gave an example of a steady current I flow down a wire and calculate the power flow down the wire ( Poynting vector S). Where is use E= (voltage across wire) divided by the length of wire. B is calculated by current I.

 

[vanhees71]

The Poynting theorem follows from the complete Maxwell equations and thus is valid always.

E.g., it is interesting to calculate the energy flow of a DC conducting coaxial cable (I choose this as an example, because this is a very simple to solve stationary problem). Calculate both, the electric and magnetic fields and then the Poynting vector. Then think about, what this means concerning energy transport.

 

[yungman]

Thanks
What you suggested is very similar to problem 8.1 in Griffiths and I worked it out already.