Poynting theory apply to both static and time varying fields?

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?

 PhysOrg.com physics news on PhysOrg.com >> Promising doped zirconia>> New X-ray method shows how frog embryos could help thwart disease>> Bringing life into focus
 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.
 Recognitions: Science Advisor 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.

Poynting theory apply to both static and time varying fields?

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