## 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?

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 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.

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