Poynting vector in static electromagnetic field

1. Oct 21, 2010

zql

There is a situation, we have an electric field and a magnetic field, both are static. And we know the density of energy is u=E·D/2+B·H/2, so dU/dt=0, but Poynting vector S=ExH is not zero, which means energy is flowing. This confused me. Static field also has energy flux?

2. Oct 21, 2010

DrDu

Yes, correct. Look also for "hidden momentum".

3. Oct 21, 2010

zql

can you give me more details？thanks.

4. Oct 22, 2010

clem

The static magnetic field is produced by a constant electric current. That means there is resistance, and energy is flowing into matter. "Hidden" momentum is not involved.

5. Oct 22, 2010

Andy Resnick

The relevant expression, from the conservation of energy, is:

$$\frac{\partial u}{\partial t} + \nabla \bullet S = -J \bullet E$$.

Does this help?

6. Oct 22, 2010

zql

I think I got it, thanks.

7. Oct 22, 2010

zql

8. Oct 22, 2010

DrDu

Probably the best source on these matters is still Jackson's book on Electrodynamics.