Poynting vector in static electromagnetic field

[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?

 

[DrDu]

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

 

[zql]

can you give me more details？thanks.

 

[Meir Achuz]

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?

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.

 

[Andy Resnick]

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?

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

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

Does this help?

 

[zql]

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

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

Does this help?

I think I got it, thanks.

 

[zql]

And how about "hidden momentum"? I didn't know about this.

 

[DrDu]

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