# Poynting vector in static electromagnetic field

by zql
Tags: poynting vector
 P: 5 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?
 Sci Advisor P: 3,593 Yes, correct. Look also for "hidden momentum".
 P: 5 can you give me more details？thanks.
P: 1,261
Poynting vector in static electromagnetic field

 Quote by 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?
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.
P: 5,523
 Quote by 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?
The relevant expression, from the conservation of energy, is:

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

Does this help?
P: 5
 Quote by 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?
I think I got it, thanks.