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Poynting vector in static electromagnetic field

by zql
Tags: poynting vector
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zql
#1
Oct21-10, 07:06 AM
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=ED/2+BH/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?
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DrDu
#2
Oct21-10, 07:23 AM
Sci Advisor
P: 3,593
Yes, correct. Look also for "hidden momentum".
zql
#3
Oct21-10, 08:51 AM
P: 5
can you give me more details?thanks.

clem
#4
Oct22-10, 12:04 PM
Sci Advisor
P: 1,261
Poynting vector in static electromagnetic field

Quote Quote by zql View Post
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=ED/2+BH/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
#5
Oct22-10, 01:16 PM
Sci Advisor
P: 5,523
Quote Quote by zql View Post
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=ED/2+BH/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:

[tex]\frac{\partial u}{\partial t} + \nabla \bullet S = -J \bullet E[/tex].

Does this help?
zql
#6
Oct22-10, 01:26 PM
P: 5
Quote Quote by Andy Resnick View Post
The relevant expression, from the conservation of energy, is:

[tex]\frac{\partial u}{\partial t} + \nabla \bullet S = -J \bullet E[/tex].

Does this help?
I think I got it, thanks.
zql
#7
Oct22-10, 01:28 PM
P: 5
And how about "hidden momentum"? I didn't know about this.
DrDu
#8
Oct22-10, 02:45 PM
Sci Advisor
P: 3,593
Probably the best source on these matters is still Jackson's book on Electrodynamics.


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