Poynting vector in static electromagnetic field

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Discussion Overview

The discussion revolves around the behavior of the Poynting vector in static electromagnetic fields, specifically addressing the apparent contradiction between a static energy density and a non-zero energy flux. Participants explore concepts such as energy flow, hidden momentum, and conservation of energy in this context.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that in a static electromagnetic field, the energy density is given by u=E·D/2+B·H/2, and while the time derivative of energy density is zero (dU/dt=0), the Poynting vector S=ExH is not zero, suggesting energy is flowing.
  • Another participant mentions the concept of "hidden momentum" as a relevant factor in understanding the situation.
  • A participant reiterates the initial confusion regarding energy flux in static fields and emphasizes that the static magnetic field is produced by a constant electric current, implying energy flow into matter without involving hidden momentum.
  • One participant introduces the conservation of energy expression, \(\frac{\partial u}{\partial t} + \nabla \bullet S = -J \bullet E\), as a potential clarification for the discussion.
  • Another participant expresses understanding after the introduction of the conservation of energy expression.
  • A later post inquires about hidden momentum, indicating a lack of familiarity with the concept.
  • One participant suggests that Jackson's book on Electrodynamics is a valuable resource for further exploration of these topics.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the implications of static fields and energy flow. There is no consensus on the role of hidden momentum, and the discussion remains unresolved regarding its relevance to the situation described.

Contextual Notes

Participants reference specific equations and concepts, but the discussion does not resolve the implications of these expressions fully. The role of hidden momentum and its connection to the static fields remains unclear.

zql
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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?
 
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Yes, correct. Look also for "hidden momentum".
 
can you give me more details？thanks.
 
zql said:
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.
 
zql said:
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:

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

Does this help?
 
Andy Resnick said:
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.
 
And how about "hidden momentum"? I didn't know about this.
 
Probably the best source on these matters is still Jackson's book on Electrodynamics.
 

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