Why does the Poynting vector subtract stored electric and magnetic fields?

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    Poynting vector Vector
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Discussion Overview

The discussion revolves around the Poynting vector and its relationship to stored electric and magnetic fields, specifically addressing why these terms are subtracted rather than added in the context of energy conservation and dynamics in electromagnetic theory.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the physical interpretation of subtracting stored electric and magnetic energy in the Poynting theory, suggesting that it might make more sense to add them when discussing conservation laws.
  • Another participant explains that while the total energy density is indeed the sum of the two, the subtraction is necessary for understanding dynamics, drawing a parallel to the Lagrangian mechanics where kinetic energy is subtracted from potential energy.
  • A participant mentions that in their notes, the energies are added together, referencing Wikipedia and suggesting that Poynting's theorem relates the work done on charges to the decrease in energy stored in the field minus the energy transported by the fields.
  • There is a mention of a version for harmonic fields where the field densities are subtracted, which some find counterintuitive.
  • Another participant notes their understanding of the dynamic behavior argument is improving and seeks references that describe the relationship between phasor and time-domain representations, highlighting differences in how energy is represented in each case.
  • It is clarified that the two formulations (phasor and time-domain) are equivalent, with the time-harmonic case being a Fourier basis decomposition of general time-domain fields.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the Poynting vector and the treatment of stored energies, indicating that multiple competing views remain without a clear consensus.

Contextual Notes

Some participants reference specific textbooks and articles for further reading, indicating that interpretations may depend on the context of the discussion, such as harmonic versus time-domain representations.

Who May Find This Useful

This discussion may be of interest to students and professionals in physics and engineering, particularly those studying electromagnetic theory and energy dynamics in fields.

mohammed.omar
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Hi All,

I have been revising the Poynting theory and I cannot interpret "physically" why do we have the terms of stored electric(We) and magnetic field (Wm) minus each other; doesn't it make more sense to have the total energy stored in the field added together when we talk about the Poynting theory as of a conservation law?
 
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To get the total energy density you do add them together. You subtract them to get the dynamics, which is most likely rooted in the lagrangian of the same form.
 
Hi kcdodd,

Thanks for the prompt reply but I do not really get your point. Could you please elaborate more?
 
For Newtonian objects, the lagrangian is usually the kinetic energy minus the potential energy (T - V), as opposed to the total energy (T + V), which is a constant. But we use the lagrangian to determine the dynamics of the objects. The lagrangian for em interaction is a similar kind of idea. The dynamics are governed by (E^2 - B^2), instead of (E^2 + B^2).
 
in my notes it is added together. have a look at wikipedia too: http://en.wikipedia.org/wiki/Poynting's_theorem.

unless of course I am misunderstanding your question?

basically poyntings theorem tells you that the work done on the charges is equal to the decrease in energy stored in that field minus the energy that flowed out the surface (ie the energy transported by the fields.

I recommend the textbook "introduction to electrodynamics" by D. Griffiths if you haven't already looked at it - it is very good for most electrodynamic material for an undergraduate :)
 
There is a version for harmonic fields where you subtract the field densities, which seems counterintuitive at first.
 
Thanks lavster and kcdodd.

Griffiths book seems a good place to start :)

I'm using the harmonic field version, as kcdodd said, and I believe I'm starting to get grips of the "dynamic behavior" argument. It is a very neat explanation actually, and it has a very appealing agreement with circuit theory. Is there any reference that describes the problem or the technique as you describe it?

I've looked at Pozar's "Microwave Engineering" and Collin's "Foundations of Microwave Engineering". I noted that using the phasor representation, we use Wm-We, while using time-domain representation it has the form Wm+We. Does this mean that using the phasor representation we study the dynamic behavior while when using the more general time-domain representation we study the more general "large signal" case?
 
mohammed.omar said:
Thanks lavster and kcdodd.

Griffiths book seems a good place to start :)

I'm using the harmonic field version, as kcdodd said, and I believe I'm starting to get grips of the "dynamic behavior" argument. It is a very neat explanation actually, and it has a very appealing agreement with circuit theory. Is there any reference that describes the problem or the technique as you describe it?

I've looked at Pozar's "Microwave Engineering" and Collin's "Foundations of Microwave Engineering". I noted that using the phasor representation, we use Wm-We, while using time-domain representation it has the form Wm+We. Does this mean that using the phasor representation we study the dynamic behavior while when using the more general time-domain representation we study the more general "large signal" case?

No, the two formulations are equivalent, the time-harmonic case is just a Fourier basis decomposition of the general time-domain fields. Remember though, to go back to the true time-domain you have to take the real part of the complex time-harmonic fields.
 
Tanks a lot. I believe I've got grips of it :).
 

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