Clarification on the Poynting theorem

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In summary: The second example would be a capacitor, where the electric field induces an electric charge on the dielectric, and the work done on this charge is the EM energy stored in the capacitor.
  • #1
fisico30
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hello forum,

the famous Poynting theorem is an expression for the energy balance. Please, could anyone make sure I have the right understanding ?

The EM energy in a volume V with bounding surface S can change with time if:

1) energy leaves or enter that volume through S (net flux).

2) if the energy in the volume is used up by the free and induced currents and charges and then transformed into heat. Those currents and charges then behave as sinks.

3)If there are impressed sources (currents and charges) that generate new energy.

Regarding 2): the free and induced currents and charges could not only dissipate EM energy but also re-emit some of the absorbed energy once set into motion... so they would act as both sources and sinks.

In free space, there can only be free sources (if any) in the volume.
The dot product of E and J represents the lost power. Where is the charge density gone?

thanks
fisico30
 
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  • #2
Fisico. Are you asking if there is lost energy due to the charge density acted upon some some other field conditions?
 
  • #3
Hi Pharak:

my questions are:

1) The EM field does work on the charges and currents that are present in the volume and loses some of its energy. What type of work are talking about? I guess the EM field energy causes motion of the charges (it gives them Kinetic energy). What happens to the currents? Do they move, speed up?...

2) The same currents and charges, when moved, emit EM radiation too, that gets returned to the field. Probably some of the energy that they absorb is turn into heat, so not all the energy they receive is return...

Is this correct?
thanks
 
  • #4
fisico30 said:
Hi Pharak:

my questions are:

1) The EM field does work on the charges and currents that are present in the volume and loses some of its energy. What type of work are talking about? I guess the EM field energy causes motion of the charges (it gives them Kinetic energy). What happens to the currents? Do they move, speed up?...

The electric field expressed in the Poynting vector does work on current, not charge per se. What sort of work depends. The typical, first example is a resistor, where the work done results in heat.
 

Related to Clarification on the Poynting theorem

1. What is the Poynting theorem?

The Poynting theorem is a fundamental principle in electromagnetism that describes the relationship between electromagnetic fields and energy flow. It states that the time-averaged power flow through a given area is equal to the cross product of the electric and magnetic fields at that point.

2. How is the Poynting theorem used?

The Poynting theorem is used to calculate the direction and magnitude of energy flow in electromagnetic fields. It is also used to understand the transfer of energy between electric and magnetic fields in various systems, such as antennas, transmission lines, and optical fibers.

3. What is meant by "clarification" in the context of the Poynting theorem?

In this context, clarification refers to further explanation or elaboration on the concept of the Poynting theorem, including its derivation, assumptions, and applications. It may also involve addressing common misconceptions or clarifying confusing aspects of the theorem.

4. Why is the Poynting theorem important?

The Poynting theorem is crucial in understanding the behavior of electromagnetic fields and their role in energy transfer. It forms the basis for many practical applications, such as power transmission, satellite communication, and medical imaging. Without it, we would not have a comprehensive understanding of electromagnetism.

5. Are there any limitations to the Poynting theorem?

While the Poynting theorem is a powerful tool, it does have some limitations. It assumes that the fields are time-harmonic, the medium is linear and isotropic, and there are no sources or losses. In reality, these assumptions may not always hold, and additional considerations may be necessary for a more accurate analysis of electromagnetic systems.

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