# Clarification on the Poynting theorem

1. Nov 1, 2008

### fisico30

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

2. Nov 2, 2008

### Phrak

Fisico. Are you asking if there is lost energy due to the charge density acted upon some some other field conditions?

3. Nov 2, 2008

### fisico30

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. Nov 3, 2008

### Phrak

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.

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