Instantaneous poynting vector for EM radiation

[WRGmedphys]

Have viewed PF, first time post (have searched for this question on forum):

The energy of EM radiation can be described by the Poynting vector S = E x B (insert conversion factor for cgs, MKS, etc).

For a traveling EM wave, what happens to the instantaneous value of S when E and B are max as compared to when E and B are 0?

Alternatively, how is the energy of the EM radiation shared between E and B with both E and B having maximum and zero values at the same instant of time for a plane wave?

Thank you for your input.

WRG

 

[Creator]

hi WR;
The eqn. you gave is actually the TIME AVERAGED Poynting vector.
The instantaneous Poynting vector whcih depends upon time and position, r, is given by:

S = (1/u) EB[cos^2(wt -kr)]...where w is the freqency.

Good question.
Creator

 

[WRGmedphys]

Thank you for your response Creator. Believe my confusion was considering E and B as sharing the energy of the wave (similar to K.E. and potential sharing the total E). Will dig out my undergraduate intermediate EM book and review more throughly (still confused as to where the energy is stored when E and B are both zero as compared to when E and B are both maximum).

WRG

 

[Creator]

Thank you for your response Creator. Believe my confusion was considering E and B as sharing the energy of the wave (similar to K.E. and potential sharing the total E).

No problem;
In a (monochromatic) plane wave Maxwell's equations ensure E and B are always in phase, (in vacuum).
The energy is proportional to the square of the MAX. E field OR the square of the MAX. B field, and yes, alternately it can be written as the sum of 1/2 of each field squared (with appropriate epsilon and mu factors) since each "contributes" half the energy of the wave.

(still confused as to where the energy is stored when E and B are both zero as compared to when E and B are both maximum).

The energy is not 'stored' but rather it is moved ...the energy of the waves moves with the wave. At the zero point (minimum phase) we can say the energy has moved ahead. The energy is still "stored" in the E & B field, but the fields have moved position.
Remember Poynting Vector is an energy FLUX, meaning a rate of transfer of energy.

Your worry is a common concern among those who question that the 'in phase' relation of E & B implies violation of conservation of energy.
But the question is mis-placed since even though the instantaneous energy "disappears" AT ONE LOCATION, it "reappears" simultaneously at another location, namely, 1/4 wavelength ahead in the wave (where the fields are at maximum).

Creator

 

[Antiphon]

Thinking about circular polarization really helps clarify this. Here there are no nodes. Circular polarization is the sum of two linerly polarized waves at right angles in space and 90 degrees apart in time.

Think of a helix instead of a sinewave.