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The energy(density) of an electromagnetic wave is described by the Poynting vector. This is the function of the $E$ and $B$ field. (the exact formula is well known). The magnitude of the $E$ and $B$ vector oscillates as the wave propagates - at some point both of them reaches its maximum (so $S=max$), at some point both of them are zero (so $S=0$). The question is: where is the energy 'stored', when both these vectors are zero?

Qmechanic
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redbaron
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  • "The energy(density) of an electromagnetic wave is described by the Poynting vector."- In addition to the correction made by Rob Jeffries, I would like to add that Poynting's vector represents electromagnetic radiation. You need to add Poynting's vector with the power stored in the field in order to get the power of an electromagnetic wave – UKH Aug 03 '16 at 09:02
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    @Unnikrishnan Thanks for your reply and I apologize for not formulating my question correctly. Anyhow, at the point, where the EM wave has no E and no B vector, its 'energy' should be 0, while at its maximum is has some 'energy'. As an analogy, in case of a wave on the surface of the water, at a certain point the wave has potential energy or kinetic energy (or both) - this transforms to each other. This analogy doesn't hold for the electromagnetic wave - it's not the energy of the 'E field' which transforms into the energy of the 'B field', as they are in the same phase, right? – redbaron Aug 03 '16 at 10:00
  • What are photons, electromagnetic radiation and radio waves – HolgerFiedler Aug 07 '16 at 19:55

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The Poynting vector is not the energy (density) in the electromagnetic fields, which would have units of J m$^{-3}$, it is the flux of energy per unit time with units of W m$^{-2}$.

That the Poynting vector is (instantaneously) zero tells you that there is (instantaneously) no flux of energy per unit time carried by the electromagnetic fields.

As you correctly point out, this is because the E- and B-fields are simultaneously zero (for a TEM wave) and it is the magnitude of the E- and B-fields which give the energy density $u = 0.5(\epsilon E^2 +B^2/\mu)$. Where has the energy gone? Everywhere else. The E- and B-fields are only instantaneously zero at that point in space, they are not zero everywhere. The energy can be moved around, which is what the Poynting vector and its divergence) are telling you about.

ProfRob
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  • Thanks for your reply - does that mean that you can't isolate the electromagnetic wave from the rest of the world? I mean the conservation of the energy would suggest that such a wave cannot exist on its own... – redbaron Aug 03 '16 at 09:10
  • @redbaron Your wave is travelling is it not? So how can it be isolated? Of course you could have a standing electromagnetic wave, in which case the E-field and B-field are not together zero at the same point in space and time and the time-averaged Poynting vector is zero because there is no net energy flow. – ProfRob Aug 03 '16 at 13:05
  • sorry for being not clear - I try to imagine these waves - I imagine them as a propagation of disturbance in the EM field - does this disturbance have a kind of 'length'? I mean a spatial extension? or is this something which falls under the uncertainty principle? – redbaron Aug 03 '16 at 13:31
  • @redbaron It has a wavelength... – ProfRob Aug 03 '16 at 14:01
  • I know it has a wavelength - but that doesn't necessarily mean that the wave itself is one wavelength long, right? It could be longer - can it be shorter than that? – redbaron Aug 04 '16 at 05:57