EM Wave - basic question on energy conservation in a wave

[mgkii]

I've searched threads and can't find easy explanation - sorry if I'm missing something basic / have a basic understanding error!

In the classic picture of an EM wave with the Electric and Magnetic components oscillating at 90 degrees to each other, both components cross the middle axis at the same point. If this means that both the components are at Zero "something" that relates to the strength of the field, is that something related to energy? If so, then where does that energy "hide" at the points in the oscillations that are not at their maximum? If it's not related to energy, then how do we use the strength of that field to do work?

Thank you
Matt

 

[vanhees71]

The energy density (!) of the free electromagnetic field is (in SI units)
$$u=\frac{\epsilon_0}{2} \vec{E}^2 + \frac{1}{2 \mu_0} \vec{B}^2.$$
It's not a conserved quantity. Only the total energy for a free em. field
$$E=\int_{\mathbb{R}^3} \mathrm{d}^3 x u(t,\vec{x})$$
is conserved.

 

[PeroK]

Summary:: where does the energy "hide" (wrong word I know!) at the points in an EM wave oscillation where the two field components cross the axis and are zero.

I've searched threads and can't find easy explanation - sorry if I'm missing something basic / have a basic understanding error!

In the classic picture of an EM wave with the Electric and Magnetic components oscillating at 90 degrees to each other, both components cross the middle axis at the same point. If this means that both the components are at Zero "something" that relates to the strength of the field, is that something related to energy? If so, then where does that energy "hide" at the points in the oscillations that are not at their maximum? If it's not related to energy, then how do we use the strength of that field to do work?

Thank you
Matt

The energy associated with any wave is propagating. In the simple case of a pulse moving along a string, the kinetic energy and elastic potential energy of the wave moves along the string, so that a particular section of the string is distrurbed for a short time, then returns to its equilibrium position, and the energy is now manifest at a different part of the string.

The case of EM waves is similar. The total energy of a pulse of EM radiation is associated with the electric and magnetic fields over the region of space where the fields are non-zero. This region changes as the wave propagates. There is no particular significance of the points in space within this region where the fields happen to be zero instantaneously as the wave moves through.

PS I see @vanhees71 has expressed this somewhat more mathematically.

 

[mgkii]

Thank you! I have a feeling I'm making a rookie mistake of trying to treat light as an EM wave and a photon at the same time... In my head I am following the EM diagram and thinking "at that point there where the E & M components cross the axis, where is the <whatever> in the photon?" The string analogy quickly dispels that thought!

Much appreciated all.

 

[vanhees71]

Light is an electromagnetic wave with the relevant frequencies in a certain range, our eyes are sensitive to. A photon is a one-particle Fock state of the electromagnetic quantum field. It is not localizable to begin with, i.e., it is completely wrong to think of it in terms as a point-particle-like object. You cannot even define a position for a photon in the strict sense but only probabilities for being detected at a given point at a given time.

In almost all cases it's much closer to the true picture to think about electromagnetism as field phenomenon. It's also amazing how far you get with the completely classical field picture as described by Maxwell's equations.