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Q & A: electric and magnetic field phases in waves

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Most recent answer: 04/22/2013
Q:
Are the electric field and the magnetic field of a photon (of a electromagnetic wave) in phase or out of phase? and why? they seem to be out of phase if a sine wave of magnetic or electric field is plugged into the Maxwell's equations (two of them with time change:Maxwell–Faraday equation and Ampère's circuital law (with Maxwell's correction)) because the derivative of a sine wave is a cosine wave, and they are out of phase by 90 degree. but many electromagnetic waves are represented by "in phase" model(picture). Under what conditions(propagating/standing wave, distance from the light source etc.) are they in phase or out of phase? and why this is so?
- Anonymous
A:
Let me skip the "photon" part for starters. In a classical propagating EM wave a spatial derivative of the E field matches up with the time derivative of the B field, and vice-versa. So they're both changing (say crossing zero) or not changing (say at a peak) at the same places. For a linearly polarized wave, that leaves E and B in phase in the sense that they have nodes and peaks at the same places,  but they're at 90 angles to each other, thanks to the type of spatial derivative involved (a curl). For a circularly polarized wave, both fields have uniform intensity. The circularly polarized wave can be expressed as two linearly polarized waves, shifted by 90 in phase and rotated by 90 in polarization. If you pick some direction to measure the fields along, the components of E and B along that direction have a 90 phase shift with respect to each other.

Now we get to the interesting part, brought up by your incidental use of the word "photon". If you have a well defined number of photons (e.g. one), then the phase of the wave is completely undefined, thanks to one of the quantum uncertainty relations. So you might think that it makes no sense to say anything about the relative phases of E and B. Nevertheless, E and B can be "entangled" so the relative phases can have the classical relations described above, depending on the type of photon, even though neither field has a defined phase!

Mike W.

(published on 04/22/2013)

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