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In a physics-book I read that "it should be noted that the [electric and magnetic] fields [in a moving EM-wave] alternate at first, 90 degrees out of phase with each other. As they travel, they gradually come into phase". Is this true ?? I've never read or heard this before.

PERFESSER CREEK-WATER
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  • This is surely a duplicate, but I can't find one. The statement is correct. – garyp Oct 12 '16 at 02:13
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    Context please! What do you mean by a moving EM wave? Moving from where to where and generated by what? – ProfRob Oct 12 '16 at 06:45
  • -1. Which physics book? You should not "quote" an authority without giving the reference for it. Context is also important. – sammy gerbil Feb 28 '17 at 04:01

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Consulting the late J.D. Jackson's "Classical Electrodynamics, 3rd edition", page 411, we find the following expressions for the fields due to a sinusoidally excited, center-fed, linear antenna that is small compared to a wavelength:

$$\mathbf{H} = \frac{ck^2}{4\pi}\left(\mathbf{n} \times \mathbf{p}\right)\frac{e^{ikr}}{r}\left(1 - \frac{1}{ikr}\right)$$

$$\mathbf{E} = \frac{1}{4\pi\epsilon_0}\left\{k^2\left(\mathbf{n} \times \mathbf{p}\right)\times \mathbf{n}\frac{e^{ikr}}{r} + \left[3\mathbf{n}(\mathbf{n}\cdot \mathbf{p}) - \mathbf{p}\right]\left(\frac{1}{r^3} - \frac{ik}{r^2}\right)e^{ikr}\right\}$$

We note that there are magnetic and electric terms that decay as $1/r$ and $1/r^2$ as well as an electric term that decays as $1/r^3$ where $r$ is the distance from the antenna.

The $1/r$ terms are in phase (always) and thus transport energy away from the antenna; these are the radiation terms and they dominate in the far-field:

$$\mathbf{H} = \frac{ck^2}{4\pi}\left(\mathbf{n} \times \mathbf{p}\right)\frac{e^{ikr}}{r}$$

$$\mathbf{E} = \frac{1}{4\pi\epsilon_0}k^2\left(\mathbf{n} \times \mathbf{p}\right)\times \mathbf{n}\frac{e^{ikr}}{r} = Z_0 \mathbf{H} \times \mathbf{n}$$

In the region near the antenna (near-field), the dominant terms approach

$$\mathbf{H} = \frac{i \omega}{4\pi}\left(\mathbf{n} \times \mathbf{p}\right)\frac{1}{r^2}$$

$$\mathbf{E} = \frac{1}{4\pi\epsilon_0}\left[3\mathbf{n}(\mathbf{n}\cdot \mathbf{p}) - \mathbf{p}\right]\frac{1}{r^3}$$

which are out of phase (reactive) and thus energy flows back and forth between these fields and the antenna.

In summary, it is true that the dominant fields near the antenna are out of phase but these aren't the fields that propagate to the far-field since these fields decay as the inverse square and the inverse cube of the distance from the antenna.

Alfred Centauri
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    Thank you for this nice demonstration that the electromagnetic "near fields" at an antenna are not propagating waves as opposed to the "far fields". This is the reason why the terms "near field" and "far field" at an antenna have been introduced. – freecharly Oct 12 '16 at 14:49
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The electric and magnetic fields in a linearly polarized sinusoidal plane electromagnetic wave in vacuum or in a simple dielectric are always in phase, but their planes of oscillation in space are orthogonal to each other. The mentioned statement "they gradually come into phase" seems not to hold for such a wave.

freecharly
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  • NO: they START out of phase by 90 degrees, right ?? – PERFESSER CREEK-WATER Oct 12 '16 at 01:07
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    Are you talking about the phase relations of electrical and magnetic fields at an antenna? – freecharly Oct 12 '16 at 01:10
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    @PERFESSERCREEK-WATER, the answer clearly refers to a sinusoidal plane wave which, as you must know, extends to infinity in time and space, i.e., there is no 'START out' for a plane wave. – Alfred Centauri Oct 12 '16 at 01:40
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    @AlfredCentauri I don't see the reference to a plane wave. I think the question is about fields generated by a source (e.g., antenna). Hence the mention of "at first". – garyp Oct 12 '16 at 02:08
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    The question does not mention plane waves. @PERFESSERCREEK-WATER is correct. The $E$ and $B$ fields near a source are 90 degrees out of phase, but after some distance they are in phase. – garyp Oct 12 '16 at 02:10
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    @garyp, the answer clearly refers to a sinusoidal plane wave - "The electric and magnetic fields in a linearly polarized sinusoidal plane electromagnetic wave..." – Alfred Centauri Oct 12 '16 at 02:29
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    @Alfred Centauri - If the question had been better formulated a lot of unnecessary guesswork could have been avoided. The OP reads a book but fails to mention that the radiation from an antenna (e.g. dipole) is considered. It is clear that the near-field of an antenna is different from freely propagating waves at a larger distance. – freecharly Oct 12 '16 at 04:45
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    In my comments, I made no reference to the intent of the question but rather to the OPs response to your answer - an answer which is factually correct. This seems so obvious to me that I can't imagine why so this is so difficult for anyone else to see. – Alfred Centauri Oct 12 '16 at 10:44
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    @AlfredCentauri Sorry. I didn't read carefully enough, and I thought the comment was directed toward the question, not this answer. This answer is factually correct, but does not address the question. But the question is very poorly constructed, begging for misinterpretation. – garyp Oct 12 '16 at 11:58
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    @garyp - I agree that the OP question was not well posed. In addition, the OP did not respond to my question in an early comment whether he was talking about phase relations of electrical and magnetic fields at an antenna. – freecharly Oct 12 '16 at 12:19
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    This answer is indeed right for a plane wave. It is not what the OP wants to know about, but what exactly is needed is not clear. – Selene Routley Oct 12 '16 at 13:10
  • MANY THANKs to those of you who answered !! Because I had never read or heard that EM-waves gradually become in-phase as they travel, I doubted the info in the book ... now I know otherwise !! Sorry for formulating the question in a confusing way ..... – PERFESSER CREEK-WATER Oct 15 '16 at 17:11