EM Waves, Kinks, and the interaction of Electric and Magnetic Fields

Question

Looking for explanations of what electromagnetic waves (light, etc.) are, I found apparently contradicting explanations. According to the first, which seems wrong to me, EM waves are explained using the following two facts:

1. A changing electric field causes a magnetic field, and
2. a changing magnetic field causes an electric field.

So, if you cause an electric field to change this will create a magnetic field (thus a change in the magnetic field), which will in turn generate an electric field, and so on. And so the EM waves self-propagate in this way, as in a "chain" reaction. This explanation seems wrong and misleading to me, for when a magnetic field is generated by a changing electric field, the former is far weaker than the latter (unless I am missing something); and the same is the case when an electric field is generated by a changing magnetic field. So according to this explanation, the EM waves should not be able to propagate very far, for at every turn (from magnetic to electric, or from electric to magnetic), it should become weaker and weaker, and die out very soon.

The second explanation has to do with the fact that when an electric field changes (or a magnetic field changes), this information cannot propagate faster than the speed of light c, and this limit in the speed of propagation of the information creates a "kink" in the EM field, a kink that propagates with the speed of light. This kink is indeed a disturbance of the electric-magnetic field - thus a disturbance in the E-field accompanied by a change in the magnetic field, but this dance between electric and magnetic field, captured by facts (1) and (2), is not really pivotal in the explanation of why and how the wave can propagate (as the first explanation implies!)

So, my question is: what role do facts (1) and (2) play in the explanation EM waves's ability to propagate? More specifically: I am right to suppose that the first explanation reported here should be dismissed?

Answer 1

It is conventional to claim from, say, $\rm{curl} \bf{E} = -\partial B/\partial t$ that the change of the B-field in time "creates" the curl of the E-field. It is equally correct to say that the curl of the E-field is the one that generates the change of the B-field in time. In fact, there is no physical way to tell which creates which, or more precisely which is the cause and which is the effect for they (E and B) always appear simultaneously. This is why some people prefer the integral form of the Maxwell's equation where the time varying but properly retarded currents and charges act as sources of the fields and thus the currents and charges can be taken as being the cause while the fields as effect. See for example the Ignatowsky-Panofsky equations in https://en.wikipedia.org/wiki/Jefimenko%27s_equations

Answer 2

I’ll try to show how the strength of the generated fields vary. And what better place than to begin with the relevant Maxwell’s equations (in free space): $$\nabla\times \vec{E}=-\partial_t \vec{B}\\ \nabla\times\vec{B}=\frac{1}{c^2}\partial_t\vec{E}$$ The first equation just retells faraday’s law and relates the changing magnetic field to an electric field generated. The second is ampere’s law that relates the opposite.

Assuming a harmonic solution as any form can be decomposed into harmonics, the above two equations (magnitudes) reduce to: $$ik{E}=-i\omega{B}\\ ik{B}=\frac{1}{c^2}i\omega{E}$$ Now, using the fact that $c=\omega/k$ we can see that the strength of an electric field generated by a changing magnetic field (given by the first of the two equations) is:$$E=cB$$

Plugging this strength into the time varying electric field that generates the magnetic field (second of the two equations) gives us:$$B=\frac{1}{c}(cB)=B$$ As you can see we are back to where we started from! The strengths of the generated electric from magnetic and magnetic from electric fields are just right to keep the exact same strength sustained throughout!

Answer 3

The two propositions are entirely correct. However your assumption that the cycle is lossy is wrong; there is nowhere for any lost field energy to go, so the cycle perpetuates according to the law of energy conservation. This was perhaps one of James Clerk Maxwell's fundamental insights.

The "kink" in the field is not governed by c, rather the reverse. The kink is the wave energy. Tts speed of propagation c is governed by the electrical permittivity and magnetic permeability of free space, which just happens to work out at the familiar value. It is this which in turn sets the fundamental limit on the propagation of information.

You may wonder then, what is this field that kinks to form a wave? It arises in quantum field theory as a "zero-point" field which pervades all of space and time. At this point, it can be wise to ascribe such things to quantum weirdness and save them for later. Maxwell's classical theory has no such complication and works in all practical circumstances.