Maxwell's equations and electromagnetic (waves)

[Sefrez]

By Maxwell's equations, electromagnetic waves seem to come about by means of magnetic fields generating electric fields and in turn electric fields generating magnetic fields (the loop continues.) But how is this not perpetual in the context that energy is not conserved? It seems as if a magnetic field is decreasing, the electric field that is generated should not in turn be able to "out weigh" the magnetic field that generated it in the first place giving rise to a, again, maximized magnetic field and thus a continued rhythm, if you will. If it was a simple conversion of energy, maybe, but they are supposedly in phase? They hit both maximum and minimum at the same instant, supposedly.

Also, if these are the attributes of electromagnetic waves, (this continuous "re-induction"), does the same apply with conductors? That is, take two solenoids, one within the other. If a change in current in the outer exists, then there exists a change in magnetic flux through the inner solenoid. This in turn induces a current within it, which then again, creates a change in flux though the outer solenoid bring about re-induction of its coils. Does that make sense? Nevertheless, it seems like a never ending loop, and possibly a logic fallacy (on my part) that I can't seem to straighten out.

 

[Born2bwire]

In terms of causality, it is erroneous to consider that a changing magnetic field creates a changing electric (and vice-versa). One does not cause the other, they both exist simultaneously.

 

[Sefrez]

If they both exist simultaneously, would this imply that one has no affect on the other, that is they are two separate entities? That is, how could something have any influence over something else if neither is said to come first (or last)?

Also, with Maxwell's equations, don't you have to assume one influences the other? (at which can't be if they exist simultaneously)

 

[Born2bwire]

They are not separate entities, they are essentially the same entity. One does not influence the other, they both exist together in a time-varying fashion or not at all. Maxwell's Equations does not state that a changing electric/magnetic field creates a changing magnetic/electric field. All four of Maxwell's Equations must be satisfied simultaneously. As such, if we have time-varying fields then we conclude that there must be both electric and magnetic fields to create an electromagnetic wave. Perhaps you would be more comfortable if you were to view it purely from a source perspective. Take a look at the Jefimenko's Equations which solve for the electromagnetic fields that are excited by arbitrary charge and current sources. You will see that any time-varying source always excites electric and magnetic fields.

 

[PhilDSP]

In terms of causality I believe Maxwell thought in terms of the vector and scalar potentials. Jefimenko echoes that thinking (and he developed a mathematical derivation showing it is so) but uses what he calls "retarded potential" that can be calculated and that produces an observable.

 

[Born2bwire]

In terms of causality I believe Maxwell thought in terms of the vector and scalar potentials. Jefimenko echoes that thinking (and he developed a mathematical derivation showing it is so) but uses what he calls "retarded potential" that can be calculated and that produces an observable.

Quite so. Jefimenko uses retarded potentials which become rather cumbersome in all but the simplest source arrangements but the illuminating quality of Jefimenko's equations is that he now has completely separated the electric and magnetic fields. In Maxwell's Equations, the electric and magnetic fields are intertwined in Faraday's and Ampere's Laws and this sometimes leads to the confusion that the OP is experiencing. With Jefimenko's we can view the two fields without this coupling in a simple source-centric view. We now can easily see that any time-varying source (charges and currents) gives rise to both electric and magnetic fields simultaneously as opposed to mistakingly assuming that one field acts as the source for the other field.

 

[Bob S]

The energy (power) flow in a TEM (transverse electric magnetic) wave is given by the Poynting vector. It is represented by the vector cross product of E and H. See http://en.wikipedia.org/wiki/Poynting_vector

 

[Sefrez]

There is a widespread interpretation of Maxwell's equations indicating that spatially varying electric and magnetic fields can cause each other to change in time, thus giving rise to a propagating electromagnetic waves[3] (electromagnetism). However, Jefimenko's equations show an alternative point of view.[4] Jefimenko says, "...neither Maxwell's equations nor their solutions indicate an existence of causal links between electric and magnetic fields. Therefore, we must conclude that an electromagnetic field is a dual entity always having an electric and a magnetic component simultaneously created by their common sources: time-variable electric charges and currents." [5]

As pointed out by McDonald,[6] Jefimenko's equations seem to appear first in 1962 in the second edition of Panofsky and Phillips's classic textbook.[7] Essential features of these equations are easily observed which is that the right hand sides involve "retarded" time which reflects the "causality" of the expressions. In other words, the left side of each equation is actually "caused" by the right side, unlike the normal differential expressions for Maxwell's equations where both sides take place simultaneously. In the typical expressions for Maxwell's equations there is no doubt that both sides are equal to each other, but as Jefimenko notes, "... since each of these equations connects quantities simultaneous in time, none of these equations can represent a causal relation." [8] The second feature is that the expression for E does not depend upon B and vice versa. Hence, it is impossible for E and B fields to be "creating" each other. Charge density and current density are creating them both.

Jefimenko clears this up perfectly! Thanks for forwarding me here. No wonder I was having problems with Maxwell's equations. They simply show a relation; in terms of causality it is another source that creates them all together! I wish my book explained these things. I am beginning to think that the writers don't know what they are talking about considering it so strongly speaks of Maxwell's equations being the cause.