# Do Electromagnetic Waves really propagate through continuous Induction?

I've often seen it said that in an Electromagnetic Wave the changing Electric Field component creates the Magnetic Field Component and the changing Magnetic Field Component in turn creates an Electric Field Component. This is then used as an explanation that Electromagnetic Waves are "self-sustaining" and do not require a medium.

Do modern Physicists really think about Electromagnetic Waves in this way? Is this kind of propagation "mechanism" really even needed?

The first thing I noticed is that the Electric and Magnetic Field Components oscillate in-phase which suggests (to me at least) that energy isn't being transferred in between them as they both reach their maximum simultaneously.

As well it seems as if the Magnetic Field would be much too weak at 1/c proportional to re-create an Electric Field ~300 million times stronger than it. (See comments.)

Finally if Electromagnetic Waves are simply changes in the Electromagnetic Field propagating through space is any kind of additional "mechanism" even really needed?

• As well it seems as if the Magnetic Field would be much too weak at 1/c proportional to re-create an Electric Field ~300 million times stronger than it. In SI units, the E and B fields have different units, so you can't compare their strengths. In this sense, cgi units are more sensible. But in cgi units |E|=|B| for an EM wave. – user4552 Sep 25 '13 at 15:45
• I was lead to believe from a Physics Instructor that the Electric side of Electromagnetic Waves is much stronger than the Magnetic part. Is this not true? – jcelios Sep 25 '13 at 18:11
• No it is not. As Ben mentioned they have different units you can't compare them simply by comparing numbers – Gotaquestion Sep 25 '13 at 19:22
• Well I think of the second quantised electromagnetic field as a kind of Aether. I hasten to add that this is not like any mechanical medium thought of before Einstein and the wave effects in this "aether" are Lorentz covariant. Even so, the quantum ground state becomes apparent in an accelerated frame (see the Unruh effect) in a "medium"-like way. The main reason I find this idea appealing is not so much to say there's a light "medium", but that it gets rid of the disturbing concept of "empty space", which is now the quantum fields that fill it. – Selene Routley Oct 21 '13 at 0:14

Do modern Physicists really think about Electromagnetic Waves in this way? Is this kind of propagation "mechanism" really even needed?

I expect there is variability among all the people who study Maxwell's equations. Here's my take. The equations and all the quantities they contain are mathematical abstractions. We use these abstractions in prescribed ways to come up with some predictions for field values, powers, etc. We map these predictions to observable, measurable phenomena like resistors heating up or needles flicking on a dial. How you get these predictions really doesn't depend on how you think about the details of propagation. The solutions to Maxwell's equations are, regardless of how you think about them. We then go out and do some experiments to see if our predictions matched our measurements. When we do this, we find that Maxwell's equations are good predictors of every observed classical EM phenomenon. In this context, questions about the nature of $E$ and $B$ "creating" each other become kind of meaningless. What we have is a theory that describes experiment when we use it. How we choose to interpret the details of the theory don't change it's predictions; the only benefits to thinking about it one particular way or another is to help us intuit, recall, explain, or reason about the theory. In those areas, I find the idea that "$E$ begets $B$ begets $E$ begets $B$ begets ..." can be useful for recalling the two curl equations and how they combine into wave equations, or for how the Yee grid FDTD method works. But if you ask me if this is what is "really" happening when I flip on the light switch, my answer is "I can predict many useful things about the light when the switch is flipped without knowing the answer to your question."

Yes, electromagnetic waves do indeed propagate through continuous induction. In fact, this was the brilliant feature that Maxwell added to the theory that allowed him to write down equations that can be formed into wave equations.

Faraday had shown that changing magnetic fields induce electric fields, which we now write as

$$\nabla \times \vec E = - \frac{\partial \vec B}{\partial t}$$

Oersted had shown that a current carrying wire induces a magnetic field -- which was quantitatively studied and put in mathematical form by Ampere:

$$\nabla \times \vec B = \mu_0 \vec J$$

But a (idealized) current carrying wire is a not a changing electric field.

Maxwell, through a thought experiment, devised the so-called displacement current. Essentially, A wire charging a capacitor carries a current that generates a magnetic field. However, an Amperian surface that goes through the middle of the capacitor is not punctured by the current, so there should be no magnetic field. Maxwell realized that the changing E-field in the capacitor must also generate a magnetic field. With this observation, he added the so-called Maxwell term to Ampere's law:

$$\nabla \times \vec B = \mu_0 \bigg( \vec J + \epsilon_0 \frac{\partial \vec E}{\partial t} \bigg )$$

Add to this the source equations (see this, or any other source (NPI)), do some vector algebra, and you get the famous wave equations:

$$\frac{1}{\mu_0 \epsilon_0} \frac{\partial \vec E}{\partial t} - \nabla ^2 \vec E = 0$$

and

$$\frac{1}{\mu_0 \epsilon_0} \frac{\partial \vec B}{\partial t} - \nabla ^2 \vec B = 0$$

Thus an EM wave consists of a continuous process of induction of electric and magnetic fields.

I think it's always good to try to intuitively understand physical phenomena as much as possible instead of blindly relying on equations. As long as it still is feasible, like for classical electromagnetism and not so much for quantum mechanics for example.

If Electromagnetic Waves are simply changes in the Electromagnetic Field propagating through space is any kind of additional "mechanism" even really needed?

This sounds like you're trying to assimilate electromagnetic waves as the propagation of the disturbance of a medium (space, aka aether in Maxwell's era). Getting rid of that intuition is what allowed Einstein to develop special relativity. So yes, the self-sustaining intuition is a better intuition.

The first thing I noticed is that the Electric and Magnetic Field Components oscillate in-phase which suggests (to me at least) that energy isn't being transferred in between them as they both reach their maximum simultaneously.

Right, as the wave advances, it's not like they need to be out of phase so that E entertains B and then sequentially B entertains E. This actually happens simultaneously: at a given point, changes in B generate changes in E at its surroundings, and at that same point and time , changes in E generate changes in B at its surroundings.

• Upon further reading about Relativity and Electromagnetism I also have to wonder if the fundamental error I was making was treating the Electric Field and Magnetic Field as distinct entities when they really both seem to be manifestations of the same underlying "thing" namely what we call the Electromagnetic Field. – jcelios Oct 21 '13 at 5:06
• Magnetism is indeed a relativistic phenomenon, but treating the magnetic field and the electric field separately is not a mistake, as long as you stick to Maxwell's equations, which are already coherent with special relativity. – Alejandro Pedraza Oct 21 '13 at 12:45

Well actually the electric field never propagates. Yeah it's true the e-field just inducecs a magnetic field which actually propagates and when it reaches another antenna it reproduces the same current that made it (this is how really a chagigng m-field produces a changing e-field and vice versa). Then this induced e-field again produces another m-field. This m-field again travels through vaccum or whatever reaching another transmitter. This is how it works. The e-field is simply induced on antennas which cause current movement in it. And this do not travel anywhere but simply induces an m-field which reaches out to another transmitter. That is the correct picture

• I think this is false, in the concrete sense that if you put a stationary electron in the path of an EM-wave, it would accelerate. – user12029 Jul 18 '14 at 19:12