# How do EM waves propagate?

I have read about how electromagnetic waves propagate and what I surmise is that when charged particles such as electrons accelerate they produce time-varying electric fields. These electric fields produce magnetic fields and the process goes on.

Are the EM fields really moving? My textbook says it's changes in the field that is moving. I don't understand this part.

If EM waves are just changes in electric fields that seem to propagate along space, I have seen people on this site saying it happens because of continuous induction of electric and magnetic fields. How can I relate both of these ideas?

Are the EM fields really moving.

Classically, electromagnetic waves are propagating disturbances in the electric and magnetic fields.

Remember, the electric field of a point charge extends to infinity. It does not simply stop somewhere.

When the point charge is briefly accelerated, a disturbance in the field (and the associated magnetic field) propagates with speed c outward away from the point charge.

The disturbance will continue to propagate even after the point charge has stopped accelerating; the disturbance has "a life of its own".

There's a nice applet for visualizing this here:

But, do keep in mind that we must ultimately understand electromagnetic radiation in terms of photons and that requires quantum field theory.

So EM waves are just Changes in electric fields that seem to propogate along space.

As I wrote above: electromagnetic waves are propagating disturbances in the electric and magnetic fields. Now, how and why does that happen?

But i have seen people on this site saying it happens because of continous induction of Electric and Magnetic Field. How can i relate both of these?

Think carefully about what I wrote above: the disturbance has "a life of its own" and think about how that might be.

• @AlfredCentauri My views about these Field "Disturbances" is that when a charged particles is accelerated, their is a change in field lines. These changes then continue to happen through out the Field and travel at the speed of light.These changes are called EM waves. These changes dont require induction to sustain themselves. The change can go on forever. So how does Induction fit in here. Oct 15, 2013 at 8:45
• @AlfredCentauri But ofcourse induction is required. My textbook and so many people cant be wrong. So either my views about FIeld disturbances are wrong or i am missing a valuable point. Can you point out my mistake? Oct 15, 2013 at 9:06
• @opethDamnation The distinction between electric field and magnetic field is an artefact of describing electromagnetism in terms of classical mechanics. In terms of relativistic physics there is a single field: the electromagnetic field. The visualization of EM wave propagation as mutual induction of electric and magnetic fields isn't necessarily wrong (it's good classical physics), but it doesn't carry over to relativistic physics. No theory is exhaustive, we make do, but relativistic physics is deeper than classical physics of course. Oct 15, 2013 at 21:10
• With gentle respect, the quest for knowledge is absolutely impersonal. Statements like "My textbook and so many people cant be wrong" have no place in the pursuit of knowledge. Virtually EVERY textbook has been wrong, as knowledge is fluid, and understanding grows. Knowledge is a transient snapshot of understanding. To challenge by requesting proof of invalidity is a backwards defense. I do not post this to disparage, but to remind us of the greater path. Jun 26, 2016 at 16:40
• How is regenerative induction taking place here?phet.colorado.edu/sims/radiating-charge/… In this simulation, E field is being varied due to oscillation of charge. Then I imagine that H-field will be induced.So wont these H-field produce additional E-field? Feb 13, 2019 at 3:47

The answer to your questions requires that you understand how EM waves are generated. Imagine an electron which is not moving and stationary. According to Coulomb's law, a field is produced by this electron. The field will be static and not changing as long the electron isn't moving.

Imagine now you start to vibrate the electron in a sinusoidal way. What is going to happen to the field? The field will be changed in a way that conforms to the motion you're doing to the electron. Basically this change in the field is an EM wave, which is travelling at the speed of light.

So yes, the EM field's change moves, like the book has told you.

A cute simulation is available at this website (link changed because the first one doesn't work):

Hope this helps.

• I understand your point. So a change in EM field will propagate at the speed of light, resulting in EM waves with no actual movement of Field, or rather movement of field was not possible to begin with. But then my understanding of EM fields inducing each other becomes wrong? Oct 14, 2013 at 13:29
• Not able to edit so gonna write it here. So if i take the above model, then i run into a problem. Isnt Electric Field based on the inverse square law. So after some distance shouldn't its value decrease. I am not sure about the relation of E-field magnitude with EMR. But in this case its better to think about EM waves being constantly renewed with induction. Can someone clarify? Oct 14, 2013 at 15:56
• @opethDamnation In the simple model you saw in the simulation, you have a plane wave. When you talk about the field that has the inverse low, you have spherical planes. Oct 14, 2013 at 16:04
• @opethDamnation Because you have no mechanism for dissipation, and the energy is propagating in 1-direction with no problems. If you solve the Maxwell equations for spherical waves, then you'll see that inverse relation comes up. Though in realily, plane waves are just an approximation of a source which is very far away over a short span distance. Like for example the sun. If you study the rays coming from the sun along 100 meters, you'll find that the conditions are approximately suitable to consider them plane waves. Oct 14, 2013 at 16:11
• Oct 17, 2019 at 11:53

Propagation is defined as the movement of waves across the medium defined within the limits for the nature of wave. The propagation speed varies accordingly depending upon the various characteristics of the medium and waves.For instance, the electromagnetic wave, the mechanism of propagation involves mutual generation of periodically varying electric and magnetic fields and is far more difficult to understand than sound.

Wave Propagation Speed of a transmission medium is the speed at which a wavefront passes through the medium, relative to the speed of light. For optical signals, the velocity factor is the reciprocal of the refractive index.

Time T of a wave, is the time that elapses between the arrival of two consecutive crests (or troughs) at a certain location X. This definition is identical with the statement that the period is the time the vibration at X takes to complete a full cycle from crest to trough to crest. The period of a wave is given in seconds.

Source

Are the EM fields really moving. My textbooks says it's changes in field that is moving. I don't understand this part.

In your post, you mention a wobbling rope. Well, each fragment of that rope does not move along the rope. They just wobble where they are, without moving forward. But the wobbles themselves do move forward.

Likewise, the electric and the magnetic field do not move themselves. But every point of a field changes its state, and those changes propagate.

That said, the depiction of a EM wave as wobbly rope is inherently wrong.

The wobbly rope image is not a depiction of a radio wave itself. It's a graph where X axis is distance (in the direction of the wave propagation) and Y axis is the "strength" (or "tension") of the field in each point of that distance.

After investigating this matter further, reading answers on this site (specifically from dmckee and CuriousOne, thanks!) and a lot of thinking, I've figured out that:

• In almost every graph, one of the axes is time. But the wobbly rope graph is an exception, it doesn't demonstrate time. To demonstrate time, those graphs are animated.
• Sometimes, Z axis is added. Y and Z both mean the same thing: "strength", but one is for the magnetic field and the other one is for the electric field.
• The fields don't wobble. It's just every point of the field changes it's state. Each point of the field is a vector. This means that each point's state consists of two values: a "strength" and a direction. Each point of a field is always stationary, but each is associated with a direction and "strength". When an electric or a magnetic wave propagates through a field, the points of the field change their directions and "strengths" but they themselves never not move.
• The direction of each point of the field is always perpendicular to the direction of the wave that propagates through that region of the field.
• Electric and magnetic waves always travel together, and their directions in every point are perpendicular to each other. On the wobbly graph, the Y and Z axes are also perpendicular, but that's just a coincidence. Y and Z demonstrate amplitude, the "strength" of the field in every point, but the X axis demonstrates distance. Distance and "strength" are different things and don't correspond with each other! That's why those images are graphs, not illustrations of waves themselves.
• Electromagnetic waves normally travel in fronts, i. e. they spread spatially like sound waves or water ripples. But the graph represents not a spatial wave but a single line cropped from a spatial wave. That's merely a thought experiment.
• Though it's technically possible to emit exactly one photon (a photon is a single unit of a wave), a photon is a quantum particle. It abides to quantum laws. Human-world laws do not apply to photons. This means that it is not correct to speak about such thing as a "trajectory" of a single photon. (I can't get my head around this statement, please help me find a mental model for it! SOS!) This means that the wobbly rope illustration does not demonstrate a "single" wave. It merely demonstrates an 1D fragment of a 3D wave.
• When an electromagnetic wave travels as a front, the photons interact with each other, they kinda form a single "object" -- a spatial wave. This wave would, roughly speaking, bounce off a metal mesh (a Faraday cage), even though a single photon could easily come between wires of the mesh.

I too had the same problem, so I started constructing EM wave just as Maxwell did.To get a EM wave he combined two simple laws.

1. When an electron moves with velocity $v$, some magnetic field will be associated around it. As an electron moves, the electric field associated with it also moves; this results in a change in the electric field in space around the electron where we see magnetic field.

Here, the magnetic field is found only in the space where the electric field is changed and the strength of magnetic field at a point depends on the strength of electric field changed.

2. Similarly, the changing magnetic field produces an electric field only in space where the magnetic field is changed and limited to that region. Though there is no boundary for these two fields, let's neglect the weak field away from the electron.

Now, let an electron is vibrating in space bounded by an imaginary sphere(electric field out side the sphere is negligible). We have changing electric field and magnetic field inside the sphere. Change in electric field produce change in magnetic field where the electric field is changed and vice versa but the region out side the sphere is not effected.

The cross product, $\hat i\times \hat j=\hat k$, the resultant is directed in $\hat k$ direction, but it is not enough to say that it is proceeding in $\hat k$ direction it just say it directed in $\hat k$ direction.

How do EM waves propagate?

Like other waves propagate. IMHO the best way to appreciate this is to shake a rubber mat. When you do this you stretch a portion of the mat, and then the elasticity of the material contracts it back to its original size, but in doing so the rubber is stretched further along. What you then have is a shear wave with speed v = √(G/ρ), where G is the shear modulus of elasticity, and ρ is the density. In electrodynamics the expression is similar, and is written down as c = √(1/ε0μ0) where ε0 is electric permittivity and μ0 is magnetic permeability.

These E-fields produce H-fields and the process goes on.

You can read that light doesn't require a medium, and propagates because the E-field variations induces the B-field variation which induces the E-field variation. This is wrong I'm afraid. Read this:

Robert B. Laughlin, Nobel Laureate in Physics, endowed chair in physics, Stanford University, had this to say about ether in contemporary theoretical physics: "It is ironic that Einstein's most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity] was that no such medium existed [..] The word 'ether' has extremely negative connotations in theoretical physics because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it rather nicely captures the way most physicists actually think about the vacuum..."

Are the EM fields really moving. My textbooks says it's changes in field that is moving.

Your textbook is right. When you shake your rubber mat the wave moves away from you at say 2m/s, but the rubber mat doesn't. You've still got hold of it.

Do they disappear or continue with their movement.

They continue. The rubber mat doesn't go totally flat the instant you stop shaking.

But I have seen people on this site saying it happens because of continuous induction of Electric and Magnetic Field. How can I relate both of these?

You can't. See Wikipedia:

"Also, E and B far-fields in free space, which as wave solutions depend primarily on these two Maxwell equations, are in-phase with each other. This is guaranteed since the generic wave solution is first order in both space and time, and the curl operator on one side of these equations results in first-order spatial derivatives of the wave solution, while the time-derivative on the other side of the equations, which gives the other field, is first order in time".

You need to read up on four-potential. But for now think back to that rubber mat and imagine we're looking at a portion of it. It isn't flat, it's curved, and the slope of this curve at some point is the spatial derivative E, whilst the rate of change of slope is the time derivative B. There's only one wave there, not two. An electromagnetic wave. Check out Jefimenko's equations:

"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 wave (electromagnetism). However, Jefimenko's equations show an alternative point of view. 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."

Edit:

Duh, I have just noticed that this question is two years old!