Conceptual difficulties with the generation and description of EM waves

[ak71]

Hello all,

I had a question about Electromagnetic waves. Although it isn’t homework (just to settle something in my own mind) I thought this would be the best place to put it.

Perhaps it would be best if I could explain a situation I could understand and then hopefully someone could bridge the gap between that point and the accepted theory.

Firstly, as I understand it, if you have a point charge in a vacuum, electric field lines will exist radially from the charge. Close to the charge the E-field will be very strong, and will decay with distance according to a normal 1/r^2 dependence.

Now, if I were to take that charge and move it a little to the right, and then back to its starting position, any point to the right of this system would have noticed a slight increase in the E-field (due to the charge being a little closer). If I were to repeat this process again and again, then a graph could be made of time vs. E-field strength at a certain point and a simple sinusoidal wave would be seen.

The above is a situation I can grasp. It is getting from this (incorrect) picture to the accepted theory of the generation of EM waves that I need some assistance with.

As I understand it, an E-field is represented mathematically as E=E_0*sin(kz-wt) and so the strength of the field varies with position along the z-axis (in this case) and time.
In one of the lovely diagrams where we see a sinusoid oscillating in the x-z plane (the E-field) in phase with another sinusoid oscillating in the y-z plane (the B-field) as the wave travels along in the z-directing, where is the change in the strength of the E-field being represented? The sinusoid is spatial, it graphs the x or y-axis against the z, there is no mention of an oscillation in the strength of the field.

Again, I could appreciate if we were graphing z-position against E-field, but it confuses me to no end that the E-field has a spatial amplitude and not just a Vm^-1 amplitude.

In summary, if someone could explain why there is no mention of a change in the strength in the field and why there is an actual motion in the e-field, it would be much appreciated.

It’s a difficult question to get across and so I apologise if it has not seemed too clear to you. I’d be more than happy to clear up any hazy parts if you ask below. Thank you very much for taking the time to read this!

 

[TSny]

Again, I could appreciate if we were graphing z-position against E-field, but it confuses me to no end that the E-field has a spatial amplitude and not just a Vm^-1 amplitude.

In summary, if someone could explain why there is no mention of a change in the strength in the field and why there is an actual motion in the e-field, it would be much appreciated.

It’s a difficult question to get across and so I apologise if it has not seemed too clear to you. I’d be more than happy to clear up any hazy parts if you ask below. Thank you very much for taking the time to read this!

Hi ak71. I'm not sure I'm fully understanding your question, but I remember having somewhat similar puzzling thoughts when I was a student.

It's important to understand that the graph of the oscillating electric field should not be interpreted as indicating that any "thing" is actually oscillating spatially in a direction perpendicular to the z-axis. The arrows simply indicate the magnitude and direction of the E-field vector at various points along the z-axis.

For a transverse wave on a string there is spatial displacement of the medium (string). But for an EM wave there is no medium and nothing is oscillating spatially transverse to the propagation direction. An electric field vector is fairly abstract. It should not be interpreted as indicating that anything has moved from the tail to the tip of the vector.

Here is a http://blogg.lnu.se/optics/page/2/ that might help. In the animation it's tempting to think that something's actually oscillating spatially. But one of those oscillating E-vectors just indicates that the electric field at one fixed point is changing magnitude and direction. The tail of the vector is at the fixed point where the field is being represented by the vector. As the vector grows in size, the tail of the vector remains at that point and the increased size of the vector simply indicates that the field at that fixed point is stronger. The field only has a V/m amplitude, never a spatial amplitude. The V/m amplitude is represented by the length of the E-vector.