I Electromagnetic Field vs Electromagnetic Wave

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1. Dec 6, 2018

When there is electric charge, then there is an electric field in space aorund it. Or when the electric charge is moving (without acceleration), then it is produced magnetic field in a space around it. Both of these fields permeated to infinity according to Maxwell theory. But how fast electromagnetic field permeated? Is that faster than electromagnetic waves produced by accelerating charge? How possible electromagentic waves with speed c traveling without there is electromagnetic field in the first place (as per definition)?

2. Dec 6, 2018

Delta2

An electromagnetic wave is an electromagnetic field that varies in time and space in such a way that it satisfies the wave equation. We cant have an electromagnetic wave if we don't have electromagnetic field!

3. Dec 7, 2018 at 4:14 AM

sophiecentaur

. . . conversely you can't have a field if it hasn't been established by an electromagnetic disturbance (AKA Wave) reaching that point from some cause. The 'static' situation is only a convenience to make the analysis simpler.

4. Dec 7, 2018 at 4:54 AM

Delta2

I think I understand what you saying, however we have to agree that the concept of the electromagnetic field is more fundamental than the concept of the electromagnetic wave.
The electromagnetic field, when it is dynamic (varying in time) it turns out that it satisfies the wave equation (homogeneous or inhomogeneous wave equation), hence it is a wave. When the electromagnetic field is static, it satisfies the Laplace's equation or the Poisson's equation. You are right that in order to establish a static field, that field was dynamic (hence a wave) earlier in time (during the process that was establishing the field).

5. Dec 7, 2018 at 5:04 AM

sophiecentaur

That's a bit like saying Position is more 'Fundamental' than Velocity. Whether or not it can be argued to be 'true' in some way, how actually relevant is the statement? Does it help with calculations or with problem solving?
People often to be preoccupied with what things 'actually are'. As far as I'm concerned, we just have a set of relationships (usually equations) that relate variables. The rest is essentially a personal thing or based on convenience.

6. Dec 7, 2018 at 5:18 AM

Delta2

Deep down maybe you are right, but at least for pedagogical reasons we should consider position more fundamental than velocity and the field more fundamental than the wave.

7. Dec 7, 2018 at 5:28 AM

sophiecentaur

Like I said. It's for Convenience and, "for pedagogical reasons" it would be a good idea to present it in those terms. (e.g. "We find it convenient to start with Fields . . . .") Students (in particular) want things to be presented to them in the form of rigid rules. By the time they are the level of Fields and Waves they should be above that way of thinking, imho. Using 'rules' too much can invite them to challenge apparent contradictions, later on. In teaching a sophisticated subject you are obliged to qualify all statements, firstly so students don't get conflicted and secondly so they don't waste hours of their lesson time whingeing about it. Science is really not a 'certain' field of knowledge and everyone should be aware of that, from the start.

8. Dec 7, 2018 at 5:58 AM

hilbert2

It's possible to have a solution for the equations of electromagnetism, where sinusoidal time dependent $\vec{E}$ and $\vec{B}$ fields fill the space but there are no static or moving charges anywhere. This is a kind of a situation where the source of the EM waves is "somewhere in infinity".

9. Dec 7, 2018 at 7:50 AM

Klystron

Forum members learning basic electronics should ponder the first sentence in hilbert2's post. Elegant.

Last edited: Dec 7, 2018 at 8:39 AM
10. Dec 7, 2018 at 8:06 AM

hilbert2

Yes, I can see how this is in some way related to the question "how do conduction electrons in the whole electric wire almost immediately know that a voltage has been turned on".

11. Dec 12, 2018 at 7:13 PM

But electromagnetic wave can travel up to far distance like how the light from the sun arrive on earth. But for (static) electromagnetic field it is diminish even when not far away from the source. So when I close the circuit and current travel at the wire loop, do you think there is magnetic field in 3x10^8 km away during one second?

12. Dec 12, 2018 at 7:23 PM

So the only way EM field exist at infinity (or at far distance) is when it appear as a wave. There is no other way to detect it (using measurement) at far distance except when it transform into a wave?

13. Dec 12, 2018 at 7:31 PM

Klystron

Pardon, just noticed the 'advanced' level designation. The question could be "Can we measure ...? "Can we discern the emf generated by the loop from noise?".

14. Dec 12, 2018 at 9:18 PM

Delta2

This is true but the reason for this is that the electrostatic (=near field=static+induction ) field strength drops as $\frac{1}{r^3}$ or $\frac{1}{r^2}$, while the electromagnetic field as wave (radiation field or far field) drops as $\frac{1}{r}$ where $r$ is the distance from the source. So the attenuation the electrostatic field has at $r=100m$ which is proportional to $\frac{1}{r^2}=\frac{1}{100^2m}=\frac{1}{10000m}$, is equal to the attenuation of the electromagnetic field as wave at $r=10Km$ which is $\frac{1}{r}=\frac{1}{10000m}$. So all in all, where the electrostatic field "survives" for 100m, the electromagnetic field as wave survives for 10km.

One more reason that we can detect the EM field as wave far from source, is because we can look for specific frequency. All kinds of waves , so EM waves too, have frequency and wavelength. On the contrary, the electromagnetic field as static has zero frequency and all the sources of static field add up and there is no way to discriminate between them.

Last edited: Dec 12, 2018 at 9:50 PM
15. Dec 13, 2018 at 4:04 AM

sophiecentaur

Not "during" but after one second, there would be a step function in the E field.
There is an inconvenient practical problem with measuring (nearly) steady state values of any variable. System noise needs to be coped with and that implies a measurement time that's can allow the detection of a change yet eliminate random variations with 'zero' - or very narrow bandwidth. When we measure a step in volts in a straightforward circuit, we tend to ignore the noise problem. It only becomes a problem with very low signal amplitude where the 'drift' due to outside causes is relevant.
That would apply to the situations described in this thread.