# Electromagnetic Field vs Electromagnetic Wave

Mohammad Fajar
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)?

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## Answers and Replies

Homework Helper
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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!

Science Advisor
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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!
. . . 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.

Homework Helper
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. . . 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.
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).

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however we have to agree that the concept of the electromagnetic field is more fundamental than the concept of the electromagnetic wave.
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.

DaveE
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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.
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.

Klystron
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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.
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.

Klystron
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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".

Klystron and sophiecentaur
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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".

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

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

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".

Mohammad Fajar
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?

Mohammad Fajar
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.
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?

Gold Member
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?

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?".

Homework Helper
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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?
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.

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Klystron
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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?
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 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.

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Klystron
alan123hk
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)?View attachment 235342

Suppose there is certain static electric charge or static current established in the empty space, how fast electromagnetic field permeated?
The boundary between the static field and the EM wave, or the frontwave of the EM wave will certainly propagate outward at the speed of light.
We can also imagine that the region of static field will inflate at the speed of light.

How possible electromagnetic waves with speed c traveling without there is electromagnetic field in the first place ?
There is definitely no need to have static field in the first place for generating and propagating of EM wave .
Just consider a simple radio transmitter, does it need or intend to establish either electrostatic or magnetostatic field before starting to emit radio wave ? The answer is certainly NO.
When the radio transmitter has been turned off, the EM wave will also continue to exist and propagate through the space until it has been absorbed.

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?

I think so.
The Information must be carried and conveyed by EM wave when we try to measure anything about the EM field.

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Science Advisor
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or static current established in the empty space,

you cannot have a static current ... "current " by definition is moving

alan123hk
you cannot have a static current ... "current " by definition is moving

You are right.
I think the correct term should be "steady electric current" which can create certain static magnetic field, and that is actually what I want to say.

Delta2
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You are right.
I think the correct term should be "steady electric current" which can create certain static magnetic field, and that is actually what I want to say.

OK, which makes the rest of hat you say meaningless

since if you have a current, there must be a circuit. You have not defined what this circuit is.

We can also imagine that the region of static field will inflate at the speed of light.

if it is static, again by definition it cannot be spreading out (inflating <- your word) ... it is STATIC ... it isn't going anywhere

How possible electromagnetic waves with speed c traveling without there is electromagnetic field in the first place ?
There is definitely no need to have static field in the first place for generating and propagating of EM wave .
Just consider a simple radio transmitter, does it need or intend to establish either electrostatic or magnetostatic field before starting to emit radio wave ? The answer is certainly NO.
When the radio transmitter has been turned off, the EM wave will also continue to exist and propagate through the space until it has been absorbed.

I can see it's time you went and did some reading up of EM fields and waves as you have a few misconceptions ...
Here's a starting point ...

https://en.wikipedia.org/wiki/Electromagnetic_field

cheers
Dave

alan123hk
if it is static, again by definition it cannot be spreading out (inflating <- your word) ... it is STATIC ... it isn't going anywhere

Firstly, please pardon me if there is any grammatical mistakes in my writing, I am not a native speaker of English.

I just found similar description in a book as "If any region is uniform and static, it will inflate and eventually encompass our observable universe"
https://books.google.com.hk/books?id=lZOBAgAAQBAJ&pg=PA213&lpg=PA213&dq=static+region+will+inflate&source=bl&ots=LCfiH7cSye&sig=LC5w87VxJRMlpkTuL3N6ohp0bWM&hl=en&sa=X&ved=2ahUKEwi_yrW24M7fAhUBa94KHVAzDS4Q6AEwAHoECAcQAQ#v=onepage&q=static region will inflate&f=false

Just one question, so what is the fundamental logical difference here that makes "the region of static field will inflate.." wrong?

Thanks.

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Science Advisor
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Firstly, please pardon me if there is any grammatical mistakes in my writing, I am not a native speaker of English.

That's OK, no problems .... I don't claim to be an expert at that myself

I just found similar description in a book as "If any region is uniform and static, it will inflate and eventually encompass our observable universe"
https://books.google.com.hk/books?i...=onepage&q=static region will inflate&f=false

I'm pretty sure that isn't referring to EM fields ... It's referring to cosmic/cosmological inflation.
Those with more knowledge than me would be able to confirm that
@PeterDonis ?

D

alan123hk
since if you have a current, there must be a circuit. You have not defined what this circuit is.

I also don't understand why the circuit must be strictly defined if I just want to assume certain "steady electric current" has just been established in the space which can create certain static magnetic field, but it is certainly come from some dynamic change of electromagnetic field prior to the "steady electric current" has been established, and that dynamic change constructed the wavefront which enchoseing the boundary of the inflating region of the static magnetic field (pardon, I may be wrong once again since I really can't find other more appropriate wording to describe my idea in the moment..).

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Science Advisor
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Note that the current density of a moving point charge is not steady (even when the point charge is uniformly moving):
$$\vec{j}(t,\vec{x})=q \vec{v} \delta^{(3)}(\vec{x}-\vec{v} t).$$

Science Advisor
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"If any region is uniform and static, it will inflate and eventually encompass our observable universe"
I think you are implying a cause and effect here when really it's just a description of a situation. There can be no such thing as an unchanging situation in EM. A field that you can measure will have taken time to establish - by an accumulation of charge difference (E) or a flowing current (H) that was altered on at some time. The Maths of these situations allows the use of infinite times and distances but they have no real meaning in the World and the Maths is/was not aimed at them; when we consider a 'DC' situation. what we are doing is to use a time frame that's big enough (and a bandwidth that's low enough) to assume that switch-on was long enough ago and to let us just get on with the actual problem we are considering.
In another context, people glibly discuss the Fourier Transform as if it describes the frequency spectrum of a waveform but, in reality, we always assume that the values outside a particular range are near enough zero to neglect them. There is no point in trying to get philosophical about this - it just pragmatic.

alan123hk
There can be no such thing as an unchanging situation in EM. A field that you can measure will have taken time to establish

This seems to be an interesting and profound argument.
Are you saying that the electrostatic / magnetostatic field - one basic topic of classical electromagnetism may not actually exist ?

Science Advisor
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This seems to be an interesting and profound argument.
Are you saying that the electrostatic / magnetostatic field - one basic topic of classical electromagnetism may not actually exist ?
It depends on what you mean by "exist". Personally, I don't have a problem with the existing or not existing of physical terms. Just because the Maths runs out of meaning at infinity doesn't mean we can't use the Maths to describe and (more importantly) predict things. There is not a single experiment on anything that can start off with a truly static situation; you have to bring the kit into the Lab and turn it all on and then you have to turn it off and de-rig it, at the end. Your 'fixed' conditions are not actually fixed but we do not worry about it. But you still need to be aware of the time to wait before doing your actual experiment. The power supply volts have to stabilise, so does the floor of the lab and the temperature in the room - all to within the accuracy you are working.
If the above doesn't upset you and if you are prepared to consider your experiment is valid then the deeper existence or non-existence of an 'electrostatic' field need not bother you either. I don't think this is any big deal - it's just practical.
Edit. People can get too philosophical about such matters and it's easy to treat Science as a Religion. Our scientific beliefs should be restricted to things that can be verified or falsified by experiment. More than that is outside the realm of Science.