Propagation of EM-Waves, Independence of B and E, and Grav...

[Anton Alice]

Hello Forum,

I have a lot of questions concerning Wave propagation, but I will not pose them all into one thread, because of my experience, that part of them will be overlooked.

So let's get started:

1. Phase shift, E-B- Independence
Consider a plane wave generated by a distant dipole antenna, propagating in the x direction. Seemingly the phase between E and B shifts from 90deg to 0deg during the travel. And seemingly this is a contradiction to the argument, that E and B create each other, because if one would look at one position x in space, E and B would have the same "slope", therefore it would not be possible for them to be created by oneanother. I am not sure about that, because one shall not only look at one position x. One has to look at the whole "history", I mean the whole plane wave, because otherwise, by just looking at one point I would ignore the fact, that this is actually a plane wave, which is an important information.

Even if I look at for example an spatial interval of λ, I can not yet resolve this issue. Maybe that spatial interval is not enough, do you have an idea?

Nevertheless, my question is actually: Does that picture of E and B creating each other hold?
I see the fact, that E fluctuations are always accompanied by B fluctuation and vice versa and they are inseparable. So there is no way to create or absorb the E-part without creating or absorbing the B-part.
But that does not mean at all, that they should be existentially dependent on each other.

If I am not straying , that would mean for the planewave in the far-field of the dipole-antenna, that the E-plane and B-plane are generated equivalently by the dipole, but not by each other. So the B-planes are not a product of the E-planes and vice versa, but both are simply a product of the radiation source. Doesnt make that sense? I mean, if you now take another antenna, to absorb that plane wave, you have to adjust it such that the E-Field is parallel to the antenna, in order to create a voltage drop inside of it. If E and B would be somehow existentially related, then I could also calculate that same voltage drop inside the antenna by just looking at the B-field. But that B-field is a plane, and it can not possibly create a voltage drop inside the same antenna.
Similarly, and even more impressive, if you try to absorb the plane wave by using a ring-shaped antenna, then you have to adjust it such that the plane normal of the ring antenna is parallel to B. The B would then create a voltage drop inside the ring by creating an eddy E-field. Again, if that picture of E<-creating->B would hold, then that eddy E-Field which I just mentioned, that has been created by the magnetic field inside the antenna loop should also be a part of E-plane-field, which is (vainly) a product of the B-plane according to the picture.
But this can not be the case, because the E-plane is not able to create a voltage drop inside that ring-antenna. Therefore that Eddy-E-Field is not a Part of the E-plane accompanying the B-Plane.

Conclusion: that picture of E<-creating->B does not hold.EDIT:

I thought about that phase-difference question again and actually found, that there is no contradiction. One has to link spatial variation of the one Field wit time variation of the other Field. Not spatial-spatial or time-time. Then it makes sense. Now B and E could be actually existentially linked... But I still doubt that, because my explanation above is still active.

 

[davenn]

Conclusion: that picture of E<-creating->B does not hold.

considering that Maxwell's work clearly defines that a varying B creates a varying E with creates a varying B and so on

Maybe you need to review your thoughts

I will let those more learned, than I, on the fine details of the topic, lead you further to see where you are going astray
@DaleSpam , @mfb

regards
Dave

 

[Simon Bridge]

Welcome to PF,
The description of E and B creating each other is kind of a yes and no thing.
If the field you have obeys Maxwells equations then the picture is fine because that is how you get EM traveling waves out of them.

 

[Anton Alice]

Well, what is then wrong with my Ring-antenna gedankenexperiment?

 

[Simon Bridge]

I don't understand the description.
You seem to be asserting that, if E makes B, then the eddy E field must be aligned to the plane wave E field. Is that correct? If so, then there's your error.

 

[Anton Alice]

If that picture holds, then the B-part of the Planewave creates a lot of E-curls, which all should add up to an E-plane. So that E-plane is made up of E-curls.
Therefore that E-Planes should also be able to create a voltagedrop inside the ring-antenna. Can they do that? I realize that the Planes have a curl (unless I only move perpendicular to propagationdirection).
But how can... oh my god... you are right... OK. question Nr.1 is solved. thank you for that.

 

[Simon Bridge]

Why should they add up to an E plane?
It is OK for an EM field to induce another one with different properties... the field in the presence of a conductor is going to be different from the field without the conductor.

 

[Anton Alice]

They must add up to a E plane. You yourself said sir, that the picture holds. therefore all of E must be a product of B. And B nothing but lots of little eddies. so it is these eddies, which in the end make up the plane. Of course we are still talking about vacuum. There is no free charge yet... wait... I will come to that tomorrow in another thread.

 

[Anton Alice]

what is the difference of an electric field to a gravitational field? why can gravitational waves exist on their own, and why should the same be false for electric fields?

consider the following example:

imagine an electron somewhere in freespace. the electron creates an electric spherically symmetric field.
now the electron is moved in the z-direction by 1 meter, with a velocity of ,say, 100 meters per second.
now the electric field constellation has been change, since the position of that electron has been change.
But in that transition of the electron from one position to another, also the electric field had to undergo a transition from one constellation to another.
That transition of constellation can only occur with the speed of light. In other words: if someone, who is sitting at a distance of one lightsecond apart from the electron, and wants to estimate the position of the electron by looking at the fieldconstellation, that person has to wait 1 second until the information about the new position has reached him/her.

And my conclusion then would be: because there is an information content in that transition field, there is also an energy transmission, because information is energy.PS: I really would like to see some kind of field simulation, where I can move a charge around with the cursor, and see how the field-change propagates through space. There is no other way of convincing me of the opposite. I need a simulator. Do you know something?

 

[davenn]

what is the difference of an electric field to a gravitational field? why can gravitational waves exist on their own,

because they are generated by different mechanisms

maybe you should google some basic explanations of each ?

 

[davenn]

PS: I really would like to see some kind of field simulation, where I can move a charge around with the cursor, and see how the field-change propagates through space. There is no other way of convincing me of the opposite. I need a simulator. Do you know something?

google gave that answer too

http://phet.colorado.edu/en/simulation/radiating-chargeDave

 

[Anton Alice]

cool, that's great. but after looking at that simulation it seems to me, that electric field waves can propagate without consideration of magnetic fields?
Is there something wrong with my eyes?... or with my brain?
If there wouldn't be a magnetic field for some reason, then what problem would occur? I don't see the necessity of B.

 

[davenn]

that electric field waves can propagate without consideration of magnetic fields?

no, its just that they are only showing the electric field for clarity of the simulation
the moment you have a moving charge/electron, an EM ( electromagnetic) field is generated and radiated

Dave

 

[Dale]

Nevertheless, my question is actually: Does that picture of E and B creating each other hold?

I don't really understand your post, but you may be interested in this:

https://en.m.wikipedia.org/wiki/Jefimenko's_equations#Discussion

 

[davenn]

I don't really understand your post, but you may be interested in this:

https://en.m.wikipedia.org/wiki/Jefimenko's_equations#Discussion

Thanks for that link

 

[Dale]

If there wouldn't be a magnetic field for some reason, then what problem would occur? I don't see the necessity of B

What do you mean by "necessity"? If you have the E field and relativity then the B field is logically required. But does that make it a "necessity" in your view? Is the E field necessary? Is relativity necessary? Is logic necessary?

Regardless of whether you consider it necessary, the B field is clearly a feature of the world around us.

 

[Anton Alice]

Thank you Dale for the link. yes, my first post was a little chaotically written.

 

[sophiecentaur]

Well, what is then wrong with my Ring-antenna gedankenexperiment?

The near field arrangement of fields can have many forms in different antennae. 'Inside' a multi element array, it can be very hard to calculate and, afaik, approximations are needed. Loop antennae have different impedances from dipole impedances. But the 90° phase difference that people talk of is not exactly 90°. The departure from 90° represents the resistive component, which corresponds to an inphase component, which accounts for the energy lost / radiated. When you match the input to a transmitting antenna, the reactive parts of the input impedance are canceled and the Radiation resistance is all that's left - the V and I at the drive point are in phase. Within the antenna itself and near to it, the phases can be all over the place. 90° for a simple structure but those fields are evanescent and die out (because they cannot be radiating energy). All that's left is the in phase components.
I would agree with other replies that you have been getting in that there's no point looking for a 'cause and effect' between E and H. They just exist together in free space but, inside a structure, one can be storing or propagating much more energy than the other so it may be regarded as existing on its own.

 

[Simon Bridge]

They must add up to a E plane. You yourself said sir, that the picture holds. therefore all of E must be a product of B. And B nothing but lots of little eddies. so it is these eddies, which in the end make up the plane. Of course we are still talking about vacuum. There is no free charge yet... wait... I will come to that tomorrow in another thread.

... just because the E and B fields generate each other to propagate in air or in a vacuum does not mean the same fields will do so in a conductor. Indeed, if the conductor is ideal, there should be no E field inside it at all.

This is due to the interaction of the incoming wave with the conductor. Conditions outside the conductor are different to inside the conductor. There is no reason to suppose that a B field that generates a particular E field in air will generate the same field in a medium. This is why I directed your attention to Maxwell's equation so you can do physics by maths instead of by rule of thumb.

You'll notice my original reply was actually:

The description of E and B creating each other is kind of a yes and no thing.

... the link is as you explained in your edit post #1. The rest of what you need comes under the heading "boundary conditions"... which is how these equations describe different fields in different situations.

If you prefer a microscopically detailed model, you'd need to account for the fields due to the atoms and "free" electrons of the conductor, and the fields resulting from their interactions with the incoming wave. The end result is well modeled by the usual set of boundary conditions for a classical conductor.

 

[Simon Bridge]

If there wouldn't be a magnetic field for some reason, then what problem would occur? I don't see the necessity of B.

An EM field with no B component is a static electric field... it does not change with time.
This would be a problem in any physics that hopes to model a non-static electric field.

 

[Anton Alice]

I am only interested in the propagation of Energy.
And from my point of understanding Maxwell's Equations only state, that for non-static Fields there is no E without B, so they always appear together.
Maxwell's Equations don't say anything about whether the E-part of the non-static propagating field can propagate and carry energy on its own, or if E needs the help of B in order to propagate.

Regarding propagation:

Consider a dipole-antenna. It has a certain directivity (I don't know if this is the right english word. I mean the radiation characteristics), which looks something like cos^2.
Suppose I place a positive charge q right above the dipole antenna, in the direction parallel to the dipole-axis. According to the directivity of a dipole antenna there should be no radiation at that point, where I placed the charge.
Disregarding the directivity, the charge q should experience an alternating repulsion and attraction by the electric field of the dipole-antenna, because of the oscillating charge distribution inside the dipole antenna. So at t=0, the upper section of the antenna is positively charge, while the lower part is negative, therefore q should be repelled. And for t= T/2 there should be an attraction etc.

In short: The charge q experiences an alternating push and pull, which I can use, to get energy out of it, right? Is this a different kind of radiation? Is this at all radiation? To me this looks like a kind of radiation, where the E-field is longitudinal to the propagation.
Please elaborate on this.

Thank you in advance.

 

[Dale]

I am only interested in the propagation of Energy.
And from my point of understanding Maxwell's Equations only state, that for non-static Fields there is no E without B, so they always appear together.
Maxwell's Equations don't say anything about whether the E-part of the non-static propagating field can propagate and carry energy on its own, or if E needs the help of B in order to propagate

The E field has an energy density proportional to $E^2$ (the B field also has a similar energy density). However, EM energy flux density is given by the Poynting vector which is proportional to $E \times B$. So, while the E field can store energy without the B field, it cannot move it anywhere without the B field.

In short: The charge q experiences an alternating push and pull, which I can use, to get energy out of it, right? Is this a different kind of radiation? Is this at all radiation? To me this looks like a kind of radiation, where the E-field is longitudinal to the propagation.
Please elaborate on this.

What you are describing is the near field of the dipole antenna. It is not considered radiation because the energy does not radiate out to infinity, but rather stays localized near the antenna. In this region E and B need not be perpendicular to each other nor proportional to each other.

 

[Anton Alice]

EM energy flux density is given by the Poynting vector which is proportional to E×BE \times B. So, while the E field can store energy without the B field, it cannot move it anywhere without the B field.

Hello Dale. What is the origin of the Poynting Vector? Is there a derivation of it, that proofs, that I have to take the crossproduct of E and B (why not BxE?), to get the direction of energyflow?

EDIT:
The fact, that you have to take ExB instead of BxE seems to me like a pure definition of what we consider as the direction of energy flow, right?

, while the E field can store energy without the B field, it cannot move it anywhere without the B field.

How can I know that, without arguing with poynting?

 

[Dale]

Hello Dale. What is the origin of the Poynting Vector? Is there a derivation of it, that proofs, that I have to take the crossproduct of E and B (why not BxE?), to get the direction of energyflow?

Here is my favorite derivation for Maxwell's microscopic equations.
http://farside.ph.utexas.edu/teaching/em/lectures/node89.html

And here is my favorite derivation for the macroscopic equations.
http://web.mit.edu/6.013_book/www/chapter11/11.2.html

As you can see, the sign of the $E\times B$ term falls naturally out of the derivation. However, the interpretation of the various terms as energy density, energy flux density, and power density is perhaps not as obvious. It requires some familiarity with continuity equations.