Five questions about electromagnetic radiation

[Dale]

Not enough if there can be misinterpretations like vanhees71 is talking about.

vanhees71 is merely pointing out that the diagram is not the math. It is, in fact, a very incomplete graphical representation of a small portion of the math. There is much missing from the graph. That is not in any way an indictment of the math, but rather an acknowledgment of the incompleteness of the graph.

The math is always clear, even if the graph is not.

 

[pleco]

In the second paragraph vanhees71 was talking about the italics text I quoted in post #29, and said it's utter nonsense and misinterpretation of Maxwell's equations. I'm not sure how that reflects on EM waves and what difference does it make.

 

[Dale]

It doesn't make any difference to the math. What vanhees71 is saying is that the quoted paragraph is not a good math-to-English translation. I agree, although I probably wouldn't go as far as to call it "utter nonsense". Both vanhees71 and I tend to be rather math-oriented, perhaps with him being even less tolerant of English vagaries than I am.

 

[pleco]

The electric field is only shown at p0. The end of the vector is not a point in space, it is just a representation of the strength and direction of the E field at p0.

"The electric field describes the electric force experienced by a motionless positively charged test particle at any point in space relative to the source(s) of the field."
http://en.wikipedia.org/wiki/Electric_field

It's supposed to be relative to some point, what Wikipedia calls "test particle". I introduced those points, they are not originally in the diagram. Does electric field have some value at those points? If yes, then how does value at p1 and p3 compare to p0: greater or less, positive or negative?

Regarding the polarity, that depends on the direction of the coordinate axes, which are not explicitly shown. If right is x, up is y, and out of the screen is z, then the E and B at p0 are both positive.

Is magnetic field not supposed to be a dipole? Does magnetic field north-south orientation have bearing in lateral left-right direction relative to k vector, or is it aligned front-behind parallel to k?

Does the magnetic field in "full 3D" look like this:

 

[Dale]

It's supposed to be relative to some point, what Wikipedia calls "test particle". I introduced those points, they are not originally in the diagram. Does electric field have some value at those points?

The test charge would be located at p0, and the electric field value is only plotted at p0. I am sure that it has some value at other points, but no information about those other points is provided.

Is magnetic field not supposed to be a dipole? Does magnetic field north-south orientation have bearing in lateral left-right direction relative to k vector, or is it aligned front-behind parallel to k?

To get information about the overall shape of the magnetic field you would need to have a more complete plot of the field. There simply is not sufficient information here to do a multipole expansion and determine.

The magnetic field of a single proton, neutron, or electron, is a dipole field. However, that does not mean that all magnetic fields are dipole. However, Gauss' law for magnetism does show that you cannot have a monopolar magnetic field.

If the plot you are showing is meant to show one line from a plane wave then the field is planar, and not well described by a multipole expansion. If the plot you are showing is meant to show one line from a dipole antenna then the field is dipolar even though you cannot tell from this plot.

 

[vanhees71]

Sigh, precisely what you don't want to know is what answers your question! As I said earlier: Your confusion comes from looking at an utterly wrong picture. Calculate the field yourself and then draw the field lines, etc. You find these pictures in any good E+M book. Look for "Hertzian dipole solution". This is the most simple time-dependent field you can have!

I'm not setting up conditions or deciding how charges are moving, just trying to interpret the diagram. I'm looking at any instant in time where blue vectors are depicted as vertical arrows pointing upwards.

Forget the diagram. It's misleading!

I'm not asking for any numerical values now, only about general properties and basic relations: greater, less or equal, positive or negative.

Well, you cannot answer these questions, if you do not define the conditions under which the electromagnetic field is created. So nobody can answer your question.

It doesn't make sense to me either. As I remember Ampere's and Faraday's law it's moving E field that creates B field, not changing, just moving, and moving E fields are electric current. So basically it's electric currents that create B field depending on current density. In return changing magnetic field can create an electric current by making E fields move, but I never thought B field can change E field or create new ones.

There are four local (!) equations governing the entire business of electromagnetism. That are Maxwell's equations. Those equations have solutions, giving the electromagnetic field (consisting of six components, usually written in terms of two three-dimensional vector fields, $\vec{E}$ and $\vec{B}$) as being caused by electric charge and current distributions, which can be clearly interpreted by a cause-effect relation: The charge-current distribution is the source of the electromagnetic field, which is connected to the sources by retarded integrals, which takes into account that the em. waves travel always with the speed of light (in a vacuum). There cannot be faster-than-light cause-effect relations due to the causality structure of relativistic spacetime, and electrodynamics is a relativistic theory.

If you wish, you can artificially write the electric field in terms of the magnetic field, using Faraday's Law, but if you plug in the solution of the magnetic field, you see that it this is a very complicated, non-local and not expclicitly causal expression. Thus, it is not possible to interpret the electric field as being caused by a time varying magnetic field. In the same way you can express the magnetic field in terms of the current density and the time derivative of the electric field by solving the Ampere-Maxwell Law, and again you don't find an easily interpretable cause-effect relation.

 

[pleco]

The test charge would be located at p0, and the electric field value is only plotted at p0. I am sure that it has some value at other points, but no information about those other points is provided.

Information for p0 is provided by some equation which I suppose can also provide values for any arbitrary point as well. Do you know if such equation exists?

To get information about the overall shape of the magnetic field you would need to have a more complete plot of the field. There simply is not sufficient information here to do a multipole expansion and determine.

I guess then what I'm really looking for is some more complete type of diagram or animation.

 

[pleco]

Sigh, precisely what you don't want to know is what answers your question! As I said earlier: Your confusion comes from looking at an utterly wrong picture. Calculate the field yourself and then draw the field lines, etc. You find these pictures in any good E+M book. Look for "Hertzian dipole solution". This is the most simple time-dependent field you can have!

Wouldn't a single oscillating electron be sufficient? Let a single electron accelerate vertically up and down 5 times per second over 1 meter distance, that is total of 10 meters per second. How many waves will be emitted in one second?

Thus, it is not possible to interpret the electric field as being caused by a time varying magnetic field.

Makes sense. So what do you say the equation really means?

 

[Dale]

Information for p0 is provided by some equation which I suppose can also provide values for any arbitrary point as well. Do you know if such equation exists?

Yes, that is Maxwell's equations in general.

There are additionally specific solutions for Maxwell's equations that are well-known. The two most common (either of which could be what the diagram is referring to) are a dipole antenna and a plane wave:

https://en.wikipedia.org/wiki/Dipole#Dipole_radiation
https://en.wikipedia.org/wiki/Plane_wave#Polarized_electromagnetic_plane_waves

 

[pleco]

Yes, that is Maxwell's equations in general.

There are additionally specific solutions for Maxwell's equations that are well-known. The two most common (either of which could be what the diagram is referring to) are a dipole antenna and a plane wave:

https://en.wikipedia.org/wiki/Dipole#Dipole_radiation
https://en.wikipedia.org/wiki/Plane_wave#Polarized_electromagnetic_plane_waves

Unfortunately that opens even more questions for me, I don't know where from to even begin asking. I'll see if I can boil down some useful questions.