B Interpreting light as Maxwell's EM wave

[robphy]

Regardless of what is happening with "electromagnetic waves" propagating in space
and possible superpositions of time- and space-varying field configurations,...
...at a given instant of time,
for each point in space
there is one electric field vector and one magnetic field vector.

 

[Rev. Cheeseman]

Are you thinking that these waves actually have spatial extent? If so, that's wrong. The arrows illustrate the magnitude and direction of the electric and magnetic fields at some point (usually the base of the arrow) but say nothing about the electric or magnetic field anywhere except that single point.

Regardless of what is happening with "electromagnetic waves" propagating in space
and possible superpositions of time- and space-varying field configurations,...
...at a given instant of time,
for each point in space
there is one electric field vector and one magnetic field vector.

But the electric field and magnetic field for each point in space doesn’t have to be necessarily perpendicular, correct? For example, like in this picture the electric field and magnetic field is not perpendicular http://physics.thick.jp/Experimental_Physics/Section1/figures/fig1-4-2_en.png

 

[Ibix]

But the electric field and magnetic field for each point in space doesn’t have to be necessarily perpendicular, correct?

If you want an electromagnetic wave they must be perpendicular. Otherwise you can have any relationship you like.

For example, like in this picture the electric field and magnetic field is not perpendicular http://physics.thick.jp/Experimental_Physics/Section1/figures/fig1-4-2_en.png

Those fields are perpendicular. You can see that from the 1:4 relationship between the offset and pitch of the helices.

 

[Rev. Cheeseman]

If you want an electromagnetic wave they must be perpendicular. Otherwise you can have any relationship you like.Those fields are perpendicular. You can see that from the 1:4 relationship between the offset and pitch of the helices.

What about unpolarized electromagnetic field? Because next to every magnetic fields are literally electric fields? The perpendicularity of E and M fields only applied to linearly polarized EM field if I'm not mistaken, but natural EM fields are unpolarized.

 

[weirdoguy]

What about unpolarized electromagnetic field?

Every EM wave has magnetic field perpendicular to electric one, and both are perpendicular to direction of propagation (that is, to the wave vector $\vec{k}$). One usually prove that right after deriving wave equations for $\vec{E}$ and $\vec{B}$. Polarisation is about direction of $\vec{E}$ (and hence $\vec{B}$) field in the plane perpendicular to $\vec{k}$.

 

[Ibix]

What about unpolarized electromagnetic field?

The same.

Because next to every magnetic fields are literally electric fields?

So what? The magnetic field at each point is perpendicular to the electric field at that point. At some other point the electric field there is perpendicular to the magnetic field there. The electric field at that other point may or may not be parallel to the electric field at the first point, but that doesn't mean that the electric field is not perpendicular to the magnetic field - why would you compare the electric field here to the magnetic field there when there's a magnetic field here too?

 

[Drakkith]

What about unpolarized electromagnetic field? Because next to every magnetic fields are literally electric fields? The perpendicularity of E and M fields only applied to linearly polarized EM field if I'm not mistaken, but natural EM fields are unpolarized.

What is an 'unpolarized' EM field? I'm only familiar with the concept of polarization in the context of waves and charge separation, not in a static EM field.

Also, note that even an unpolarized EM wave will have ONE electric field vector and ONE magnetic field vector for any point in space, and both of these will be perpendicular to each other. The field vectors of a nearby point may point in an entirely different direction. What makes the wave unpolarized is that the vectors at any single point will change orientation randomly over time with the constraint that both the electric and magnetic vectors must remain perpendicular to each other and to the direction of propagation.

 

[weirdoguy]

@wonderingchicken you are skeptical about the very basic knowledge about EM waves (and I know it's basic, I teach it to high school students). What textbooks you are using, that say something different than we (physicists and other knowledgable people) do?

 

[Ibix]

A "skeptical" response from @wonderingchicken, so I will repeat a question I asked in #50: you have posted a lot of diagrams of electric fields that look like this:

Do you think that they are meant to imply anything about the electric field anywhere except exactly on the zero-width black line?

 

[vanhees71]

Every EM wave has magnetic field perpendicular to electric one, and both are perpendicular to direction of propagation (that is, to the wave vector $\vec{k}$). One usually prove that right after deriving wave equations for $\vec{E}$ and $\vec{B}$. Polarisation is about direction of $\vec{E}$ (and hence $\vec{B}$) field in the plane perpendicular to $\vec{k}$.

How do you come to that conclusion? Can you prove it from Maxwell's equations?

It's true for plane-wave modes, but in general...

 

[weirdoguy]

It's true for plane-wave modes

Well, I'm implicitly in the high-school mode, so I can't say anything about general case since I don't remember much about that (I took upper level classical electrodynamics course in 2012...).

 

[Dale]

But the electric field and magnetic field for each point in space doesn’t have to be necessarily perpendicular, correct? For example, like in this picture the electric field and magnetic field is not perpendicular http://physics.thick.jp/Experimental_Physics/Section1/figures/fig1-4-2_en.png

They are perpendicular.

Your question has already been answered. In the far field (aka a EM wave) they are perpendicular. In the near field they do not need to be perpendicular.

Why are you still re-asking this question more than 20 posts later?

 

[Rev. Cheeseman]

A "skeptical" response from @wonderingchicken, so I will repeat a question I asked in #50: you have posted a lot of diagrams of electric fields that look like this:
View attachment 325468
Do you think that they are meant to imply anything about the electric field anywhere except exactly on the zero-width black line?

The axis is imaginary, correct? We can put the axis anywhere whether on top of the field, below, etc.

I have my own opinions regarding the electric and magnetic fields but this is not the "right" place to say anything about it because this entire forum is almost like a cult. Sorry for the honesty.

 

[Dale]

The axis is imaginary, correct? We can put the axis anywhere whether on top of the field, below, etc.

This shows a pretty big misunderstanding of the whole concept here, as well as a misunderstanding of the question asked. I am going to repeat my original recommendation that you get a computer algebra software package, write a known solution, and try plotting it. That exercise will be more beneficial for you than another 20 posts asking the same questions again.

this entire forum is almost like a cult. Sorry for the honesty.

Sorry for the thread ban, honesty is not a good justification for insults.

@ other participants, you may respond further if you wish but be aware that the OP will be unable to reply here

 

[weirdoguy]

I have my own opinions regarding the electric and magnetic fields

Opinions based on what? Lack of knowledge? You have shown in this and other threads that you are not here to learn. You just waste our time.

@ other participants, you may respond further if you wish but be aware that the OP will be unable to reply here

So is there any point in keeping this thread open? @wonderingchicken reply will be with "skeptical", as usual...

 

[Ibix]

The axis is imaginary, correct? We can put the axis anywhere whether on top of the field, below, etc.

The axis is the thing in the diagram with the strongest claim to being real. The red line is a visualisation of the values of the electric field on that axis and only on that axis, nowhere else. It is no more real than a graph of economic growth - do you think a graph of a rising share price means that there's actually a set of hydraulic jacks somewhere lifting the price up off the ground?

The black line at least has the virtue of representing a set of points in a straight line by a set of (near) points in a straight line.

this entire forum is almost like a cult

If I stand on Earth and drop a ball then it will fall. Would you agree? Would anybody disagree? Are we all part of a cult of gravity, then? Or are we just dealing with reality?

We are trying to describe a shared understanding of a well-studied phenomenon in this thread, an understanding that we routinely use to design and build devices like the one you are reading this on. Dismissing it as a "cult" is just as daft as dismissing gravity as a cult. It just takes a bit more work to understand what we're describing because the details are not in your every day experience.