B Interpreting light as Maxwell's EM wave

[Rev. Cheeseman]

I wonder if there are actually instances or if there are possibilities for the electric fields and magnetic fields to be parallel (or non-perpendicular) to each other instead of being perpendicular.

What happens if the electric fields and magnetic fields are parallel (or non-perpendicular) to each other?

 

[Drakkith]

I wonder if there are actually instances or if there are possibilities for the electric fields and magnetic fields to be parallel (or non-perpendicular) to each other instead of being perpendicular.

I don't think they can be anything but perpendicular to each other.

 

[Dale]

I wonder if there are actually instances or if there are possibilities for the electric fields and magnetic fields to be parallel (or non-perpendicular) to each other instead of being perpendicular.

What happens if the electric fields and magnetic fields are parallel (or non-perpendicular) to each other?

Such fields are called "near fields". The near fields are called "near" because they do not propagate very far from the antenna. Away from the antenna the fields are called "far fields" and are orthogonal. That is what radiates far away.

 

[robphy]

This might help.

https://glowscript.org/#/user/Rob_Salgado/folder/My_Programs/program/robphy-maxwell-EMwave-2022

It's an animation of an electromagnetic plane wave in vacuum (no source charges or currents),
together with an animation of the Maxwell Equations
...the Gauss Laws for E and for B (using the Gaussian surface shown),
and the Faraday Law and the Ampere-Maxwell Law ( the "mechanism" for telling B and E (at each point) how to change with time, depending on the curls of E and of B ).

The result of what B and E should do is
to propagate the configuration of the entire electromagnetic field
by a little displacement in the direction of $\vec E \times \vec B$. Repeat.Tap the 'w' key to see the wavefront.

 

[Rev. Cheeseman]

Any thoughts on this https://www.researchgate.net/figure...asurements-l780-nm-of-parallel_fig1_51591625?

 

[robphy]

Can we actually distinguish an electric field from a magnetic field in reality?

Note, in a plane electromagnetic wave, the wave travels parallel to $\vec E\times \vec B$.
(Since $\vec B\times \vec E \neq \vec E\times \vec B$ in general, we have that $\vec E$ and $\vec B$ are distinguishable.)

Note:
A proton would feel an electric force parallel to the electric field.
A proton would feel a magnetic force perpendicular to the magnetic field (and perpendicular to its velocity vector).
$\vec F_{Lorentz}=q\vec E + q\vec v\times \vec B$

(This is associated with the fact that electric field is an ordinary [polar] vector
and the magnetic field is an axial vector [so, a pseudovector] .)

 

[Rev. Cheeseman]

Is this an example of a parallel electromagnetic wave? https://qph.cf2.quoracdn.net/main-qimg-d5afa8922da2e560dda3342b9c2cbda3-pjlq

 

[renormalize]

Is this an example of a parallel electromagnetic wave? https://qph.cf2.quoracdn.net/main-qimg-d5afa8922da2e560dda3342b9c2cbda3-pjlq

The electric and magnetic fields are parallel in that image so it can't be any type of far-field electromagnetic wave that I'm aware of. And the increasing-pitch helical motion of the charge suggests that those fields are steady, not oscillating like a wave.

 

[vanhees71]

No, this is the motion of a charged particle in an electromagnetic field. Of course one cannot say much from the picture alone. You need to give more context, to understand, what's shown there.

 

[Rev. Cheeseman]

The electric and magnetic fields are parallel in that image so it can't be any type of far-field electromagnetic wave that I'm aware of. And the increasing-pitch helical motion of the charge suggests that those fields are steady, not oscillating like a wave.

No, this is the motion of a charged particle in an electromagnetic field. Of course one cannot say much from the picture alone. You need to give more context, to understand, what's shown there.

So, we are still not sure? Sorry, I'm confused. The only context I can find is here https://www.embibe.com/exams/motion-in-combined-electric-and-magnetic-fields/ and I'm not sure if this is the right context.

 

[vanhees71]

That's the motion of charged particles in an em. field. It's not about electromagnetic waves, i.e., time-dependent solutions for the fields themselves.

 

[Rev. Cheeseman]

That's the motion of charged particles in an em. field. It's not about electromagnetic waves, i.e., time-dependent solutions for the fields themselves.

How about this https://cdn.comsol.com/wordpress/sites/1/2022/07/TE11-mode-10-GHz.png the electric fields and magnetic fields are both perpendicular and parallel there.

 

[Dale]

How about this https://cdn.comsol.com/wordpress/sites/1/2022/07/TE11-mode-10-GHz.png the electric fields and magnetic fields are both perpendicular and parallel there.

That looks like the field near some source in the center. Hence it is a "near field" as I described above.

So, we are still not sure?

I am sure about what I have stated. I cannot speak for you or others.

 

[vanhees71]

How about this https://cdn.comsol.com/wordpress/sites/1/2022/07/TE11-mode-10-GHz.png the electric fields and magnetic fields are both perpendicular and parallel there.

If you don't give a clear context, I can't say anything. Pictures don't speak for themselves!

 

[Rev. Cheeseman]

That looks like the field near some source in the center. Hence it is a "near field" as I described above.

Now I got it. First I was a bit confused about what is near field. Thank you.

I am sure about what I have stated. I cannot speak for you or others.

If you don't give a clear context, I can't say anything. Pictures don't speak for themselves!

Nevermind, even myself are not sure what the context is.

 

[Rev. Cheeseman]

@Dale @vanhees71 regarding unpolarized electromagnetic field, are the electric and magnetic fields still can be distinguished from each other? Are there pictures that show the orientations or angles of electric fields and magnetic fields if the electromagnetic field is unpolarized? Thank you.

 

[Dale]

are the electric and magnetic fields still can be distinguished from each other?

Yes. They exert different forces on charges.

Are there pictures that show the orientations or angles of electric fields and magnetic fields if the electromagnetic field is unpolarized?

I don’t have any.

 

[Drakkith]

@Dale @vanhees71 regarding unpolarized electromagnetic field, are the electric and magnetic fields still can be distinguished from each other? Are there pictures that show the orientations or angles of electric fields and magnetic fields if the electromagnetic field is unpolarized? Thank you.

Did you mean an unpolarized EM wave instead of field? If so, here's a few depictions of varying accuracy:

Note that these all show the electric field vectors along a single axis. The magnetic field vectors would be perpendicular to each e-field vector.

 

[Rev. Cheeseman]

Did you mean an unpolarized EM wave instead of field? If so, here's a few depictions of varying accuracy:
View attachment 325414
View attachment 325413
View attachment 325415

Note that these all show the electric field vectors along a single axis. The magnetic field vectors would be perpendicular to each e-field vector.

Because the electric fields are distributed randomly in unpolarized electromagnetic fields, between every magnetic fields will be electric fields too. I hope I can see more pictures of unpolarized EM fields.

 

[Ibix]

Because the electric fields are distributed randomly in unpolarized electromagnetic fields, between every magnetic fields will be electric fields too. I hope I can see more pictures of unpolarized EM fields.

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.

 

[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...