/sci/ - Science & Math

Looks pretty much like the picture you posted.

>>6723031
I don't fucking get it

>>6723032
look for electromagnetic waves on hyperphysics

>>6723022
i'm studying this shit right now

that in the pic is a transverse wave. If there's a longitudinal component then that just means that the fields have a component in the direction of propagation. This is only possible if the wave propagates with velocity less than c, like in a waveguide where waves are constrained to propagate in a particular direction

>>6723040
how would electromagnetic waves coming from a source through all directions look like?

Why isn't it longitudinal?

>>6723051
because in the pic the feelds (E, H) are only transversal to the direction of propagation
(so it looks)

>>6723022
They're both because the wave has a certain direction of propagation (longitudinal), and the E & H fields are transverse to the direction of propagation.

In reality, this diagram shows the maximum points in strength of the fields. When an antenna releases electromagnetic waves the look like the waves in the pic. The blue lines would be the peaks of the red wave in your pic, and the red lines would be the peaks of the blue wave in your pic.

>>6723064
I'm dumb, please elaborate

>>6723071
Just to clarify some wierd wording I had.

Your pic shows the points where the field strength is at maximum. Along a longitudinal line away from the source of the wave.

The pic I posted shows the the same places of maximum field strength, just as lines. To rlate the two pics. OP's pic's red is blue in this pic, and vice versa.

>>6723071
>>6723075
what do the arrows represent?

>>6723022
this graph has always looked wrong to me, that the E and B fields should not be in phase, because E is greatest when <span class="math">-\frac{\partial B}{\partial t}[/spoiler] is greatest, and vice-versa

>>6723078
the direction of the field

how do light waves behave in this representation?

>>6723071
>They're both because the wave has a certain direction of propagation (longitudinal)
yea but usually by "longitudinal wave" is meant a wave in with the perturbations (in this case, the fields) are longitudinal to the direction of propagation, not that it propagates longitudinally to the direction of propagation, that's obvious

OP, look at the pic you posted. The fields (red and blue segments) are perpendicular to the direcion of propagation (right pointing axis). That's what tranverse em wave means

>>6723079
it's shown in free space, where there is no impedance, and in such case the electric and magnetic fields should be in phase

>>6723079
wait, maybe i got ya

like you said, |E| is maximum when when |dB/dt| is maximum, which is when |B| is maximum. When |B| is zero, then dB/dt=0 -> E=0. So they actually are in phase
it's like a spring oscillator

>>6723088
Yeah okay you're right, then OP's pic doesn't show any longitudinal components. My pic here...

>>6723071

..then shows the longitudinal waves.

>>6723073
here>>6723088

>>6723086
I might be wrong, but I'm certain that light waves can be modelled as electromagnetic of particular frequency

inb4 muh tesla

>>6723022
>waves transverse and longitudinal?
here's an example for sound
>>6722914

it like >>6723088

it's all about the perturbations and direction of travel

>>6723041
>i'm studying this shit right now

this shit being antenna theory? or just EM in general

>>6723091
>My pic here...
>>>6723071
>..then shows the longitudinal waves.
well, i don't know, that's a little confusing. For simplicity's sake, let's replace the dipole you posted with a point charge q=1 sen(t) C generating a sferical em wave in 3D space with the charge at its center. In this case the "direction of propagation" isn't just one direction, but, for every point in space, it's given by the radius from the charge to that point. There's radial symmetry.
But the wave is still transverse, being from point to point the fields perpendicular to the radius

let's say we cut out a volume in space where the em waves propagate

would it look like this?

Doesn't light naturally travel in a corkscrew or spiral? That's what someone here told my ass...

>>6723099
both of em

>>6723100
Well by the longitudinal waves in my pic meant by the separate closed loops. I'm trying to clarify what the longitudinal parts of the EM wave is, I understand the rest, but this has me confused now

>>6723109
worst drawing I've ever seen lol, but yeah it would probably look like that

>>6723110
This is still the representation of light as an EM wave, just with circular polarisation as it states in the pic

>>6723110
>Doesn't light naturally travel in a corkscrew or spiral? That's what someone here told my ass...
nah man. Not always at least

>>6723115
>>6723126
So, someone has to manually change the polarization for the light to corkscrew forward? Or can it sometimes happen in nature?

>>6723115
>Well by the longitudinal waves in my pic meant by the separate closed loops. I'm trying to clarify what the longitudinal parts of the EM wave is, I understand the rest, but this has me confused now

I was confused about this myself. From what i know, Maxwell's equation imply that em waves can only be transverse, FROM POINT TO POINT. which is, in every point, E and H are always perpendicular to the point direction of propagation.
In a waveguide (which is pic related), waves bouce off the internal walls in directions not // to the guide, making possible for longitudinal components to exists (although, they're not really longitudinal, from point to point)

please if i got something wrong somebody correct me

>>6723129
yes, it can happen in nature and we can make that too, with machinery generating polarized light

>>6723144
pic related

Is there a way to intuitively understand this stuff?

pictures can help
http://www.amanogawa.com/archive/wavesB.html

>>6723100
anon>>6723091
>..then shows the longitudinal waves.

is very confusing, a dipole radiating into a non bounded space produces a wave that has no longitudinal component.
and it appears to me as if the E & B field labels are transposed as the E field radiated from a line (dipole) is a cylinder and the red circles seem to be circumferences of said cylinder.

>>6723111
well then you got one point I'd like to quibble with here >>6723041
>This is only possible if the wave propagates with velocity less than c, like in a waveguide where waves are constrained to propagate in a particular direction

EM waves never travel at C because no medium they travel through is a perfect vacuum.
Secondly being bound by a waveguide is not a reason for a reduction in velocity, it's the medium inside the waveguide that is the cause for EM waves traveling slower than the theoretical limit.

>>6723144
you've got it,
when you start doing the math you find that imaginary components of the tensor become real and real components become imaginary
or you can think of it as the wave is folded and travels sidewise and expresses an electric or magnetic component perturbation in the direction of travel and thus appears as a longitudinal wave

>>6723197
>EM waves never travel at C because no medium they travel through is a perfect vacuum.
Right, v=1/sqr(eu) < c, except in a perfect vacuum where v=c.

>Secondly being bound by a waveguide is not a reason for a reduction in velocity, it's the medium inside the waveguide that is the cause for EM waves traveling slower than the theoretical limit.

Okay, but if the wave reflects at the inner walls of the waveguide the group velocity is less than the mere velocity of a wave in a dielectric, which is v=1/sqr(eu). It's not JUST because of the dielectric, or is it?

>>6723193
>and it appears to me as if the E & B field labels are transposed as the E field radiated from a line (dipole) is a cylinder and the red circles seem to be circumferences of said cylinder.

the simmetry is a spherical one (meaning, direction of propagation always radial from the dipole). But the B field is always // to cilinders with axes containing the dipole, and the E field has direction in the zenith angle versor direction.

>>6723250
>simmetry

Trust this guy, he's legit, I swear.

>>6723206
right, thanks for confirming

How are waves even produced?

>>6723274
it's a complicated subject, and one I find near and dear to my heart from both my profession and an admiration for a certain inventor who's name we shall not invoke for fear of arising the ire of the dreaded troll

>>6723241
>It's not JUST because of the dielectric, or is it?

it would seem geometry and length of path traveled would be a factor

>>6723299
usually by movement of charged things (such as electrons), but not only

>>6723308
you know, i think you know i think i know who you're talking about

but i actually do
i think

>>6723380
anyway... it's a subject I understand and if you wanna conversate about EM I'm usually around somewhere

>>6723090
>|E| is maximum when when |dB/dt| is maximum, which is when |B| is maximum
No, E and B are sinusoidal, so |dE/dt| is maximum when E=0, similarly for B.

>>6724160
the end result is that the peak of the E field leads (or lags) the peak of the B field by 1/4 wavelength
since E is max when <span class="math"> \frac {\partial B} {\partial T} [/spoiler] is greatest, which is at zero crossing they have a 90º offset

>>6723331
what kind of movement? I assume it's vibration how fast and at what distance? The same as the amplitude of the waves? at what angles do they move around?

>>6724160
Yeah, the problem is that E is not proportional to dB/dt. To calculate B, you gotta take the rotor of E,which gives dB/dt, and then integrate B.
so, if E has only a sin component in the x direction, taking the rotor gives a cos in the y direction (for dB/dt), which integrating turns into a sin.
This without any kind of phase shift, only an amplitude change
(E_x/H_y=impedence)

>>6724519
>what kind of movement? I assume it's vibration
yes, the most simple case is a sinusoidal vibration (generating a sinusoidal wave).
usually though you have a current with a certain waveform (opon which is stored the information to transmit, modulated in a certain way. Eg, on the frequency of the wave, like FM radio)
and this current passes through an antenna which radiates the EM wave, that ideally maintains the exact waveform. This wave is carried through space in different patterns, depending on the antenna/ratiator.
eg, pic related, hertzian dipole antenna ->>>6723071

>>6723110
A circular polarized wave can be seen as a combination of two linear polarized waves.
And vice versa.

Test

>>6725044
>Test
eureka
it worked

>>6723022
How would this look like in three dimensions?

Do particles that emit waves vibrate in only two direction(i.e. up and down)

>>6726970
>Do particles that emit waves vibrate in only two direction(i.e. up and down)

I didn't know particles emitted waves

>tfw wave particle duality

I think you are confusing mechanical waves and EM waves they are not the same although they do have some similarities

>>6727023
what's the difference?

>>6727077
in one we know exactly what is oscillating in the other it's all theory

>>6727082
goddammit

In a mass-spring oscillator the sum of the two components (kinetic and potential energy) is constant and the phase shift between them is pi/2. The same holds for a pendulum.

For a propagating wave this is also the case close to the antenna (the near field) but not in the far field.

When both E and H are zero, where's the energy stored that drives the next cycle?

>>6727931
the energy is being carried away in the direction of propagation, and yes there are certain points in space, at a particular time, in which the energy density is zero. If S=ExH is the Poynting vector, which represents the electromagnetic energy flux density, this is gonna have a peak when/where E and B are at their max, and a zero when/where they're both zero.
It's not like a spring oscillator in that the energy doesn't stay in the same place, but gets radiated in all directions.

>>6727931
kek.

this is the "classical image"

photons have spin. you can't show spin with just 1 E x B wave. you need two in superposition, specifically, one that is +-pi/2 phase shifted from the other.

so energy moves from 1 wave to another.

This allows spin to be conserved, since the E field now "spins", or oscillates in a circulatory fashion. If it scatters to an electron, the electron will follow the circling E field, and impart its spin angular momentum into orbital angular momentum of the electron.

>>6727931
>>6728068

The red arrows are the E fields.

When you add 2 poyting vectors, lets just care about the E fields.

<span class="math">

\\E_1 = E_0 e^{i(kx-wt)} \;\hat{x}\\

E_2 = E_0 e^{i(kx-wt)\pm i\frac{\pi}{2}} \;\hat{y}\\
E_1+E_2 = (E_0e^ {i(kx-wt)}) (\;\hat{x} + e^{i\frac{\pi}{2}} \;\hat{y})\\
[/spoiler]

Now, E_1 oscillates in x, E_2 oscillates in y, and you is at the peak while the other in in the 0

and if you add the e fields, you get an e field that turns in a circle.

>>6728077
God damn latex

<span class="math">
E_1 = E_0 e^{i(kx-wt)} \;\hat{x}\\

E_2 = E_0 e^{i(kx-wt)\pm i\frac{\pi}{2}} \;\hat{y}\\
E_1+E_2 = (E_0e^ {i(kx-wt)}) (\;\hat{x} + e^{i\frac{\pi}{2}} \;\hat{y})\\

[/spoiler]

>>6728080

latex doesn't want me to have more than 1 equation, so heres the last one.

<span class="math">
E_1+E_2 = (E_0e^ {i(kx-wt)}) (\;\hat{x} + e^{i\frac{\pi}{2}} \;\hat{y})

[/spoiler]

>>6727931
>When both E and H are zero, where's the energy stored that drives the next cycle?

when in an EM wave are the electric field and the magnetic field both zero at the same time ?

isn't the electric field maximum when the magnetic field is changing the quickest (which is at zero crossing)? and the magnetic field maximum when the electric field is changing quickest (again at zero crossing).

so the two fields are never at zero at the same instant

>>6728198
No, that is only true for the near field because voltage and current in the dipole behave that way (they have a pi/2 pase shift). But while propagating E and H gradually lose their phase difference and at a distance of a few wave lengths not much is left.

>>6728082
Just put them on different lines...you aren't in the align environment anymore
<span class="math"> E_1 = E_0 e^{i(kx-wt)} \;\hat{x}[/spoiler]
<span class="math"> E_2 = E_0 e^{i(kx-wt)\pm i\frac{\pi}{2}} \;\hat{y}[/spoiler]
<span class="math"> E_1+E_2 = (E_0e^ {i(kx-wt)}) (\;\hat{x} + e^{i\frac{\pi}{2}} \;\hat{y}) [/spoiler]

>>6728251
i don't wish to open math /math 3 times doe.

So i can't really find a graphical way to elaborate spin with waves, so heres one that mean about the same.

Ex and Ey are out of phase, either by +- pi/2

When propagating, Ex and Ey form a circularly oscillating E field.

This constitutes as spin. Linearly polarized light are just a superposition state of the +pi/2 and -pi/2 circularly polarized lights, so light is never represented as just 1 EM wave.

tl;dr E field is never 0 when light propagates.

>>6728247
>But while propagating E and H gradually lose their phase difference and at a distance of a few wave lengths not much is left.

[citation needed]

>>6723197
>Secondly being bound by a waveguide is not a reason for a reduction in velocity, it's the medium inside the waveguide that is the cause for EM waves traveling slower than the theoretical limit.

ehhhmm, no, gonna have to shoot you down there. Even if it's perfect vacuum inside the waveguide, the group velocity can be slower than c

http://www.met.reading.ac.uk/~clouds/maxwell/waveguide.html

The animations on this website may help a lot of the people in this thread get a better intuitive understanding of what happens with propagating EM waves

>>6728385
thanks anon that's very helpful indeed

>>6728306

www.google.com/search?q=near+field+far+field

In the immediate vicinity of the antenna, we have the reactive near field. In this region, the fields are predominately reactive fields, which means the E- and H- fields are out of phase by 90 degrees to each other (recall that for propagating or radiating fields, the fields are orthogonal (perpendicular) but are in phase).

www.antenna-theory.com/basics/fieldRegions.php

>>6723110
Normal light isn't polarized, so it does all kind of random shit.

>>6728413
I guess I had become confused. in the free space radiating form the fields are in phase.

>tfw I sit corrected

i look upon this visage b4

sum1 doth intently inquire

>>6723071
I've never seen this image before. I am guessing this is just a time point of an EM wave with just a cross section of it?

How do the EM waves stack in 3d space? They are generated by moving electrons so I imagine they radiate outwards radially away from the direction of motion.

>they radiate outwards radially

pic shows phases...

...animated

>>6723022
Have youve ever gone out on a very hot day and your field of vision looks wavy.
Thats what they look like

>>6723022
Like a spinning double helix.

Good Lord!

The picture is a mathematical representation. Waves don't go shooting through space like a graph! We use this representation because if you put a physical antenna anywhere along the graph, it would show the movement of energy in the antenna.
Energy doesn't look like anything. It is only apparent when it interacts with matter, whether the water of the ocean, the molecules in the air, or the change in voltage readings in a detector.

Stop trying to look at EM as it propagates. You can't know what it looks like because it doesn't look like anything until it interacts with matter. The graph of a transverse wave is just showing you that, if your antenna was stationary, the energy in the antenna would fluctuate between the top and the bottom of the sine wave, unlike a standing wave where a stationary antenna wouldn't change at all; also that the magnetic field would be fluctuating orthogonally to the electric field.

>>6730396
>unlike a standing wave where a stationary antenna wouldn't change at all;

if we are talking EM here and I assume we are, then:
you can't have a standing wave in unbounded space.
once a wave is bounded and becomes a standing wave the parameters change and a stationary antenna can both release energy into and receive energy from a standing wave.

>>6730396
of course, it's not like there's little blue and red arrows in the real space. On the other hand a pictorial representation does give a qualitative insight into how fields (and therefore photons, information...) spread.
Also, when you say it doesnt look like anything that's true if you're thinking of the usual meaning of "look" (which is, how we look with the eyes), but if you had a different kind of sight maybe, with which you could perceive the fields themselves, in the different directions, at a distance (magically), then it would look like that. would it not?

>>6728419
Normal light is randomly polarized