# Shape and speed of electromagnetic waves

## Main Question or Discussion Point

What are electromagnetic waves supposed to look like in 3D?

Also, in the vacuum of space, electromagnetic waves are supposed to travel at light speed. Is this the linear speed? Or the speed of the flux as it curves?

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The sine wave of the electric field, the sine wave of the magnetic field, and the direction in which the wave propagates (at velocity c) are all mutually perpendicular.

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I guess i'm trying to picture what a electric / magnetic sine wave looks like, if it were possible to view in 3D. Maybe an 3D electromagnetic wave would appear as a vortex?

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GT1
If I look at a single Photon on EM wave, how does its trajectory looks like ? does it move on a straight line or does it move like a Sine wave ?

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So, for example, if a very large electromagnetic wave is moving at light speed, the actual curves of the sine wave would have cover more distance that the axis of the wave(s). Would that be considered the flux? And could it be moving faster than light?

the curve is the amplitude and gives information about the energy at a certain location on the wave and is not the way in which light travels (which would be sphereical waves or planar waves when viewed from far away from the source) if you follow a single peak it can go faster than light, but the "wave-itself" is going c if in vacuum. according to general relativity, light always travels in straight lines and it is space-time that is curved... i think

So a 30hz electromagnetic wave, has a wavelength of 10,000,000 meters.
it moves at 300,000,000 m/s (c)

Now, If this sine wave was converted to a circle, with a circumference of 10,000,000 meters.
And a diameter of 3,183,098 meters. It would travel this distance 60 times, every second, which would be traveling at a linear speed of 190,985,900 m/s. ?

Another example could be the theoretical frequency of the earth 7.5hz, with a wavelength of 40,000,000 meters, which is basically the circumference of the earth (40,075.16 km) . Would travel the distance of15 diameters of the earth every second. 190,985,900 m/s ?

Am I doing something wrong?

rbj
So a 30hz electromagnetic wave, has a wavelength of 10,000,000 meters. it moves at 300,000,000 m/s (c)
so far you're making sense.

Now, If this sine wave was converted to a circle, with a circumference of 10,000,000 meters.
now you're not. that sine wave of one cycle is on a radial line that extends 107 meters outward from your sinusoidal source (antenna).

And a diameter of 3,183,098 meters. It would travel this distance 60 times, every second, which would be traveling at a linear speed of 190,985,900 m/s. ?

Another example could be the theoretical frequency of the earth 7.5hz, with a wavelength of 40,000,000 meters, which is basically the circumference of the earth (40,075.16 km) . Would travel the distance of15 diameters of the earth every second. 190,985,900 m/s ?

Am I doing something wrong?
maybe.

i think it goes arount the earth about 7.5 times in a second. 15 times pi isn't 7.5.

I've realized that the picture I posted from Wikipedia is somewhat misleading. The sine waves do not represent motion. They represent the variation in the electric and magnetic fields. These fields are vectors, which means that they have a magnitude and a direction. Sometimes the electric field points up; sometimes it points down. But the field is not moving up or down in space. It is just varying in direction.

There is nothing following a longer path than the axis. The fields are on the axis. It is only their directions which oscillate.

I'm sorry; I didn't think about that when I posted the picture.

GT1
I've realized that the picture I posted from Wikipedia is somewhat misleading. The sine waves do not represent motion. They represent the variation in the electric and magnetic fields. These fields are vectors, which means that they have a magnitude and a direction. Sometimes the electric field points up; sometimes it points down. But the field is not moving up or down in space. It is just varying in direction.

There is nothing following a longer path than the axis. The fields are on the axis. It is only their directions which oscillate.

I'm sorry; I didn't think about that when I posted the picture.
So a single photon on EM wave moves on a straight line ?
What is the physical meaning of the amplitude ? the field becomes weaker and then stronger ?

Mentz114
Gold Member
For an EM wave travelling in the z direction, there are two mutually perpendicular fields, one electric and one magnetic

$$E_x = E_0sin(\omega t + kz)$$

$$B_y = B_0c^{-1}sin(\omega t + kz)$$

This satisfies Maxwells equations. For instance,

$$\frac{d\vec{E}}{dt} = c^2( \nabla\times\vec{B})$$

which you can easily verify.

$$\frac{d\vec{E}}{dt} = \frac{d}{dt}$\left[ \begin{array}{c} E_x \\\ 0 \\\ 0 \end{array} \right]$$$
which is
$$$\left[ \begin{array}{c}E_0\omega cos(\omega t + kz) \\\ 0 \\\ 0 \end{array} \right]$$$ ------------------ (1)

The right hand side -
$$\nabla\times\vec{B} = \nabla\times$\left[ \begin{array}{c} 0 \\\ B_y \\\ 0 \end{array} \right]$$$

only has one non-zero term
$$$\left[ \begin{array}{c} \frac{d}{dz}B_y \\\ 0 \\\ 0 \end{array} \right]$$$

and, because $$\omega = kc$$ this is the same as (1) if $$cB_0 = E_0$$

I leave the details (and spotting any errors) as an excercise.

So a single photon on EM wave moves on a straight line ?
Yes, unless it interacts with matter.

What is the physical meaning of the amplitude ? the field becomes weaker and then stronger ?
Yes, the fields become weaker and stronger. More than that, they flip direction periodically (hence the sine wave).

So, there is no known 3D form to an electromagnetic wave, it is just two 2D planes?

now you're not. that sine wave of one cycle is on a radial line that extends 107 meters outward from your sinusoidal source (antenna)..
A full wave? I'm having a hard time seeing this.

ZapperZ
Staff Emeritus
2018 Award
So, there is no known 3D form to an electromagnetic wave, it is just two 2D planes?

A full wave? I'm having a hard time seeing this.
This thread is getting to be a bit strange. Why isn't there a 3D solution to the EM wave? Solve the field of a simple dipole antenna in 3D and you'll see the 3D solution. Or solve the Poisson equation for a waveguide, and you'll have a 3D solution.

So what is the problem here? Or am I missing something?

Zz.

Mentz114
Gold Member
nuby,
Yeah, that is a good graphic. But the equations also say it all.

So, there is no known 3D form to an electromagnetic wave, it is just two 2D planes?
There is a theorem that says that just about any function can be expressed as a sum of sines and cosines. So if you know the plane wave solution, then in principle you know all that you need to know. Any solution can be constructed by adding together plane waves.

Maybe the best picture that I have seen showing a plane wave is http://http://en.wikipedia.org/wiki/Image:Onde_plane_3d.jpg" [Broken]. It shows red planes that represent the maximum of the electric or the magnetic field. The very tops of sine waves in three dimensional space, if you like.

But I think what nuby means is three dimensional picture of the vector field of a single photon. ;)

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