# Medium of EM Waves?

1. Dec 15, 2007

### barnaby

Another thing that I've never really understood...

As fas as I'm concerned, waves need a medium to travel through, but electromagnetic waves seem not to need one at all. I just can't visualise them as oscillations in anything.

It sort of helps if I visualise EM waves as photons, because then they're particles in their own right... but that gives rise to a whole lot of physics I simply am not equipped mathematically or conceptually to tackle yet (I started AS Physics this year).

Is it necessary to go into quantum mechanics to understand electromagnetic waves?

EDIT: I'm reading this: http://hyperphysics.phy-astr.gsu.edu/hbase/forces/funfor.html#c3 at the moment, but a lot of it is slightly over my head.

Another question that I forgot to ask when I initially posted this thread was basically the same, but for actual electrical/magnetic attraction between magnets and coils of wire and whatnot...

Last edited: Dec 15, 2007
2. Dec 15, 2007

### Staff: Mentor

No, you really don't need QM to understand a very wide range of EM phenomena, just Maxwell.

You are right, EM waves do not need a medium to travel through. In a simplified sense the oscillating E field sustains the oscillating B field which sustains the oscillating E field ...

3. Dec 15, 2007

### barnaby

Come again?

4. Dec 15, 2007

### cepheid

Staff Emeritus
He means that if you look at two of Maxwell's Equations:

A time varying magnetic field induces an electric field:

$$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$$

A time varying electric field induces a magnetic field (assume zero current density)

$$\nabla \times \mathbf{B} = \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t}$$

So the oscillating fields E and B continue to generate/sustain each other, explaining why an EM wave can propagate through free space and exist far from the source that generated it.

The fact that either can exist as a wave can be shown more explicitly by starting with these two first order PDE's and decoupling them to produce a single second order PDE in terms of either ONLY B or ONLY E (your choice). This second order equation turns out to be a vector wave eqn, i.e. both E and B are governed by a wave eqn in free space.

Last edited: Dec 15, 2007
5. Dec 15, 2007

### Kurdt

Staff Emeritus
If you've just started AS physics you might find the Maxwell equations hard to follow since you won't have the mathematical tools necessary to understand the equations. cepheid's post basically explains how the mathematics was done to predict that light was a wave that could propagate through free space without a medium.

6. Dec 15, 2007

### barnaby

You're right. I have no idea where to start with partial differential equations. As far as I know, ordinary differential equations don't crop up until FP1 of Further Mathematics, which I won't do till next year.

$$\epsilon_0$$ - that's the 'permittivity of free space', right?

Ah well, curiosity killed the cat I s'pose, I'll have to wait till undergraduacy.

Thanks a lot, though.

7. Dec 15, 2007

### Danger

No, curiosity killed one cat; the other learned from the experience and continued on in an alternate time-line.

8. Dec 15, 2007

### Kurdt

Staff Emeritus
That is correct.

If you're really interested there is no harm in reading ahead as long as it doesn't interfere with other studies.

9. Dec 16, 2007

### barnaby

Can you suggest any books (other than the Feynman Lectures) which might help me do that?

10. Dec 16, 2007

### Kurdt

Staff Emeritus
If you want to read ahead on the mathematics then a good undergraduate first year maths book is 'Guide 2 Mathematical Methods' by John Gilbert and Camilla Jordan. This covers most of the basic mathematics you will need during a university physics course.

AS far as pop sci EM books go I'm not sure what's out there. Perhaps someone else will have a better idea.

11. Dec 16, 2007

### Staff: Mentor

I'm sorry about that. Let me try again. When you look at a wave on the water you notice that it changes in both space and time. If you take a picture you see that there are variations in space at that instant in time when you took the photo. If you look at a single piece of something floating you see that it bobs up and down, the variations in time at a single point in space. So fundamentally a wave is a variation in space and time.

Now, to make things simple let's consider for a bit a 1-D wave like a vibrating string. In a string there is basically two places to put energy, one is the kinetic energy or how fast a given piece of string is moving, the other is the elastic potential energy or how much the string is deformed from rest. The kinetic energy is related to the changes in time and the elastic energy is related to the changes in space and so a wave propagates along the string.

Let's turn to the equations provided by cephid

$$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$$
Don't worry about the funny math symbols at this point. The left-hand side describes spatial changes in the electric field and says that they are equal to how the magnetic field changes in time.

$$\nabla \times \mathbf{B} = \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t}$$
Similarly with this one. Now, spatial changes in the magnetic field are equal to how the electric field changes in time.

So, just like the string and the waves on the water we have changes in space and time. And just like the string we have two places for energy to go (electric field or magnetic field). The end result is that the "medium" for an electric wave is a magnetic wave and viceversa, or an electromagnetic wave propagates without a medium. It is self-contained and self-sustaining.

I hope that helps.

12. Dec 16, 2007

### robphy

Try my visualization
from

You'll need to install VPython.
The above visualization is the basis of a poster presentation that I'm giving at the upcoming AAPT meeting: [url=http://www.aapt.org/scheduler/wm2008/IndexResult.cfm?Code=PST2-31]www.aapt.org/scheduler/wm2008/IndexResult.cfm?Code=PST2-31[/url]

Last edited by a moderator: May 3, 2017
13. Dec 16, 2007

### cepheid

Staff Emeritus
Sorry for neglecting to take into account the background of the OP (essentially high school physics). I wasn't familiar with the UK system.

14. Dec 16, 2007

### kcodon

Back to the original question from Barnaby:
This is also what physicists back in the day used to think...they called it the aether, and it was the medium that EM travelled through. However the Michelson Morley experiment disproved the aether. The experiment went along the lines that if there was an all pervasive medium like the aether, then our earth motion in the solar system would mean that we would be travelling at different relative speeds to the aether, so then we should detect different speeds for the EM to propagate (as the EM was limited to a finite speed in the aether). MM detected no change in the speed of light, and thus concluded that there was no aether.

I myself questioned this, cause I also didn't like the idea of self-propagating waves, but there seems to be no way around there being no aether. For example if you look it up, some put forward "aether entrainment" where the aether is kind of caught up by mass, so in the case of the MM experiment, the aether around the earth would be still relative to the earth, so there would obviously be the null result by MM. However aether entrainment was disproved by other experiments by using lead blocks etc to entrain the aether etc, and also the simple fact that if the aether was entrained, then the aether around the earth would be still relative to use, but would be moving very quickly relative to the aether in other parts of the solar system and galaxy...and this would lead to some seriously whacked views of the stars that we don't observe.

The most sensible, killer blow for aether is that if EM travels through the aether as one would expect from modern physics, it would have to be seriously hard, light and dense, which it obviously isn't cause otherwise we'd kinda notice it. Unless of course you believe that EM doesn't travel through the aether as we would expect, in which case you will be in a whole mess trying to sort yourself out.

Now you move onto wave particle duality, for in your case it would be lovely if light was photons, but you'll find out that light sometimes exhibits properties only explainable by wave nature. Yup I've been through your thoughts before...I too will take AS and A2 next year.

Kcodon

15. Dec 16, 2007

### barnaby

Yep, that's exactly my trouble - I understand that Michelson-Morley disproved the 'aether', but I just don't really understand the physics behind what the truth is. It's conceptually difficult for me to visualise a magnetic 'field' - with a wave of, say, water, you can see what's carrying it - the 'field of water'. Similarly with a wave in a string.

But, as far as I can see, there's nothing to a magnetic/electric field - there's no tangible 'electromagnetism' through which the waves can travel.

What I seem to be learning from this thread (and I really can't thank you all enough for taking the time to explain this, despite the fact I'm clearly not getting any further) is that *somehow* an electric/magnetic field is generated, a fluctuation in which generates a magnetic/electric field, the generation of which causes a fluctuation.. which causes a generation...

Or am I still completely off?

16. Dec 16, 2007

### kcodon

Yup I've had the same problems too. At the moment I'm trying to figure out how waves and photons are related with respect to the "sphere" of emission, with radius=ct. I don't know if you may find it helpful, but look at

it may help - some of it is over my head but some of it is useful. I even asked the same question you are looking at...I didn't know whether EM waves were "ripples" in an EM field, or if they were self propagating. I believe the answer was self propagating. Interestingly though, the magnetic field is actually the equivalent to the electric field taking relativity into account, so I don't believe you can say one generates the other, which generates the other. In one of the posts cbacba says that due to travelling at the speed of light, time must be stopped so the wave can not actual oscillate itself...it merely appears to, or something along those lines. Maybe I will ask that...

Kcodon

17. Dec 16, 2007

### Claude Bile

Remind yourself what is meant by an E-field. It is the force a +1 C charge will feel if placed at some point in space (call it "r"). A sinusoidally varying E field simply means a +1 C charge, when placed in the path of that field, will feel a sinusoidally varying force.

There is no "substance" to E (or B fields for that matter) if you can accept that force can be transmitted through a vacuum - then it shouldn't be a big leap to accept that EM fields, which are really just "force-maps", can also be transmitted through a vacuum.

Claude.

18. Dec 16, 2007

### kcodon

Claude I have a question if you don't mind, related to what you just posted.

With the sinusoidally varying amplitude of electric field, does it vary strength, but always remain in one direction so to speak; or does the field vary from positive to negative - i.e. because the sinusoidal graph goes from a positive maxima to a negative one. I do not see how an electric field can be caused to change polarity....

Kcodon

19. Dec 16, 2007

### ZapperZ

Staff Emeritus
This actually isn't true.

In QM, you do not need separate or different formulation to describe all of the behavior of light. There's only one consistent description of it. So both the apparent wave-like and particle-like behavior can be describe by just ONE consistent formulation.

Now, the reason why we continue to go back to using the wave equation, for example, to describe phenomena like diffraction, double-slit, etc. is because it is easier to handle when you are dealing with ordinary light (i.e. large number of photons). If we force you students to deal with all this using purely QM, you'd be barely alive by the time we are done with you. It isn't as trivial, as can be seen from the Marcela's paper in EJP. Thus, we continue to use a simple wave-picture to deal with what we historically designate as wave-like behavior. But don't confuse this with there being no single formulation (thus, no "duality") for all the behavior of light.

P.S. this has been covered in our FAQ as well.

Zz.

20. Dec 16, 2007

### Claude Bile

A linearly polarised E field in an EM wave will cycle from a "positive" maximum to a "negative" minimum. The terms positive and negative though are arbitrary, whether something is positive or negative depends only on your choice of coordinates - the important thing is that there is a change in direction.

Claude.