# Propagation of electromagnetic waves

1. Apr 27, 2013

### dev70

hi pf, i have been trying to understand since last few weeks how electromagnetic waves, say light travels? Not the way transverse waves do. It must require a medium. Then in vacuum how light travels? you may answer that with oscillating electric fields and magnetic fields at perpendicular to each other, but i ask where from this electric field & magnetic field come in vacuum.
for example- if i consider the emission of radiation as em waves due to excitation of an electron in an atom, then how will the magnetic field and electric field be produced throughout the propagation of light (in this case)? i want to know exactly how it works? thanks in advance ...

2. Apr 27, 2013

### HomogenousCow

First of all, it is best not to speak of electrons in classical EM.
In the textbook treatment of EM waves, the source free maxwell's equations are solved to show how electromagnetic waves behave when there are no sources, the source themselves are not of any concern, they can be whatever matches the boundary conditions for our vacuum solution.
So to answer your question, those vacuum waves are generated by sources outside of the area in which we solve maxwell's equations, these sources are represented by the boundary conditions for our problem.

3. Apr 27, 2013

### dev70

but can you explain it theoretically, without going much into the mathematics part?

4. Apr 27, 2013

### physwizard

before i try to answer your question, i want to know what you believe the electric and magnetic fields to be? according to you, what is the electric field, and what is the magnetic field?

5. Apr 27, 2013

### HomogenousCow

mathematics is the language of the theory

6. Apr 28, 2013

### pumila

Permittivity and permeability are properties of space and define everything about EM radiation like wave impedance and propagation speed. Space has properties and is the medium through which EM waves propagate.

7. Apr 28, 2013

### dev70

well, sticking to classical part, i believe the falling of electrons from higher orbit to lower can be considered as a closed loop of current, and in it the positive proton forming the electric field. Due to the varying electric field, magnetic field can be induced, and so on. i dont really know whether it is true, in terms of reality. i want to know where from and how orthogonal electric and magnetic field resulted in the propagation of em wave perpendicular to both of them???

8. Apr 28, 2013

### dev70

well, i am not talking about impedance and speed, i am asking about em waves propagation through vacuum..

9. Apr 28, 2013

### dev70

thats true..but without having a picture of the idea..you cant apply math..

10. Apr 28, 2013

### WannabeNewton

Consider Maxwell's equations for regions of vanishing 4-current. The homogenous parts are $\partial_{i}E^{i} = \partial_{i}B^{i} = 0$ and the inhomogeneous parts are $\epsilon^{ijk}\partial_{j}E_{k} = -\partial_{t}B^{i}, \epsilon^{ijk}\partial_{j}B_{k} = \mu_{0}\epsilon_{0}\partial_{t}E^{i}$. We see that $\epsilon_{abi}\partial^{b}(\epsilon^{ijk}\partial_{j}E_{k}) = 2\partial^{b}\partial_{[a}E_{b]} = -\partial^{b}\partial_{b}E_{a} = -\partial_{t}(\epsilon_{abi}\partial^{b}B^{i}) = -\mu_{0}\epsilon_{0}\partial^{2}_{t}E_{a}$ and similarly $-\partial^{b}\partial_{b}B_{a} = -\mu_{0}\epsilon_{0}\partial^{2}_{t}B_{a}$ so we see that the electric and magnetic fields give rise to separate wave equations implying that in free space the electric and magnetic fields give rise to electromagnetic waves that propagate at a speed $v = \frac{1}{\sqrt{\mu_{0}\epsilon_{0}}}$.

That takes care of how the electric and magnetic fields give rise to electromagnetic waves, at least classically. Now it seems you are picturing the case of monochromatic plane waves. So we will have sinusoidal waves of frequency $\omega$ traveling only in whatever we define as the z-direction (with no x or y dependence). The solutions to the above wave equations turn out to be $\tilde{{B}}(z,t) = \tilde{{B}_{0}}e^{i(kz - \omega t)}, \tilde{{E}}(z,t) = \tilde{{E}_{0}}e^{i(kz - \omega t)}$. Note that because $\partial_{i}\tilde{E}^i = \partial_{i}\tilde{B}^{i} = 0$, this implies that $\tilde{E}_{0}^{z} = \tilde{B}_{0}^{z} = 0$ i.e. the electric and magnetic fields generating this plane wave have no component in the direction of propagation of the plane wave so they are both perpendicular to the direction of propagation. Similarly, since $\epsilon^{ijk}\partial_{j}\tilde{E}_{k} = -\partial_{t}\tilde{B}^{i}$, we find that after converting to a vector equation $\tilde{{B}}_{0} = \frac{k}{\omega}(\hat{z} \times {\tilde{E}}_{0})$ i.e. the electric and magnetic fields for this plane wave solution are perpendicular to each other.

By the way, your request to explain it theoretically without using any math is quite an absurd request, even you must agree. How do you expect to be shown theoretical concepts without going into the mathematics?

11. Apr 28, 2013

### mrspeedybob

There's more then 1 way to approach your question. The most common is the Maxwell equations, these have already been brought up. Percell had a different take on electromagnetism. It is equally correct in that it produces identical results, but I find it to be a much more intuitive theory. You may also.

http://physics.weber.edu/schroeder/mrr/MRRtalk.html

12. Apr 28, 2013

### pumila

It sounds like you are asking just how an electromagnetic field can exist in space - so if we look at the relationship between pressure and the fluid through which a sound wave propagates, can we identify an equivalent relationship between an EM field and the spacetime through which an EM wave propagates. If so, we simply do not know enough about space to formulate just how space is electromagnetic in structure, and demonstrate how the fields are evoked from that spacetime structure to create an EM field. You can find lots of theories but none of them are generally accepted.

13. Apr 28, 2013

### physwizard

I just want to know from you, what is the electric field, and what is the magnetic field as per your knowledge? How would you define these two things? You still haven't given me their definition, as per your knowledge.
Am I correct in assuming that you believe that the proton is synonymous with the electric field?

14. Apr 29, 2013

### dev70

well it seems i have to go through the math of electromagnetism thoroughly to understand...thanks everybody...

15. Apr 29, 2013

### harrylin

Nobody knows exactly how it works in the sense that you seem to ask; there are working models that relate to different (and incompatible) concepts. As you posted in the classical physics forum: classically the vacuum is modeled as a kind of medium (with vacuum properties) in which waves can be excited and propagated. Further references can be found in Wikipedia, for example starting with:
http://en.wikipedia.org/wiki/Vacuum
http://en.wikipedia.org/wiki/Characteristic_impedance_of_vacuum

16. Apr 29, 2013

### physwizard

Is there any evidence or even any reason to suspect that space is 'electromagnetic' in structure? I thought the 'ether' concept was got rid of a long time back(It had no right to be there in the first place.). Why introduce unnecessary concepts?

17. Apr 29, 2013

### physwizard

It is not right to quote wikipedia for these sort of things. There is no reason to consider vacuum as a 'medium'.

18. Apr 29, 2013

### physwizard

Sounds like a good idea! Do come back if you still don't understand it.

19. Apr 30, 2013

### dev70

well..do we need QED vacuum or QCD Vacuum to understand this?

20. Apr 30, 2013

### dev70

sure..i cant relax until i understand it..