Propagation of electromagnetic waves

[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 ...

 

[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.

 

[dev70]

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

 

[physwizard]

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 ...

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?

 

[HomogenousCow]

mathematics is the language of the theory

 

[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.

 

[dev70]

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?

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 don't 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?

 

[dev70]

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.

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

 

[dev70]

mathematics is the language of the theory

thats true..but without having a picture of the idea..you can't apply math..

 

[WannabeNewton]

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?

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?

 

[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

 

[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.

 

[physwizard]

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 don't 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?

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?

 

[dev70]

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

 

[harrylin]

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 ...

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

 

[physwizard]

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.

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?

 

[physwizard]

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

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

 

[physwizard]

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

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

 

[dev70]

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

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

 

[dev70]

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

sure..i can't relax until i understand it..

 

[physwizard]

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

no you don't. just classical EM.
fields are part of the mathematical machinery used to describe the force between two charges. but the force between two charges does not act instantaneously, but rather propagates at a finite speed (equal to the speed of light). however, there is no reason to expect that the electromagnetic force requires a medium to propagate, just as there is no reason to expect that gravitational forces require a medium to propagate.
vacuum is just a region of space where there is no matter (ideally) . there is no reason to expect it to behave like a 'medium'.

 

[pumila]

While the concept of the ether as such is long dead, killed by the fact that the speed of light is constant to all observers, nevertheless electromagnetic waves are intrinsically bound up with concepts of spacetime. They cannot be separated, as the origins of spacetime theory come from observations of electromagnetic wave propagation. Further, the parameters of electromagnetic behaviour are defined by constants (permittivity and permeability) that are generally held to be properties of space. This implies that the waves travel through space and are controlled by it.

Space after all is not something that simply separates two objects with a distance. It is much more complex and subtle, involving time and distance, the past and the future, and relating time to distance through the speed of propagation of light.

 

[harrylin]

It is not right to quote wikipedia for these sort of things. [..]

I fully agree, that's why instead of that I refer to the references!