Electromagnetic Waves speed in Conductor

[I_am_learning]

I am following Engineering Electromagnetic by H. Hayt,
And there, we derived, the speed of Electromagnetic wave in good copper is just around 3.2m/s.

Sure, this can't mean it takes 1 second for a light bulb 3.2 m away to glow if I press a switch? I have experience that this is almost instantaneous.

Then what does that mean? And, in simple Dc circuit, with a switch, a battery and a bulb, in which direction does the battery send EM wave? Don't it travel through the copper?

 

[I_am_learning]

Here is that page, if you like.
http://books.google.com.np/books?id...&resnum=1&ved=0CBAQ6AEwAA#v=onepage&q&f=false

 

[Phrak]

There is a difference between the propagation of the electromagnetic field surrounding a conductor, which can vary but is ~85% the speed of light, and the calculated electron velocity in a conductor which is substantially less --in the order of a centimeter per hour depending on current density.

 

[I_am_learning]

the calculated electron velocity in a conductor which is substantially less --in the order of a centimeter per hour depending on current density.

In the OP, that 3.2m/s isn't electron drift velocity, but actually the velocity of EM field inside the copper. I am not confusing drift velocity with the EM wave velocity.

After a bit search, I found that, The power from the battery, travels in the form of EM wave, , not through the copper, but along the air or insulator surrounding it.

Now I am interested in learning, why and how does the EM wave travel through the air but along the copper?

Also, since the current is flowing along the wire, then the E-Filed must also be tangential to the wire. As far as I know, the E-field (and the H field) are always perpendicular to the direction of propagation of the EM wave. So doesn't this imply that EM wave must be traveling perpendicular to the wire? If so, isn't this in contradiction to the fact that EM wave travels along the wire?

Thanks for you response.

 

[Phrak]

I think you should look at the solutions for the electromagnetic fields associated with a coaxial transmission cable.

 

[I_am_learning]

I think you should look at the solutions for the electromagnetic fields associated with a coaxial transmission cable.

I did. In case of co-axial it is said, that, at first you apply voltage between tww conductors in the input end. So, that creates transeverse E-filed. It is simply then stated that the phenomenum is just like transmission of uniform plane wave and the E-Field creates Transverse H-Field and Vice versa, and the effect propagates along the cable as a EM filed.

O.K, leave all of this and answer just this question (It applies to Co-axail too)
In simple DC circuit, I discussed previous post, When I join the battery, in which direction does it first setup Electric Field?
I find two contradictory thing
i) Becuase Current flows along the wire, The E-Field must also be directed along the wire
ii) If it does how could the direction of propagation of EM wave be possibly in the same direction?

It would be good help, if someone could answer these.

 

[Phrak]

I did. In case of co-axial it is said, that, at first you apply voltage between tww conductors in the input end. So, that creates transeverse E-filed. It is simply then stated that the phenomenum is just like transmission of uniform plane wave and the E-Field creates Transverse H-Field and Vice versa, and the effect propagates along the cable as a EM filed.

O.K, leave all of this and answer just this question (It applies to Co-axail too)
In simple DC circuit, I discussed previous post, When I join the battery, in which direction does it first setup Electric Field?
I find two contradictory thing
i) Becuase Current flows along the wire, The E-Field must also be directed along the wire
ii) If it does how could the direction of propagation of EM wave be possibly in the same direction?

It would be good help, if someone could answer these.

I like the way you put this. And you could still pose the same question with coaxial cable. It has the advantage of having much easier spatial symmetry. It's either that, or ask about a conductive loop (either superconducting or resistive) with a voltage source driving it. I'd have to think about it.

 

[I_am_learning]

Anyone please?

 

[kaushik200]

In the OP, that 3.2m/s isn't electron drift velocity, but actually the velocity of EM field inside the copper. I am not confusing drift velocity with the EM wave velocity.

After a bit search, I found that, The power from the battery, travels in the form of EM wave, , not through the copper, but along the air or insulator surrounding it.

Now I am interested in learning, why and how does the EM wave travel through the air but along the copper?

Also, since the current is flowing along the wire, then the E-Filed must also be tangential to the wire. As far as I know, the E-field (and the H field) are always perpendicular to the direction of propagation of the EM wave. So doesn't this imply that EM wave must be traveling perpendicular to the wire? If so, isn't this in contradiction to the fact that EM wave travels along the wire?

Thanks for you response.

I think the following statement, "E-field (and the H field) are always perpendicular to the direction of propagation of the EM wave", means that the instantaneous directions of E and H would be orthogonal to the direction of wave propagation. So may be you need to think in terms of the classical notion of electric field due to a charged rod.

 

[es1]

thecritic,
I have to admit I don't fully understand the question so perhaps this answer will just confuse things however, in your DC example there is more to consider than just the E-field due to the charge in the wire. There will be an E-field caused by the battery itself as well. In the DC case the battery E-field is dominate.

 

[sparkey]

i think you are confusing yourself here. go back to basics for a minute. electromagnetism is not its own entity, it is a result of electrical current. the em wave will generate in the direction of current flow perpendicular to the conductor. the wave is a result of the field being generated. remember your right hand rule?

regarding time, the magnetic field doesn't simply exist at full strength the moment current begins flowing. the field takes time (however minute it is) to expand. thus the 'lag time' between your current turning your bulb on and the em wave reaching the bulb.

 

[I_am_learning]

electromagnetism is not its own entity,

Why not? I thought Maxwell's equation are the fundamental things and the currents and voltage are the secondary things.
And that current is created by, J = σE.
or Curl H = J etc.

 

[I_am_learning]

OK, I have read like this:
In case of Co-axial cable, the Voltage and current need to vary along the cable in such a way as to follow the differential rules imposed by its capacitance and inductance. So, we get differential equation for the voltage (or current) and boundary condition due to circuit parameters; It happens to be mathematically identical to those imposed on E-Field (and H-field) by maxwell's equation. So, by direct analogy, we find the speed of travel of Voltage (or current) on the wire.
In case of co-axial cable with negligible losses, we find it as
V = 1/Sqrt(LC)
That is how it is done in the book I mentioned.

So, as sparkey mentioned, the derivation finds velocity using just the knowledge of behavior of Inductors, capacitors, voltage and currents, and ZERO use of maxwells equations.

But at the deeper level everything could be explained through maxwell's equation, isn't it?

And also, the limiting factor for the velocity of Voltages/current in transmission lines must be setup due to circuit parameters such as L and C so, we don't need to consider complexities of EM wave and its speed.

I hope more knowledgeable mentors out there will come to rescue.

 

[Phrak]

I think, would you show the derivation as presented by H. Hayt, your mentors might emerge.

As currently presented, your problem has raised curiosity, but has yet to get any braincells acting in concert. Do you know how to do LaTex on PhysicsForums? This would help with any equations that are difficult to present in ascii.

 

[I_am_learning]

I think, would you show the derivation as presented by H. Hayt, your mentors might emerge.

As currently presented, your problem has raised curiosity, but has yet to get any braincells acting in concert. Do you know how to do LaTex on PhysicsForums? This would help with any equations that are difficult to present in ascii.

My major problem isn't the derivation in the book.
I just want explanation (crudely) using max-wells equation about the propagation of Electric energy from a battery to a bulb through a pair of wires. Thats it.
And that's not done in the book mentioned.

Just tell that its not possible to explain the process in terms of B,H E and D and their relations, if it is so.

I am not asking complicated question, only that the answer may be.

 

[Phrak]

My major problem isn't the derivation in the book.
I just want explanation (crudely) using max-wells equation about the propagation of Electric energy from a battery to a bulb through a pair of wires. Thats it.
And that's not done in the book mentioned.

Just tell that its not possible to explain the process in terms of B,H E and D and their relations, if it is so.

I am not asking complicated question, only that the answer may be.

No. You are asking a very complicated question but not providing necessary details. The answer is very complicated and depends upon all the geometry of the circuit and even how the switch is moved, over time, to complete the circuit.

Did you know that, in your house, current will flow in the bulb before the switch makes contact or even arcs?

 

[I_am_learning]

No. You are asking a very complicated question but not providing necessary details. The answer is very complicated and depends upon all the geometry of the circuit and even how the switch is moved, over time, to complete the circuit.

I don't require the exact magnitude of Displacement current at the middle of the wire or something similar. So not an exact quantitative solution is required. As from the tone of the question, you could have easily filled in all the necessary details (in such a way as to minimize complexity) by yourself, and post an answer if you could.

 

[yungman]

I did. In case of co-axial it is said, that, at first you apply voltage between tww conductors in the input end. So, that creates transeverse E-filed. It is simply then stated that the phenomenum is just like transmission of uniform plane wave and the E-Field creates Transverse H-Field and Vice versa, and the effect propagates along the cable as a EM filed.

O.K, leave all of this and answer just this question (It applies to Co-axail too)
In simple DC circuit, I discussed previous post, When I join the battery, in which direction does it first setup Electric Field?
I find two contradictory thing
i) Becuase Current flows along the wire, The E-Field must also be directed along the wire
ii) If it does how could the direction of propagation of EM wave be possibly in the same direction?

It would be good help, if someone could answer these.

My understanding is this: Say your conductor is in z direction, the E is on r direction in cylindrical coordinates and H is circulating around the wire and varying between [itex]+\hat {\phi} \hbox { adn }-\hat{\phi}[/itex] direction. It is like the amplitude is in direction perpendicular to the z direction but the propagation is along z direction. I don't think there is any E field along z direction UNLESS there is resistance in the conductor that develope voltage along the conductor. Velocity of propagation has nothing to do with the velocity of the electrons moving through the conductor. I believe the pattern is similar to what is in the coax cable except all E and H supposed to stop at the outer shell of the coax where it carry the equal and opposite current as the center conductor. On an un-shield conductor, then the E and H keep going out perpendicular to the wire. remember the example of a floating object bobble in the ocean waves? the wave move forward but the object is pretty much stationary, it just ride the peak and valley of the waves.

I am no expert and I have not read the whole post but I am interested in this and I'll come back again.

BTW, if your book si Hyat and Buck 7th edition Engineer Electromagnetic. This got to be the worst book for this subject. I have 8 of the EM books, I find

1) Field and Wave Electromagnetics by David K Cheng.

2) Introduction to Electrodynamics by David Griffiths.

Are the best two books. I only bought Hyat and Buck because University of Santa Clara use this for the graduate electrical engineer program. It is no more difficult than Chengs' book but Cheng is infinitely better on field and wave. Even if your school use the Hyat and Buck, get the Cheng book as reference.

Griffiths is for physics major, about half is similar as the engineering EM books, it is quite a difficult book compare to the engineering EM book but it sure explain material characteristics, retarded potential, different math formulas a whole lot better than all the engineer books.

 

[sparkey]

Why not? I thought Maxwell's equation are the fundamental things and the currents and voltage are the secondary things.
And that current is created by, J = σE.
or Curl H = J etc.

disregard theories for a second. you are not applying a magnetic field to wire to generate current. you are using a battery to generate an electric current through the wire thus generating the magnetic field. your thinking is all jumbled up.

connect conductors to power source
power source generates electrical current
electrical current generates magnetic field

electromagnetism exists in 2 states, induction of current from an existing field, and generation of a magnetic field from current.

 

[KaluzaKlein]

In simple DC circuit, I discussed previous post, When I join the battery, in which direction does it first setup Electric Field?
I find two contradictory thing
i) Becuase Current flows along the wire, The E-Field must also be directed along the wire
ii) If it does how could the direction of propagation of EM wave be possibly in the same direction?

It would be good help, if someone could answer these.

I agree with (i) because electric field lines always point from positive to negative charge. This is what a battery does. Creates a potential difference.
What I don't understand is why do you believe there is an EM wave in DC current? If you talk about the light switch in your home, then yes, the rules about EM waves apply, where the direction of propagation is perpendicular both to the E and the M wave.

Since we are talking about books: RF Circuit Design: Theory and Applications by Ludwig
has a pretty thorough explanation about transmission lines with derivation of what you're asking from Maxwell's equations and all. I'm new in this too, and I'm studying from this book.

Concerning the speed of the EM wave inside a conductor (this is phase velocity, v, isn't it?) you can derive it very simply from the equation of the electric wave
E(x,t) = E_mcos(kx-wt):
What you want to do is change x in such a way that (kx-wt) is constant
kx-wt = const.
If you solve this by x and then substitute for x in the below equation:
v = dx/dt
You will get v = w/k
Now, v is also equal to 1/sqrt(epsilon_0*mu_0). I don't have an answer on this one yet!
This proof comes from a nice lecture in youtube
http://www.youtube.com/watch?v=0OuhwnukEKA" he says it much better than I do.

 

[shoestring]

I am following Engineering Electromagnetic by H. Hayt,
And there, we derived, the speed of Electromagnetic wave in good copper is just around 3.2m/s.

Sure, this can't mean it takes 1 second for a light bulb 3.2 m away to glow if I press a switch? I have experience that this is almost instantaneous.

Then what does that mean? And, in simple Dc circuit, with a switch, a battery and a bulb, in which direction does the battery send EM wave? Don't it travel through the copper?

I don't know how to do the maths, but take a look at the pictures in this paper by Norris Preyer, it's available online: http://galaxy.cofc.edu/pubs/AJP01187.pdf". It'll give an idea of what happens and how the field propagates. He uses a charged capacitor as a battery in the model, and makes computer simulations of the time development.

 

[shoestring]

After a bit search, I found that, The power from the battery, travels in the form of EM wave, , not through the copper, but along the air or insulator surrounding it.

Now I am interested in learning, why and how does the EM wave travel through the air but along the copper?

Also, since the current is flowing along the wire, then the E-Filed must also be tangential to the wire. As far as I know, the E-field (and the H field) are always perpendicular to the direction of propagation of the EM wave. So doesn't this imply that EM wave must be traveling perpendicular to the wire? If so, isn't this in contradiction to the fact that EM wave travels along the wire?

Thanks for you response.

As you say, inside the wire the Poynting vector will be perpendicular to the wire, because the electric field is tangental to the wire. Outside the wire, on the other hand, the electric field can have a component perpendicular to the wire, and this will give a the Poynting vector outside the wire a component parallel to the wire.

Both the Poynting vector and the potential surfaces are perpendicular to the electric field, so the Poynting vectors will be tangential to the potential surfaces.

 

[yungman]

I agree with (i) because electric field lines always point from positive to negative charge. This is what a battery does. Creates a potential difference.
What I don't understand is why do you believe there is an EM wave in DC current? If you talk about the light switch in your home, then yes, the rules about EM waves apply, where the direction of propagation is perpendicular both to the E and the M wave.
I don't think I can agree to this because E field generated by potential difference along the wire. If the wire is perfect conductor or very close, there is no voltage generate along the wire and there will be no longitudinal E component along the wire. The EM wave propagate down only have E field radiate out from the wire and is normal to the surface of the line.( conductor, not tangential component). Just a thought, correct me if I am wrong.
Since we are talking about books: RF Circuit Design: Theory and Applications by Ludwig
has a pretty thorough explanation about transmission lines with derivation of what you're asking from Maxwell's equations and all. I'm new in this too, and I'm studying from this book.

Concerning the speed of the EM wave inside a conductor (this is phase velocity, v, isn't it?) you can derive it very simply from the equation of the electric wave
E(x,t) = E_mcos(kx-wt):
What you want to do is change x in such a way that (kx-wt) is constant
kx-wt = const.
If you solve this by x and then substitute for x in the below equation:
v = dx/dt
You will get v = w/k
Now, v is also equal to 1/sqrt(epsilon_0*mu_0). I don't have an answer on this one yet!
This proof comes from a nice lecture in youtube
http://www.youtube.com/watch?v=0OuhwnukEKA" he says it much better than I do.

I have the "RF Circuit Design" by Reinhold Ludwig and Pavel Bretchko also. That is a pretty good book! I use it for my primary study the first go around. But now I am going more towards "Microwave Engineering" by David Pozar. Pozar is more advanced but it is about the best and most popular book for RF circuit design. It is a lot more detail.

 

[yungman]

Guys, please comment on the posts I wrote. That is my understanding but I could be wrong and I really want to learn about the EM wave traveling along the wire.

 

[I_am_learning]

As you say, inside the wire the Poynting vector will be perpendicular to the wire, because the electric field is tangental to the wire. Outside the wire, on the other hand, the electric field can have a component perpendicular to the wire, and this will give a the Poynting vector outside the wire a component parallel to the wire.

Both the Poynting vector and the potential surfaces are perpendicular to the electric field, so the Poynting vectors will be tangential to the potential surfaces.

As I recall, there shouldn't be any tangential component of Electric Field near the conductor boundary (Forgot why? anybody?) . So, yes, I think you are right, near the conductor boundary the E field is perpendicular to the wire so the Pointing Vector (which points in the direction of propagation of wave) is parallel to the wire just as we would expect. This will also illustrated that the velocity of EM wave is then the property (u) of the wire insulator.
Inside the wire, E field is parallel to the conductor; so the current moves along the wire.

I think, There should be some factor that will attenuate the EM field away from the wire so that most of the EM wave is concentrated along the wire.