# Speed of EM in good conductors

by yungman
Tags: conductors, speed
 P: 3,795 Speed of EM travel through the good conductor is $$\omega$$/$$\beta$$ I know the speed of signal travel in stripline is c/$$\sqrt{}\epsilon$$$$_{}r$$_{} My symbols don't look very good but I think you get what I mean. Obvious they are different. I am confuse because in both case EM wave travel in good conductor, why are they different? I know the first one is "propagation velocity" the second is "phase velocity". What is the difference? Thanks
HW Helper
P: 2,618
 Quote by yungman I know the speed of signal travel in stripline is c/$$\sqrt{}\epsilon$$$$_{}r$$_{}
What's the last term supposed to be?
Mentor
P: 37,602
 Quote by yungman Speed of EM travel through the good conductor is $$\omega$$/$$\beta$$ I know the speed of signal travel in stripline is c/$$\sqrt{}\epsilon$$$$_{}r$$_{} My symbols don't look very good but I think you get what I mean. Obvious they are different. I am confuse because in both case EM wave travel in good conductor, why are they different? I know the first one is "propagation velocity" the second is "phase velocity". What is the difference? Thanks

In general, an EM wave does not travel "in a conductor". What does it travel in instead? Start with free space (vacuum, eh?), then the atmosphere, then glass, then water, then a stripline, etc.

What is the EM wave oscillating/travelling in? What determines its speed and loss?

P: 3,795

## Speed of EM in good conductors

 Quote by Defennder What's the last term supposed to be?
It is the speed of light divided by the square root of relative permeativity. eg. If permeativity is 4, then phase velocity is 3EE8/2=1.5EE8

Thanks
P: 3,795
 Quote by berkeman In general, an EM wave does not travel "in a conductor". What does it travel in instead? Start with free space (vacuum, eh?), then the atmosphere, then glass, then water, then a stripline, etc. What is the EM wave oscillating/travelling in? What determines its speed and loss?
Speed and loss depend on $$\gamma$$ which equal to $$\alpha$$ +j$$\beta$$ . $$\alpha$$ is attenuation constant and is real. $$\beta$$ is propagation constant which is imiginary part. Both can be determined depend on classify of the dielectric medium.

EM wave do travel in sea water which is relative good conductor. Just with attenuation. The speed still approx. to $$\omega$$ / $$\beta$$ . which is very different from phase constant.

I guess my question: What is the difference between EM wave travel in stripline and EM wave travel in a media. Is it the first one is conduction current and the second is displacement current.

Mentor
P: 37,602
 Quote by yungman I guess my question: What is the difference between EM wave travel in stripline and EM wave travel in a media. Is it the first one is conduction current and the second is displacement current. Thanks for your time.
Interesting. This actually has distilled down to a very good question, and to be honest, I haven't thought about it from that angle before. Is this the question:

"What is the difference in propagation equations for an EM wave in free space, versus one confined to a transmission line? And why does there appear to be a fundamental difference in the equation for the propagation velocity for these two cases?"

I'll have to think about that some before I can try to give a useful answer. My intuition says that the difference lies in the directivity of the transmission line (TL) case -- that is, the EM wave that propagates along a TL is directed down the TL by the conductors of the TL (coaxial, or twisted pair, or stripline, etc.), so the loss is dominated by the skin effect resistive loss on the conductors, and the parasitic conductance loss in the dielectric of the TL. The only "loss" in a free-space EM wave propagation (not in a conductive media like seawater obviously) is the growing surface area of the wavefront, which gives you a power loss over distance with a 1/r^2 coefficient.

I'll PM a couple other PF'ers to try to get them to address your question, assuming I'm interpreting it correctly. BTW, since this is in the homework/coursework area of the PF, we can't do your work for you (per the PF Rules link at the top of the page). You have asked a very fundamental and interesting question, though, and have shown a lot of your own work. Can you take what I've said about the constrained nature of the Poynting vector and different attenuation mechanisms for a TL versus free space, and see if that can explain the equation differences that you are encountering?
P: 3,795
 Quote by berkeman Interesting. This actually has distilled down to a very good question, and to be honest, I haven't thought about it from that angle before. Is this the question: "What is the difference in propagation equations for an EM wave in free space, versus one confined to a transmission line? And why does there appear to be a fundamental difference in the equation for the propagation velocity for these two cases?" This is basically what I am confused about. The reason I start to question this is because in one of the problem from a book ask to find the propagation velocity of EM wave through sea water where from calculation it is consider good conductor and the velocity turn out the be in 10EE7 range which is an order slower than light. And If using copper $$\sigma$$ = 5.8EE7, the velocity will be even lower. But in stripline case, velocity is simply about speed of light divided by square root of relative permeativity. On top of it all, EM wave don't even penetrate metal very much at all and guided wave in stripline travel as far as the dielectric allowed. I'll have to think about that some before I can try to give a useful answer. My intuition says that the difference lies in the directivity of the transmission line (TL) case -- that is, the EM wave that propagates along a TL is directed down the TL by the conductors of the TL (coaxial, or twisted pair, or stripline, etc.), so the loss is dominated by the skin effect resistive loss on the conductors, and the parasitic conductance loss in the dielectric of the TL. The only "loss" in a free-space EM wave propagation (not in a conductive media like seawater obviously) is the growing surface area of the wavefront, which gives you a power loss over distance with a 1/r^2 coefficient. I'll PM a couple other PF'ers to try to get them to address your question, assuming I'm interpreting it correctly. BTW, since this is in the homework/coursework area of the PF, we can't do your work for you (per the PF Rules link at the top of the page). I am not in school, I am a self studier. Actually I had been an EE for close to 30 years and manager of EE for 14 years. I am just studying as a hobby!! I have six or seven books on EM, I am not saying I read everyone in detail, I did read at least two in very detail and go through the others. I don't recall anyone compare the difference. You have asked a very fundamental and interesting question, though, and have shown a lot of your own work. Can you take what I've said about the constrained nature of the Poynting vector and different attenuation mechanisms for a TL versus free space, and see if that can explain the equation differences that you are encountering?

This morning I thought of another example. Current travel on the surface of a block of metal where the surface is the xy plane and the depth is +ve z direction. Current is travel in +ve x direction. I sure I know how to copy a drawing onto the post without doing an attachment that require a day for approval!!

This is regarding to current density in a infinite block of metal in text book. The current mainly travel on the surface. The book mainly talk about the attenuation in z direction where it follow the attenuation constant and propagation for the current density at z direction and propagation velocity that is calculate at z direction. The surface current is traveling at higher speed closer to the speed of light.

I also re-read the materials. Propagation of EM wave in stripline is the speed of wave travel through the dielectric that make up the stripline. Which is 1/(square root of permeability X permeativity).............I know it is confusing!!! I can't do symbols and can't upload a drawing!!!
HW Helper
P: 2,618
 Quote by berkeman "What is the difference in propagation equations for an EM wave in free space, versus one confined to a transmission line? And why does there appear to be a fundamental difference in the equation for the propagation velocity for these two cases?"
Well I'm not an expert here, but this is what I think: From what I can tell the telegrapher's equation which you can derived from applying KVL to a differential length segment dz is essentially a wave equation. From this, I believe one can infer that the solution of the wave equation applies to t-lines as well; ie. voltage and current can be considered as waves on transmission lines. With that in mind, note that the equations given which seemingly appear different for both phase velocity and propagation velocity for EM waves/voltage-current waves are actually the same. The former can easily be shown to reduce to $$u_p = \lambda f$$ and the latter I believe I've seen a short derivation in a freshman physics textbook. The formulae are equivalent. They hold for waves and they are waves because in both cases, EM waves and t-lines, they satisfy the wave equation.
P: 3,795
 Quote by Defennder Well I'm not an expert here, but this is what I think: From what I can tell the telegrapher's equation which you can derived from applying KVL to a differential length segment dz is essentially a wave equation. From this, I believe one can infer that the solution of the wave equation applies to t-lines as well; ie. voltage and current can be considered as waves on transmission lines. With that in mind, note that the equations given which seemingly appear different for both phase velocity and propagation velocity for EM waves/voltage-current waves are actually the same. The former can easily be shown to reduce to $$u_p = \lambda f$$ and the latter I believe I've seen a short derivation in a freshman physics textbook. The formulae are equivalent. They hold for waves and they are waves because in both cases, EM waves and t-lines, they satisfy the wave equation.

I have been reading also, The equation both from the same wave equation like you said. I have not study the guided wave yet which I believe applies to stripline.

Further. My original question has a lot to do with the skin effect Where the current is in direction of the E field. and the EM wave propagate in direction normal to the current direction. The velocity of current is not the same as the propagation velocity of the EM wave. I wish I know how to put a diagram on the post other than as an attachment which require a day to clear. This is how I read it so far on skin effect:

Consider a long bar with x be the in direction of the length. Width be the y direction and the thickness in z direction. Let current flow in +ve x direction from one end of the bar to the other end.

1) Since the current from in +ve x direction. THis mean E wave is in direction of x. ( E wave is parallel to the length of the bar )

2) E wave induce H wave which is in y direction. ( parallel to the width of the bar)

3) The direction of propagation is normal to both E and H wave which is (x X y = z) So the EM wave actually propagate down in direction of the thickness of the bar.

Therefore the velocity of current travel along the bar is DIFFERENT from the propagation velocity of EM wave in good conductor.

THis is my understanding so far. I still studying. Please give me comments.

Thanks
P: 3,795
I think my original question might be wrong. Current conduction is not the same as propagate of EM wave in good conductor like coper. From the skin effect explaination, E wave is the same direction of current and propagation is normal to current. I attach the copy of one page of the book. Please tell me your thoughts. That still the question, what is the velocity of the current in the good conductor? Also I want to know why the speed of the stripline is higher and it is not frequency dependent.

Attached Files
 Skin effect.pdf (652.0 KB, 7 views)
P: 3,795
 Quote by yungman I think my original question might be wrong. Current conduction is not the same as propagate of EM wave in good conductor like coper. From the skin effect explaination, E wave is the same direction of current and propagation is normal to current. I attach the copy of one page of the book. Please tell me your thoughts. That still the question, what is the velocity of the current in the good conductor? Also I want to know why the speed of the stripline is higher and it is not frequency dependent. Thanks for all your time.
I found out already. Stripline is TEM mode. Still can't find the speed of the current density on the surface of a good conductor.
P: 4,513
 Quote by yungman I know the first one is "propagation velocity" the second is "phase velocity". What is the difference? Thanks
You should know that the velocity of a sinusoidal wave and a modulation of a sinusoidal wave will not, in general, be the same. In electromagnetic theory the first is called phase velocity, and the second is called group velocity. This terminology is used in wave guides. I don't claim to be up on the propagation of signals in coaxial wire, or strip line, or just a simple wire in free space, so the terminology may vary, although phase velocity will always mean the velocity of a sinusoidal wave.
P: 3,795
 Quote by Phrak You should know that the velocity of a sinusoidal wave and a modulation of a sinusoidal wave will not, in general, be the same. In electromagnetic theory the first is called group velocity, and second phase velocity. This terminology is used in wave guides. I don't claim to be up on the propagation of signals in coaxial wire, or strip line, or just a simple wire in free space, so the terminology may vary, although phase velocity will always mean the velocity of a sinusoidal wave.
I don't think so, group velocity is defined for a group of frequencies in the signal going through the medium. The velocities differ with difference frequency.

What we are talking about can be consider a single frequency, not a modulated signal. I believe Phase velocity IS the same as Propagation velocity which is the velocity of the EM wave travel through a medium. Which is $$\omega$$ / $$\beta$$.

In a good conductor like sea water which is a lossy medium, the velocity is only in 10EE7 range compare to vacuum of 3EE8 m/sec. My confusion can be seen in the skin effect paragraph that I attached. The direction of the conduction current is the direction of the E wave which is along the length of the bar. The EM wave is propagate in direction of the thickness which is perpendicular to the conduction current and is much slower than speed of light and suffer great attenuation. The conduction current only suffer from ohmic loss of the surface resistance along the length of the bar and travel at close to speed of light. My question what is the speed of the conduction current.
P: 4,513
 Quote by yungman I don't think so, group velocity is defined for a group of frequencies in the signal going through the medium. The velocities differ with difference frequency.
That's right, the group velocity is a group of frequencies. A modulated sinusoidal wave results in a group of frequencies. Our two points of view are the same. See Fourier transforms--or see Fourier sums; their easier to grog.

I re-read all of your posts, and the others, so I'm up to speed. Propagation of a signal down a conductor is a very differerent phenomena than sending an electromagnetic wave into a conductive media.

There is a hierachy one can make from free electromagnetic waves to a single wire conductor: free EM waves, to wave guide, to differential pair (like the old 75 ohm TV antenna wire), to coaxial, to single conductor. These are all dominated by inductance and capacitance. A pair of wires--like the 75 ohm TV wires--can be modeled as a ladder of infintesimal capacitors and inductors. The capacitors form the steps and the inductors the supports between each pair of steps. Coaxial cables use the same model.

The dominant effect in penetrating a conductive media is resistance such as you would be interested in with stealth technology and ultralow frequency submarine communications. This, I'm not at all familiar with.

You are correct in your assesment to distinguish the two.
P: 4,513
 Quote by yungman In a good conductor like sea water which is a lossy medium, the velocity is only in 10EE7 range compare to vacuum of 3EE8 m/sec. My confusion can be seen in the skin effect paragraph that I attached. The direction of the conduction current is the direction of the E wave which is along the length of the bar. The EM wave is propagate in direction of the thickness which is perpendicular to the conduction current and is much slower than speed of light and suffer great attenuation. The conduction current only suffer from ohmic loss of the surface resistance along the length of the bar and travel at close to speed of light. My question what is the speed of the conduction current.
You may know this, but it's a common misconception that the velocity of current in a conductor is near the speed of light. Electrons propagate at their "drift velocity" in a conductive media.

http://en.wikipedia.org/wiki/Electric_current

It doen't look like Wikipedia will suppy us with a typical drift velocity. But for a 100 Watt load such as a light bulb powered by 120 VDC instead of volts AC, it's something like one centimeter an hour in an 18 gauge conductor, give or take.

But in an attenuated wave in a conductive media, such as you are interested in, there are transverse current waves. At least I think this is the current you are interested in. The current waves have a velocity. The current oscillates back and forth in phase with the electric field. The electrons slosh back and forth at the drift veleocity. The waves themselves travel at the speed of the electric field in the media.
P: 3,795
 Quote by Phrak You may know this, but it's a common misconception that the velocity of current in a conductor is near the speed of light. Electrons propagate at their "drift velocity" in a conductive media. http://en.wikipedia.org/wiki/Electric_current It doen't look like Wikipedia will suppy us with a typical drift velocity. But for a 100 Watt load such as a light bulb powered by 120 VDC instead of volts AC, it's something like one centimeter an hour in an 18 gauge conductor, give or take. But in an attenuated wave in a conductive media, such as you are interested in, there are transverse current waves. At least I think this is the current you are interested in. The current waves have a velocity. The current oscillates back and forth in phase with the electric field. The electrons slosh back and forth at the drift veleocity. The waves themselves travel at the speed of the electric field in the media.

Thank you for taking the time. I should have known that, I just did not relate the two. I have been reading up a little, got more question than when I first posted, but I guess it is progress, at least I know enough to be confused!!! I'll think and study more before I post on this one. It is new year's eve and I have my grandson with me over night. I'll come back after tomorrow.

Happy new year to you all and thank you all for helping.
 Mentor P: 37,602 Happy New Year, yungman. You've been asking some good questions, and doing good learning on your own. Enjoy the kids!
P: 4,513
 Quote by yungman Thank you for taking the time. I should have known that, I just did not relate the two. I have been reading up a little, got more question than when I first posted, but I guess it is progress, at least I know enough to be confused!!! I'll think and study more before I post on this one. It is new year's eve and I have my grandson with me over night. I'll come back after tomorrow. Happy new year to you all and thank you all for helping.
Happy newyear, yungman!

I'm kicking myself over a statement I made about resistance being a dominate a effect in a penetrating wave. It's meaningless. A completely reflectived wave will always have a penetration depth (exponentially decreasing), even where there is no loss. But any penetration of a conductor will suffer losses due to the resistivity of the material. Sea water is especially interesting because it has both resistive losses, and additionally has a very high dielectric constant.

In any case, I've about exhusted everything I know on the topic, and at this point you should probably be instructing me in short order.

 Related Discussions Introductory Physics Homework 1 Classical Physics 3 Introductory Physics Homework 3 Introductory Physics Homework 5 Chemistry 1