Why Do EM Waves Travel Differently in Good Conductors?

[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

 

[Defennder]

I know the speed of signal travel in stripline is c/\sqrt{}\epsilon_{}r_{}

What's the last term supposed to be?

 

[berkeman]

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?

 

[yungman]

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

 

[yungman]

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.

Thanks for your time.

 

[berkeman]

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?

 

[yungman]

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?

I'll think about this a little more.

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 textbook. 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!

 

[Defennder]

"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.

 

[yungman]

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.

Thank for your input.

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

 

[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 explanation, 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.

 

[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 explanation, 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.

 

[Phrak]

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.

 

[yungman]

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.

 

[Phrak]

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.

 

[Phrak]

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.

 

[yungman]

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.

 

[berkeman]

Happy New Year, yungman. You've been asking some good questions, and doing good learning on your own. Enjoy the kids!

 

[Phrak]

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.

 

[yungman]

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.

Hey we are all leaning. The more we share, right or wrong, everyone learn. We all have our moments. I take the comfort that we learn beyond just getting the correct answer to homework and test when we start questioning more, whether we make correct assumption or not. This is the third time I read and work over the topic and all of the sudden, I stop and questioning all this.

Actually you gave me a lot of fruitful thoughs. Since your last post, I was kicking myself, I study those before, just not enough to become a common sense to apply freely! I print out your comments and the link and study it. Here is more question from thinking in the last two days.

From part A of the drawing, I proved that EM-wave propagate towards the center of the thick wire. I show in instanteneous form using sine wave in +ve and -ve direction separately to prove both case, no EM-wave propagate into space(to the surrounding medium). E wave is always in direction of current which is just AC current of cos(\omegat). That means E is along the length of the wire. Question is what is the speed of the signal through the wire even though you show me clearly that the electron move very very slow in the wire. Somehow the signal do travel close to speed of light as we all know.

Further in Part B I show a loop antenna make of the same thick wire and driven by signal generator as shown. If my intupretation is correct, no EM-wave emmited from the loop directly. Only M wave propagate out as shown. E wave can only from the M wave that propagate out, not from the original current through the loop.

This is what I think so far, please give me more feedback.

Happy new year.

 

[Phrak]

I haven't looked into the details of a conductor as much as you are now. There are some
interesting points. The negative of the integral(PdA) is quntity of energy. In the DC form
your drawing is commonly used to model cylindrical resistors, where the energy moves
into the resistive material, then is dissipated as heat. But, then, this model shouldn't work
for a superconductor. I don't see why it doesn't.

An infinitely long conductor in empty space should be the same as a coaxial cable
with the outer conductor at infinity; R-->infinity. The Poynting vector at the surface
of the outer conductor has it's own Poynting vector. This is a conserved field in empty
space ('cause energy is conserved), so somehow all of these Poynting vectors have to
origintate at the source of EMF.

Your second drawing is a loop antenna. It has the same radiation pattern as a dipole
antenna at large distances. Where the distance R>>wave_length, the space around the
loop is dominated by propagating fields. So there is an accompanying electric field, and
the ratio of the electric to the magnetic field strengths is that of radiation in a vacuum.

The near fields are not the same as the far fields, but I only know the rough details.
If we put a receiver antenna at one loop radius distance, we're more likely to call the
arrangement a transformer and the field coupling is not same as the coupling from
transmitted radiation between loop transmitter and loop receiver.

You've picked an interesting course of study. Did you say it was work related? I almost
wish I had an excuse to pursue it, myself.

 

[yungman]

I haven't looked into the details of a conductor as much as you are now. There are some
interesting points. The negative of the integral(PdA) is quntity of energy. In the DC form
your drawing is commonly used to model cylindrical resistors, where the energy moves
into the resistive material, then is dissipated as heat. But, then, this model shouldn't work
for a superconductor. I don't see why it doesn't.

An infinitely long conductor in empty space should be the same as a coaxial cable
with the outer conductor at infinity; R-->infinity. The Poynting vector at the surface
of the outer conductor has it's own Poynting vector. This is a conserved field in empty
space ('cause energy is conserved), so somehow all of these Poynting vectors have to
origintate at the source of EMF.

Your second drawing is a loop antenna. It has the same radiation pattern as a dipole
antenna at large distances. Where the distance R>>wave_length, the space around the
loop is dominated by propagating fields. So there is an accompanying electric field, and
the ratio of the electric to the magnetic field strengths is that of radiation in a vacuum.

The near fields are not the same as the far fields, but I only know the rough details.
If we put a receiver antenna at one loop radius distance, we're more likely to call the
arrangement a transformer and the field coupling is not same as the coupling from
transmitted radiation between loop transmitter and loop receiver.

You've picked an interesting course of study. Did you say it was work related? I almost
wish I had an excuse to pursue it, myself.

I have no respond on the content yet, I need some time to digest what you wrote.

I just respond to the to the last sentence. No it is not work related nor school related. I work close to 30 years as a senior engineer and as manager of EE. I am not working anymore at least for the time. This has been my passion all these years and I am still putting in 20+ hours week studying. So I am just doing it for my own interest and maybe go back to work one day if I feel like it. Microwave is the hardest subject in electronics, it is like why people climb Mt. Everest?! Because it is there!

 

[Phrak]

Microwaves are hardest? That is a nice challenge.

You know, you've got me going on the speed of a signal in a plain wire. It's easiest, so
its a good star before solving for strip line, then.

All the tools are at hand: Maxwell's equations and cylindrical symmetry. It's frequency
dependent, so it should be solved for wavelength or frequency as the independent
variable. The solutions will be periodic in wavelength. We can assume an infinitely long
conductor, with zero charge density. Assume the conductive material is uniformly
nonconductive. It shouldn't be a good dialectric--I don't know how that comes into it.
The current density, electric and magnetic fields should have a constant phase
relationship. Assume the surrounding space is the vacuum.

There are bondry conditions at the conductor surface and infinitite radius. There'll
be two solutions: one for the interior of the wire, and the other for free space. The
solutions should be continuous across the boundary in some manner.

The solutions will be a differential equation, and is probably a Bessel function or something
like it. I ran into this the last time I tried to solve a cylinderically symmetric equation for
fields surrounding a solenoid.

Where do we start?

 

[yungman]

I haven't looked into the details of a conductor as much as you are now. There are some
interesting points. The negative of the integral(PdA) is quntity of energy. In the DC form
your drawing is commonly used to model cylindrical resistors, where the energy moves
into the resistive material, then is dissipated as heat. But, then, this model shouldn't work
for a superconductor. I don't see why it doesn't.

An infinitely long conductor in empty space should be the same as a coaxial cable
with the outer conductor at infinity; R-->infinity. The Poynting vector at the surface
of the outer conductor has it's own Poynting vector. This is a conserved field in empty
space ('cause energy is conserved), so somehow all of these Poynting vectors have to
origintate at the source of EMF.

Your second drawing is a loop antenna. It has the same radiation pattern as a dipole
antenna at large distances. Where the distance R>>wave_length, the space around the
loop is dominated by propagating fields. So there is an accompanying electric field, and
the ratio of the electric to the magnetic field strengths is that of radiation in a vacuum.

The near fields are not the same as the far fields, but I only know the rough details.
If we put a receiver antenna at one loop radius distance, we're more likely to call the
arrangement a transformer and the field coupling is not same as the coupling from
transmitted radiation between loop transmitter and loop receiver.

You've picked an interesting course of study. Did you say it was work related? I almost
wish I had an excuse to pursue it, myself.

I did some refreshing on transmission line theory. I think what you said might be true, that is how I kind of thinking too.

The long wire should be treated as COAX with very thick dielectric...air. So \mu = \mu_{0}, \epsilon = \epsilon_{0}.

This will give velocity of light and \eta =377 ohm.

So RF current through a straight wire actually GENERATE 2 EM waves:
1) The usual EM wave that point inward towards the center of the wire. This is the one that cause the skin effect.
2) The EM wave from launching into the COAX line formed by the length of the wire with air as dielectric.

I hope Someone can comment with some certainty. I cannot find anything like this in 6 books I have!

To answer your question whether Microwave and EM theory are the most difficult subjests of EE. Without a doubt...Yes... By a mile! Thorughout the years, I disigned all different type of circuit, systems, embedded system, FPGAs, many years of analog opamps, pulsing circuits, power supplies, mixed signal, video capture, analog ICs, RF and signal integrety PCB layouts. Not even close. The last 5 years, I got into more and more microwave design and I love it.

My degree was in Biochemistry. I never have formal education in EE except few months in Heald College which is just a trade school. I study everything on my own. I have not been working for 3 years already. To prepare for this EM subject, I spent one year studying Vector calculus and differential equations before jumping into EM. I am planning to enroll in PDE in the future to re-study Electro Dynamics.

 

[Phrak]

We have somewhat similar design background--minus the video capture, RF and IC design.

Something looks a little fishy with your thick wire, AC conductor. For an ideal conductor the Poynting vector should point outward as often as inward--or power is lost in the conductive medium.

The electric field is proportional to the change in magnetic field. Where your magnetic field loops are at their greatest strength, their change in stength is zero. So the axially directed electric fields have their greatest strength inbetween the loops, and oppositely directed between each pair of loops. This will give you Poynting vectors alternating into and out of the conductor.

By the way, I was wrong about assuming zero charge density to zero in a conductor. Doh! Those axially and oppositely pointing electric fields have to either loop back on themselves, or terminate on charge.

Too bad we don't have someone to sort all this out. A lot of these solutions are nonanalytical, so exact solutions are probable avoided in undergraduate texts.

 

[yungman]

We have somewhat similar design background--minus the video capture, RF and IC design.

Something looks a little fishy with your thick wire, AC conductor. For an ideal conductor the Poynting vector should point outward as often as inward--or power is lost in the conductive medium.

The electric field is proportional to the change in magnetic field. Where your magnetic field loops are at their greatest strength, their change in stength is zero. So the axially directed electric fields have their greatest strength inbetween the loops, and oppositely directed between each pair of loops. This will give you Poynting vectors alternating into and out of the conductor.

By the way, I was wrong about assuming zero charge density to zero in a conductor. Doh! Those axially and oppositely pointing electric fields have to either loop back on themselves, or terminate on charge.

Too bad we don't have someone to sort all this out. A lot of these solutions are nonanalytical, so exact solutions are probable avoided in undergraduate texts.

I have to read more detail on the rest of your text before I respond. I just first respond to the high lighted part:

1) The Primary poynting vector always point inward. I was making this assumption like yours until I calculate the poynting vector separately on +ve and -ve half of the cosine wave. That is the reason I show 2 calculation in my drawing. Take a look to see whether you agree. I could be wrong. The reason is because as the E wave change direction, so is the H wave, and E X H still pointing at -r.

2) The secondary poynting vector from launching the EM wave onto the transmission line formed by the long wire is in the direction of the wire. Let me know what you think.


Electronics has always been my hobby. I started out as a guitarist in 1977 wanting to have an ideal guitar amp with natural distortion and channel switching. That was before any of those amplifiers came out. The more I got into electronics, the more I liked it. I ended up quiting music all together and got into electronics. I feel I am very lucky to find a passion of my life! I am still studying and have no plans to quit anytime soon.

 

[yungman]

It seem from reading the transmission line theory that when the wave is launched into a transmission line ( long wire in this case ), it is in form of VOLTAGE phasor and CURRENT phasor, not as E wave and H wave. So it is not EM wave travel down the line. The wave travel down as Voltage and Current.

The Current along the wire then in turn generate EM wave that radiate out into air.

Can anyone comment on this to confirm or correct my statement.

 

[Phrak]

I did some refreshing on transmission line theory. I think what you said might be true, that is how I kind of thinking too.

The long wire should be treated as COAX with very thick dielectric...air. So \mu = \mu_{0}, \epsilon = \epsilon_{0}.

This will give velocity of light and \eta =377 ohm.

So RF current through a straight wire actually GENERATE 2 EM waves:
1) The usual EM wave that point inward towards the center of the wire. This is the one that cause the skin effect.
2) The EM wave from launching into the COAX line formed by the length of the wire with air as dielectric.

If I understand you correctly you've broken the problem into two parts: the fields that transmit energy down the length of the wire, and the fields that exist as a result of resistive losses. Your drawing would show the lossive part of the electric field that results from resistance.

I found only one figure in an old physics text of the fields surrounding a coaxial cable that included the phase relationship between the electric and magnetic fields---and it was wrong! So it threw me off for a while. In a lossless wire the direction magnetic field lines are circumferal. The direction of the electric fields are radial. The two fields are out of phase.

Strictly speaking these are not electromagnetic waves. But there are electric, magnetic, and current density waves.

 

[yungman]

If I understand you correctly you've broken the problem into two parts: the fields that transmit energy down the length of the wire, and the fields that exist as a result of resistive losses. Your drawing would show the lossive part of the electric field that results from resistance.

I found only one figure in an old physics text of the fields surrounding a coaxial cable that included the phase relationship between the electric and magnetic fields---and it was wrong! So it threw me off for a while. In a lossless wire the direction magnetic field lines are circumferal. The direction of the electric fields are radial. The two fields are out of phase.

Strictly speaking these are not electromagnetic waves. But there are electric, magnetic, and current density waves.

Yes I broke into two separate parts. The last post that I wrote, I think is in agreement with yours.

1) In my original question, the signal launch into the transmission line as Voltage and Current phasor, not as EM wave. The EM field that is generated only in form of the poynting vector pointing into the center of the wire. This is the main cause of skin effect.

2) The energy launch into the transmission line only as Voltage and Current phasor. I think this is what you read in the physics textbook. The the current in the transmission line generate a secondary EM wave: Radial E field line radiating out of the the surface of the wire and is normal to the surface of the wire and the H field is circling around the wire. The result is just like the textbook drawing of the field pattern of a coax line. In the long wire case here, the surrounding space is considered as the dielectric of the coax. Current on the wire generate the secondary EM wave that travel into the space. I hope we are getting somewhere.


I think back to my original question: What is the speed of the current travel in the wire conductor. The answer should be speed of light 3EE8 m/s. The answer comes from the fact that The wire is treated as coax with infinite thick dielectric. The energy launch into the line only in form of Voltage and Current phasor with velocity = \omega / \beta . In this case, it should be close to the speed of light.

 

[Phrak]

I made an error, using B instead of the time derivative of B, so that most everything I had to say in that last post was wrong.

I better leave it alone before I throw you off any further.

 

[yungman]

I made an error, using B instead of the time derivative of B, so that most everything I had to say in that last post was wrong.

I better leave it alone before I throw you off any further.

I think you are doing fine. We both are making mistakes here and there. I think your last post on the field of the coax is correct and I believe it apply to my wire transmission line. The result is the fields radiate into the air like the fields in the coax from textbooks. Because in the wire case, the dielectric extend to far away, the E and H field extend to far away too.

This is a discussion and we both learn...Hey better you than nobody else talking! I am learning and I hope you are learning from this.

Now got a new question. How is the secondary EM wave propagate?! Now that it looks like we got a EM wave going from the current along the wire! It seem like this EM propagate along the wire! Is this true?? If you look at the coax field pattern, H is circling the inner conductor, E is radiating out normal to the outer surface of the inner conductor. so E=rE and H = -\phiH. r X -\phi = -z which is along the wire!