Speed of EM in good conductors

[Phrak]

I think your coordinate interpretation is as I intended. I can't read the subscrips for the B field.

Yes, where I said E_z, I should have said E_r.

You're picture of how you envision the fields looks good for the E field if the arrow length are intended to mean field strength. The E fields should extend until they find ground return somewhere in the enviroment. The B fields look a little funny as an envelope for the E fields stengths.

After all this I don't understand the ve+ and ve- notaton, sorry. But the instantanious voltage along the wire length is bothering me. It's the integral of the electric field, I think, so that the voltage would be out of phase with everything else. That doesn't seem right. Your equations have them in phase. I'm perplexed.

As you say, this is all about the secondary wave. The primary wave is the interesting part of it all, where the E field apparently has an axial component as you've stessed.

You probably recall that skin effect means that as the frequency increases the current is forced out of the center of the wire so that the bulk resistivity of the wire becomes more of an effect as frequency increase. So it will turn-out that finding how the secondary wave works will require the internal solution of one or both of the electric and magnetic fields inside the wire. If I don't miss my guess, this will lead to a nonanalytical equation, so your texts probably take the course of action of making approximations and dividing the full solution into parts: the primary and secondary waves, as you've called them.

 

[yungman]

I think your coordinate interpretation is as I intended. I can't read the subscrips for the B field.

Yes, where I said E_z, I should have said E_r.

You're picture of how you envision the fields looks good for the E field if the arrow length are intended to mean field strength. The E fields should extend until they find ground return somewhere in the enviroment. The B fields look a little funny as an envelope for the E fields stengths.
Yes the E arrows represent field strength, the field should reach the ground return. The M field is the typical circles of magnetic fields as shown:

After all this I don't understand the ve+ and ve- notaton, sorry. But the instantanious voltage along the wire length is bothering me.
I can't find where are the ve+ and ve- notation. The diagram was wrong, I corrected it already on the original post. It should read:

It's the integral of the electric field, I think, so that the voltage would be out of phase with everything else. That doesn't seem right. Your equations have them in phase. I'm perplexed.

As you say, this is all about the secondary wave. The primary wave is the interesting part of it all, where the E field apparently has an axial component as you've stessed.

You probably recall that skin effect means that as the frequency increases the current is forced out of the center of the wire so that the bulk resistivity of the wire becomes more of an effect as frequency increase. So it will turn-out that finding how the secondary wave works will require the internal solution of one or both of the electric and magnetic fields inside the wire. If I don't miss my guess, this will lead to a nonanalytical equation, so your texts probably take the course of action of making approximations and dividing the full solution into parts: the primary and secondary waves, as you've called them.

Do you agree the point I made that the secondary EM wave that radiate out of the wire are from the Voltage and Current traveling waves that travel along the wire? Actually it is only the Current traveling waves that generate the E field which in turn generate the M field.

After I verify with you on this, I think I better stop this thread because after doing all this digging, This really become an antenna question which I don't have any idea and I am waisting people's time here. I just order 2 books on antenna and I better do some serious study before I asked any more of this kind of question. I am on the the last chapter of electro magnetic...Boundary problems. After the EM, I'll be diving into antenna next.

Thanks for taking the time to work with me.

 

[Phrak]

Do you agree the point I made that the secondary EM wave that radiate out of the wire are from the Voltage and Current traveling waves that travel along the wire? Actually it is only the Current traveling waves that generate the E field which in turn generate the M field.

Yes, definitely, we're in agreement. You're actually approching the problem normally, beginning with current. I started guessing at the electric field and working backwards. It's a matter of taste, but I think it usually works better to assume current and charge distributions and solve for the fields as you are doing.

I'm struck with an idea. I think the primary wave can be derived by assuming the current decays exponentially over distance.

$$I = I_0 cos(kz - \omega t) exp(-frac{z}{L} )$$​

Where L is just some length along the wire where the signal strength has dropped to 36%. Either this yields a constant bulk resistivity of the wire, or it's wrong.

Thanks for taking the time to work with me.

And you, as well. I'm learning too.

What units are you using? There are several standards: SI, CGS, Gaussian... It would be good to be both working in the same system of units. Whatever units you are using I will adopt.

 

[yungman]

Yes, definitely, we're in agreement. You're actually approching the problem normally, beginning with current. I started guessing at the electric field and working backwards. It's a matter of taste, but I think it usually works better to assume current and charge distributions and solve for the fields as you are doing.

I'm struck with an idea. I think the primary wave can be derived by assuming the current decays exponentially over distance.

$$I = I_0 cos(kz - \omega t) exp(-frac{z}{L} )$$​

Where L is just some length along the wire where the signal strength has dropped to 36%. Either this yields a constant bulk resistivity of the wire, or it's wrong.

I went back and read up on this. This is what I came up with:

I don't know how to find C because of the wire is in the air. But I think you get the point. My experience is if the wire is less than 1m, I don't think you lost too much signal. Mostly all loss from dielectric loss and non in this case. If you use steel, then it might be different because $$\mu$$ is large and skin depth is much thinner than coper.


And you, as well. I'm learning too.
Still it is good that you spent the time. There is no easy quick answer. Like what you suggested here, I have to go back and read up before I come back.

What units are you using? There are several standards: SI, CGS, Gaussian... It would be good to be both working in the same system of units. Whatever units you are using I will adopt.
I use meter, kg, deg C. I guess is SI?

...

 

[Phrak]

There are some units of measurement where Maxwell's equations will pick-up a factor of pi. I'll assume you're using SI units.

The reason I brought up resistive losses, not because of signal decay, but because this is the origin of the 'primary waves'--or whatever it it that has a Poynting vector directed into the wire.

It's going to take me some time to accumulate references, as I don't have any more than an intermediate text on electromagnetism. More, I'm back working full time.