# #12 solid wire

Discussion in 'General Technical Questions and Answers' started by WB7DMX, Feb 1, 2006.

Not open for further replies.
1. ### SM0AOMHam MemberQRZ Page

The notation that I finally found
(used at pages 8 and 9 of the http://www.ece.mcmaster.ca/faculty....13.pdf)
states that the macroscopic permittivity of metals
when describing the dielectric equivalent circuit using the relaxation time model
could be approximated with the free space value.

I have no reasons to question this point of view.

As a metal, as previously discussed, cannot store charges by polarization of dipoles, the traditional &quot;dielectric constant&quot; will become undefined.

We are here trying to discuss the &quot;inner workings&quot; of metallic conductors in a way that is not present in any DC or radio frequency circuit. Only at infrared or optical frequencies do the &quot;dielectric properties&quot; of metals come into account. Below these frequencies the &quot;time independent diffusion equation&quot; describes the field distribution, and consequently the current flow, of the conductor.

In this equation, the term for permittivity vanishes, and the current flow through the conductor will be governed by the conductivity and the electric field, and will consist entirely of conduction currents. There will be no significant displacement currents.

If you want to see for yourself, go to http://www.plasma.uu.se/CED/Book and download the free E-book &quot;Electromagnetic Field Theory&quot; authored by prof. dr. Bo Thide (SM5DFW). On pages 24 to 27 the concepts of fields inside conductors are covered extensively. Look in special at Eq. (2.15) and the discussion in the paragraph below.

Another, rather roundabout, way to arrive to a very approximate capacitance value would be to model the piece of wire as an isolated half-wave resonator or dipole.

The resonance frequency in the lowest mode, corrected for the thickness factor, would be 0.9 * 150/0.0254 MHz = 5314 MHz. If we plug in this value and the self-inductance of the wire (16 nH) into the resonance formula, C = 25330/(f^2*L), we arrive at a value of 0.055 pF.

This model is however somewhat suspect, as the capacitances must be considered as lumped and non-fringing, and self-inductance is also assumed as a constant over the length of the wire. This is not always the case at microwave frequencies. The wire is also somewhat too thick to be accurately represented as an equivalent circuit using the Schelkunoff concept of average characteristic impedances.

73/

Karl-Arne
SM0AOM

2. ### KE5FRFHam MemberQRZ Page

By the time this debate is settled, you guys will have figured out how to use &quot;worm-holes&quot; for interstellar space travel or something. Maybe we should call Stephen Hawking for his opinion on the matter.

3. ### K7JEMHam MemberQRZ Page

I find it extremely illogical that the permittivity of a metal would &quot;just happen&quot; to be the same as the value for free space under any circumstance, since by any stretch of physics (or the universe as we currently know it), a piece of copper and a complete vacuum are not very closely related.

No, I think the answer is as you have stated &quot;undefined&quot;, and until we can better get a handle on what was that original question from 30 years ago, and what they said the answer is supposed to be, we are just shooting in the dark. Any supposition or equations proffered to back up one theory or another should be things that were taught and relatively available for the course being taken back then.

My own personal opinion is that someone came up with a question that they wanted answered by using a specificly taught formula, perhaps not considering all possiblities.

A true story comes to mind:

On a physics test, college students were asked this question; &quot;Given a barometer, tell how it is possible to determine the height of a very tall building.&quot;

Most of the students followed the &quot;correct&quot; course and described how to take a barometric reading at the top and bottom of the buiding, and from graphs, charts, and/or formulae they would be able to express an answer to within a certain degree of accuracy.

One student stated that there were at least three different ways he could think of, and each with a different degree of accuracy. The first, and least accurate, was described in the &quot;usual&quot; way of the other students, taking barometric readings and using charts or formulae.

His paper continued, &quot;The second, and more accurate way would be to go to the elevator and take it to the roof. Drop the barometer off the top of the building, and time how long it takes to hit the ground. From fomulae that we have already learned in this class, it is possible to determine the height of the building, with a reasonable degree of accuracy.&quot;

He went on, &quot;The third and most accurate way that I can think of would be to go to the elevator and take it to the basement. Once there you would look for the building engineer. Tell him, ' I'll give you this nice new barometer if you tell me how tall this buiding is' &quot;.

Joe

4. ### WB7DMXGuest

yes the inverse of the resistance and permittivity was use in the original problem, I can remember that much after seeing it here.
also there was a few pages in the book that gave a very clear explanation of why the capacitance existed.
and I find that your responsive is rather childish.
if you don't know or have any positive input, to the question, why do you insist on making fun of it and acting like it is some kind of joke ?

it is real, and does have a correct answere, and I am just inquireing if anyone can remember how to do it,
its not a joke.

thank you any way.

5. ### K7JEMHam MemberQRZ Page

I think you must be referring to my comment:

&quot;No, I think the answer is as you have stated &quot;undefined&quot;, and until we can better get a handle on what was that original question from 30 years ago, and what they said the answer is supposed to be, we are just shooting in the dark. Any supposition or equations proffered to back up one theory or another should be things that were taught and relatively available for the course being taken back then.

My own personal opinion is that someone came up with a question that they wanted answered by using a specificly taught formula, perhaps not considering all possiblities.&quot;

Perhaps you thought that I was referring to you in the second paragraph, but this was in reference to the original question posed by CREI. IOW, whoever made the test and the question was seeing how well people could &quot;read between the lines&quot; or &quot;think outside the box&quot;, using the information that they had been taught.

Since we don't know the exact text of the question, and since we don't know the exact answer to said question, as presented 30 years ago, I think it is safe to assume that we are &quot;shooting in the dark&quot;. This isn't to make light of the question, just again to reiterate that one possible answer is that it would be &quot;undefined&quot;, given the limited set of info. The story about the physics course is absolutely true, and it shows on a humerous side that sometimes the professors who make up the questions don't always consider all possible &quot;correct&quot; interpretations of the question and answer.

This is not to say that this is a joke, just that people look at things differently when given limited amounts of information. The student must ask himself, &quot;What is this guy wanting as an answer?&quot; and usually, but not always, the answer is in something that has been taught in the curricullum. If the subject matter just taught had been how to calculate capacitance of a cylinder, by using the end cross section and the length of an object, then that is probably the answer being sought.

Since none of us posting here have (recently) had this specific class, then we must rely on what we know, have learned, or believe. My thought is that the capacitance can only be truly expressed if there is a &quot;dielectric&quot; medium of some sort, such as this wire referenced to a ground plane, or some other object. Since this doesn't seem to be the case, we run into a situation where the answer is something contrary to normal capacitance, ie a situation where the extremely low resistance of the wire would completely and utterly swamp out any trace capacitance that might exist.

The other two questions are straight forward, easily calculable, easy to understand, and within the range of normal (non &quot;Primer&quot thinking. This makes me think that we are way out in left field with all the computations and conjecture that have gone on here. The answer is something rather simple, and it could be calculated with a slide rule. If this is the case, then we are either missing an important piece of the question, or the answer (as wanted 30 years ago) is not correct.

Joe

6. ### WB7DMXGuest

very good, maybe some day some one will have the book and be able to answere the exact question as it was printed with the explaintion, and clear this whole thing up to everyone's satifaction.
thats what I was hopeing for and the reason for the post.
and I do know that it does have it.

7. ### SM0AOMHam MemberQRZ Page

http://www.ece.mcmaster.ca/faculty....e13.pdf

The more I think about the original question, I feel
that it very well might was intended to illustrate the
conceptual analogy between conductance and capacitance, and maybe also the use of this in calculation of the capacitances of complex structures.

It is somewhat surprising to find such a high-level reasoning in correspondence course material, as this is something which today is taught at M. Sc. or PhD levels,
and in my M. Sc. electromagnetics course material from the mid 70's, it was only mentioned in passing.

My interest in this case comes from that I recall seeing
in a very old antenna engineering textbook that conductance modelling could advantageously be used as a method to determine the antenna capacitance of VLF antennas.

73/

Karl-Arne
SM0AOM

8. ### WB7DMXGuest

it was in 1962 that I took that course. I thought it would be some good background as I was planning on a career in electronics service and repair. and I was studying for the second class commercial license too. I was doing radio &amp; TV repaire at the time, working for W8NUL. in Alden Mich.

9. ### K8ERVHam MemberQRZ Page

I already called him, he did not know---

TOM K8ERV Montrose Colo

10. ### SM0AOMHam MemberQRZ Page

There is no reason to disturb Stephen Hawkins in this matter, as it was settled almost 100 yeárs ago by optics scientists.

When studying the propagation of light, especially
through thin coatings, the &quot;Lorentz - Drude&quot; relations were worked out. These explain the electrical and optical behaviours of metals using a beautiful fusion of classical electrodynamic and statistical mechanics theory.

In essence, it can be worked out from the Lorentz - Drude relations that
any material has a complex permittivity (or dielectric constant), which is dependent on the frequency and the conductivity of the material.

For low frequencies, this can be approximated by:

Permittivity = Permittivity of space + j(conductivity/2*pi*f)

There being no bound charges in a metal to polarize,
the real part of this expression corresponds to the
permittivity of the &quot;dielectric&quot; of the equivalent capacitor
formed between the wire ends in the example.

As previously discussed, the influence of this equivalent capacitance can safely be neglected at DC or radio frequencies.
This is very fortunate for us radio engineers, as ordinary wires and circuit elements would otherwise show a dispersive behaviour.

When the frequencies finally reach infrared or visible light, the dielectric properties of the metal will govern the way electromagnetic waves can be propagated through a material.

73/

Karl-Arne
SM0AOM