Discussion in 'General Science & Technology' started by timojin, May 13, 2017.
Electric current moves on conductor in two dimensional or three dimensional
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It actually moves in one direction, following the conductor.
Let me make my question little more clear. Let say you have a rod, You apply a DC voltage the current( current = electron directio movement ) flows on the surface on the rod only or through surface and the bulk of the rod ?
If the rod is an isotropic solid metallic conductor with normal electical resistance, Ohm's law says that the electrical current flows through the bulk of the rod. The conductivity of the rod is actually proportional to the cross sectional area of the rod.
Does the Ohm's law hold in thin films ? or let me posed this way I have thin tubing of the same diameter as the rod say 1/2 diameter , but the tubing wall is 1mm thick. ?
Ohms law is applicable everywhere. In certain cases impedance need to be used.
But let's take your thin shell example with resistance aspect only..
Resistance R = rho * l / A.
Where l is the conductor length and A is the cross section area. Now consider the cross section of a solid cylinder and visualise that it is made up of thin ropes of thickness 1 mm. Now give a sharp cut to this cross section from surface point till it's center, and straighten the ropes. You will get a triangular cross section, it is like if radius is 100 mm, then 100 / 1 mm, that is 100 ropes are lying on top of each other with reducing width....top most rope will have a width of 2pir and thickness 1mm.. Now if you apply a voltage V across this cylinder, then the current as per ohm law shall be V/R....and what is R ? The parallel combination of radius/ thickness number of ropes of length l...that will turn out to be pho * l / A. So for a shell it will be just pho * l / A' where A' is the cross section area of shell strip, assuming that inner empty portion is absolutely non conducting, otherwise parallel connection principle shall be applied, for example outer most shell of gold, then silver then copper etc.
When you pose a vague question with no specific modifiers, as per your #1, confusion is the general result. Evidently you are only interested in steady-state DC conduction. For AC, there is the well known phenomenon of 'skin effect' such that at e.g. microwave frequencies, currents are effectively confined to a narrow surface layer typically of the order of a few microns or less. Skin depth goes as the inverse square root of frequency.
Going back to DC, for very thin films it's also well known resistivity is greater than for a thick conductor - owing to the increased relative contribution from surface scattering. Try a web search e.g. 'thin film conductivity' for links to relevant literature. There is no reason other than geometric constraints why DC conduction should not be 3D in general.
At DC it flows equally everywhere, provided the rod is equally conductive everywhere.
AC currents flow on the surface. The higher the frequency the more pronounced this effect. Google "skin effect."
As long as we are talking about direct current, yes, Ohm's law applies.
"Skin effects" in the technology of microwave transmission lines are a different issue.
I do not know. I do know however current takes the shortest route possible.
Yes this is interesting. I vaguely recall that this is why hollow - or silver-plated- conductors are sometimes used for AC and that the limiting case of this is the hollow waveguide used with microwaves.(??)
Though I've never really understood how a current in a waveguide can be equivalent to a wave confined within it. Is this right and if it is can you point me to anything that explains this?
Good question .
Currents and fields form a coupled system in waveguides and resonators. A quick rundown with illustrations of basic mode types in rectangular guide:
A more mathematical treatment with some obvious parallels with QM (e.g. eigenmodes, eigenfrequencies, from solving boundary value conditions for harmonic form of ME's):
http://www.antenna-theory.com/tutorial/waveguides/waveguide.php (then follow the link at end, and so on.)
There are many other tutorials online and if above not helpful, keep looking and one is bound to suit. I have avoided YouTube since you have a declared phobia for that resource.Please Register or Log in to view the hidden image!
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Thanks very much for this. I'll take a look.
Thanks also for not sending me videos. I find I can read a damned sight faster than some prick on a voiceover, treating me like a 5 year old with special needs. Please Register or Log in to view the hidden image!
Hahaha. It's not all like that with YT exchemist, but I understand your pov. A bit like dealing with spam email that tries hard to imitate genuine sources, sorting wheat from chaff gets easier with some experience under the belt. There is plenty of quality YT vids that can succinctly get a message across with far greater impact and immediacy than a dry, long read could do. For other situations written source material is essential. Horses for courses - imo.
The 'phase' (but not 'group') velocities of the 'TEM' (transverse electromagnetic mode) of microwaves in a microwave waveguide is faster than the speed of light in a vacuum. This has been understood by microwave engineers for decades of the last half of the 20th century.
This is one good reason, I don't flinch at the idea that either quantum entanglement or the spin mode of propagation of energy in a bound fundamental particle of matter or antimatter may be faster than light. One would be at a disadvantage to find anything that was a more ideal waveguide than the inside of a fundamental particle like an electron.
That c^2 term means something fundamental about bound forms of energy having inertial mass that is relativistic, not Euclidean geometric. It was derived using only the linear mode of propagation of photons, which are massless.
I would suggest doing a search on that Dan. As I recall, it's only for TEM transmission lines (not waveguide), and only if vacuum is the medium, that phase velocity = group velocity = c. If there is any dielectric present (virtually always), both phase and group velocities are less than c.
[also true if line conductivity is not perfect - but iirc the effect of finite conductivity is generally far weaker than than that of dielectric filling.]
It's for hollow metallic waveguide supporting non-TEM modes that phase velocity v_p can exceed c, which in turn means group velocity v_g is always less than c, based on the usual (v_p)(v_g) = c^2.
Electrons at an energy level appropriate to absorb or reemit microwave photons in a waveguide would also be physically larger in diameter than ones at an energy level appropriate to absorb or reemit photons in the visible portion of the EM spectrum. In practice this would be near impossible to experimentally confirm, but it would make perfect sense. There is a difference between the way light behaves as opposed to microwaves.
If you charged up the metal sphere of a Van de Graf generator to keep it charged and sent it out on a 13 billion year round trip journey to the edge of the known universe, would this generate a photon of that wavelength propagating at the speed of light in all directions? Why or why not?
Electrons no doubt have a higher frequency cutoff (whatever it is). Is there a corresponding low frequency end cutoff for a procedure that moves electrons outside of the confines atomic structure such as the one described?
This procedure was proposed originally to determine the information capacity of a qubit. No lower information capacity channel than the one proposed would ever be possible.
Of course it wouldn't work (an EM wavelength the size of the know universe), but for a reason no one has thought of. A static charge electron bound to a sphere of a Van de Graf generator is still bound to atomic structure, and subject to the same atomic scale limitations as other EM waves.
The electron itself would need to expand to the size of the known universe in order to make this happen.
A superconducting transmit antenna that long might actually work, if ultra low bit rate communications ever caught on.
An interesting exercise.
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