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In Reply to: Re: The question requires context. posted by jneutron on January 23, 2007 at 11:00:30:
Hi.Here is what my book stated:
"The self-inductance of a ROUND COPPER straight wire is on the order of 0.4 micro-henry/ft & is relatively UNaffected by the diameter or length of the wire".
Also, your post gave me the impression that copper & silver share the same self-inductance. Please substantiate.
c-J
Follow Ups:
As such, it depends heavily on the actual wire spacing. The best one can hope for is zero thickness insulation and about 160 nH, or .16 uH per foot, for a wire pair. Nobody uses zero thickness insulation of course.The terman equation is best for calculation of a wire pair inductance, but that also has a component of the equations which has the 15 nH per foot internal (or self) inductance number I quoted..
Here is the self (or internal) inductance for a cylindrical wire:Albert Shadowitz, "the electromagnetic field", Dover, 1988, pages 216-217..
Note, I can't put the integral equations here, suffice it to say he completed the derivation, the formula I'll give is the end result..
The total inductance for a single cylindrical conductor is:
L int = μ 0 / 8 π.
μ 0 = 4 π times 10 -7 henries/meter.
This becomes (4 π /8 π)times 10 -7 henries/meter
or, 1/2 times 10 -7 henries/meter
this is 5 times 10 -8 henries/meter
or, 50 times 10 -9 henries/meter
50 nanohenries per meter.
12/39.4 = .304 feet/meter.
50 times .304 = 15.2 nanohenries per meter.
(Ok, so I rounded the .2 off)
Cheers, John
""12/39.4 = .304 feet/meter"" is completely inaccurate in units..That should have stated .304 meters per foot.
Then 50 nH/meter times .304 meters/foot to give 15.2 nH per foot..
Gotta keep the units straight..typed too fast..sorry
Cheers, John
cj: ""
"The self-inductance of a ROUND COPPER straight wire is on the order of 0.4 micro-henry/ft & is relatively UNaffected by the diameter or length of the wire".""For a wire pair, the external inductance is dependent on the log of the ratio of distance to diameter...so to arrive at an inductance per foot, one needs the wire diameter..
For a #12 wire pair, a spacing of 1 inch gives very close to .4 uh per foot for the wire pair.
cj: ""
Also, your post gave me the impression that copper & silver share the same self-inductance. Please substantiate.""The prev equation cited μ 0 , as it was the derivation for a material which had a relative permeability of 1.
If you substituted steel for the conductor, with a relative permeability of 100, then the internal inductance would be larger by a factor of 100..in fact, this is what Hawksford did in that '85 paper, he substituted steel for the copper...Note, JC gave me the "100" number for the steel's permeability.
If you substitute silver for copper in a wire geometry, keeping the spacing and conductor diameter the same, you will be unable to measure a difference in inductance between the two constructs. This statement will fall apart as the frequency climbs towards a megahertz, as skinning will begin to reduce the silver's internal inductance slightly as a result of current re-distribution at the wire center. Given a wire pair inductance of 200 or so nH, the 30 total that can be removed by infinite frequency could only take the inductance down to 170 nH per foot.
Most cannot measure that accurately at the onset of the current redistribution regime..
Cheers, John
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