EC as in Electrical Conductivity

[MAB]

Agree a length of a single core conductor carrying a current with be inductive and a solenoid is a coiled single conductor. As I said never read or heard of a conductors diameter affecting inductance. Came as news to me and as I said haven’t been able to find any technical website to support the claim. There are several ways to increase the intensity of a magnetic field and its inductive effect.
1, Increase the current in the conductor
2. Increase the number of turns
3. Place a material with a higher relative permeability such as a silicon iron core in the magnetic field.
Nowhere does conductor diameter come into the equation.
Not trying to be controversial so no offence intended.

You are mixing mutual inductance with self inductance concept.
I gave two references, with the exact derivation from first principles.
This formula for self inductance of a single cylindrical conductor is not typically found in college text books. It is a somewhat popular homework assignment and test problem. I know, it was on one of my electromagnetics midterms, and I got it wrong!
Also, it is used in semiconductor extraction tools to aid high speed design.

Please read the Rosa reference I posted, it lays out a first principles derivation, with a picture.

Note, you can also get the formula by taking the inductance of a coaxial cable in the limit where the outer conductor diameter approaches infinity. But it isn’t as physically intuitive as the derivation by Rosa.

 

[Suffolkhifinut]

You are mixing mutual inductance with self inductance concept.
I gave two references, with the exact derivation from first principles.
This formula for self inductance of a single cylindrical conductor is not typically found in college text books. It is a somewhat popular homework assignment and test problem. I know, it was on one of my electromagnetics midterms, and I got it wrong!
Also, it is used in semiconductor extraction tools to aid high speed design.

Please read the Rosa reference I posted, it lays out a first principles derivation, with a picture.

Note, you can also get the formula by taking the inductance of a coaxial cable in the limit where the outer conductor diameter approaches infinity. But it isn’t as physically intuitive as the derivation by Rosa.

If it was a transformer you would be right. However the same is true in a magnetically operated relay or contact or with a single coil.

 

[MAB]

If it was a transformer you would be right. However the same is true in a magnetically operated really or contact or with a single coil.

No. Did you read the Rosa paper?

 

[Suffolkhifinut]

No. Did you read the Rosa paper?

Just read it quickly will have another read tomorrow without the effects of a couple of glasses of Vouvray inside. He from what I’ve glanced through divides self inductance in a single conductor both inside and outside the conductor, pointing out the permeability inside the conductor is undoubtedly different to the relative permeability of air which from memory is 1.08.
Never really been concerned with the theory of self inductance inside a conductor. Interesting though! As he says it doesn’t apply to infinitesimal size conductor or with high frequencies. If you look at skin effect at high frequencies increased cable resistance due to reduced current carrying area may be responsible.

 

[DonH56]

Can’t argue with the fact skin effect increases as frequency increases, then conductor diameter will matter.

Skin effect is a huge problem, but not quite the same as inductance... Skin effect reduces the cross sectional area for conductance, but ideally does not add phase shift, unlike inductance.

 

[jschwender]

If you look to all formulars provided by Groover, Rosa, Strasser, Maxwell … you find a common principle, with two dependencies: Inductance is proportional to the lenght of a conductor, and the second it is proportional to the logarithm of distance/diameter. this is even common to all different applications like single wire, pair of wires, coaxial wire and so on. Additional terms are corrections to take things like skin effect current displacement and so on into account. All these formulas are more or less approximations with results from taylor developments, others are empirical approximations. Beside that, all these consider exclusively linear case. As soon as you have something nonlinear (iron wire) they don't work. In a nutshell the dependencies are evident: small wire diameter result in short magnetic flux lines around the wire, and therefore, the magnetic line length is smaller as around a larger wire. Therefore the inductance must increase. Same thing if you consider the distance of a pair of wires: with close to zero distance of the wires, the flux of both opposing currents cancels out to zero, which results in disappearing inductance. This is what all theses formulas say, and what you can easily measure. https://www.schwender-beyer.de/artikel.php?k=4&a=14

 

[DonH56]

Here is a plot of the inductance (in uH) of a single wire (isolated from the ground plane) 1 m long and sweeping diameter from 0.01 to 1 cm using the equation from Grover (Inductance Calculations) as given previously:

It is pretty much a straight line on a log scale: