Steinmetz comment concerning magnetic conductivity

[erpelding]

The well known mathematician and electrical engineer Charles Proteus Steinmetz published an article with the title "The Polar Diagram of Alternate Currents and Its Application to Inductive Resistances" in the June 20, 1891 issue of the "Electrical Review."

In the article he considers an alternating current flowing through an inductive resistance (a coil consisting of 50 turns), and he wrote:

"Let σ = 100, the magnetic conductivity of the magnetic circuit produced by the coil: that is: 1 ampere turn produces 100 lines of magnetic force surrounding all the 50 turns of the coil (or 200 lines surrounding only half the coil, etc.)"

This is clear except for the last part, "or 200 lines surrounding only half the coil."

How did 100 lines of force/"ampere turn" become 200 when considering "half the coil"?

And what did he mean by "half the coil"?

Can anyone explain this? It is a puzzler!

 

[Vailanor]

When considering "half the coil," Steinmetz was referring to the fact that the magnetic flux generated by the alternating current is only found in the portion of the coil being actively used. In other words, if you were to cut the coil in half, only one half would be actively producing magnetic flux, and thus the number of lines of force per ampere turn would be double what it is for the entire coil.