The Nagaoka coefficient C is used in electromagnetics to calculate the inductance of a solenoid. It is a function of the ratio of the solenoid diameter (2a) to its length (l).
For a long solenoid (2a/l approaches 0), the coefficient approaches 1, corresponding to the ideal case.
As the solenoid becomes shorter (2a/l increases), the coefficient decreases, indicating that the inductance is less than that of an idealized solenoid of infinite length.