Self- and mutual inductances of long coaxial helical conductors

An analytical expression for the mutual inductance for long coaxial helical conductors or solenoids is derived on the basis of Neumann's formula for the whole range from 0 to of the pitch length, including the cases of the mutual inductance of long concentric closely wound helical solenoids and that of long parallel thin conductors as two extreme cases. In addition, an approximate expression for the self-inductance for a long helical round conductor is obtained.