On the magnetic field of an infinitely long helical line current

This paper presents the calculation of the low-frequency magnetic field of an infinitely long helical solenoid. Helical solenoids can be applied, e.g., to investigate superconducting coils, twisted wires and the levitation of molten metals. With the aid of a series expansion of the reciprocal distance between the observation point and a variable point of the line current, which is a substitute for the spatial current distribution, the magnetic vector potential is calculated. This approach makes is possible to express also the magnetic field in the form of a series. Explicit formulas for the magnetic field inside and outside the solenoid are developed which include modified Bessel functions and their derivatives. Some properties of the magnetic field are shown