Thin-walled solenoid end effects

The magnetic field maximum for air-core solenoids commonly occurs at the inside turn on the mid-plane. For thin-walled solenoids, however, the magnetic field maximum occurs at the ends of the solenoid. To study this end effect, closed form expressions are derived for the axial and radial magnetic field components in the vicinity of the solenoid windings. Formulae for single and double layer solenoids are developed as perturbations on the field of a uniform current sheet solenoid. Formulae for the axial and radial load stresses are developed also.