Reluctance of Long Solenoids with Extended Core

The system studied here uses an array of parallel-connected, voltage-driven coils distributed along the solenoid core to control the magnetic flux. The ends of the core are extended, and thus take the form of magnetic poles driving magnetic flux through the air return path. When these poles are spherical and infinitely permeable an analytical expression can be obtained for the effective end return reluctance. This paper considers a more practical example and shows the reluctance of cylindrical core ends with a known permeability, and validates the results through measurements. It goes further to show how the linear current density of each coil depends on the position of the coil on the core and the core material.