Magnetic field of a finite solenoid with a linear permeable core

Abstract

The integral form of Ampere’s law applied to an infinitely long solenoid gives a good first approximation to the magnetic field of finite air-cored solenoids with length L to width w ratios (aspect ratios) significantly greater than 1. It is less well known that this approximation requires much larger aspect ratios to be applicable to solenoids whose relative core permeability μr is much greater than that of the surrounding medium. An exact expression is derived for the magnetic field and inductance of a linear permeable core spheroidal solenoid, and an inequality is obtained for the validity of the infinite solenoid approximation. It is demonstrated that the magnetic field and inductance of a spheroidal solenoid with a linear core approximate well with those of a cylindrical solenoid of the same length and width.