Magnetic field of a finite solenoid with a linear permeable core

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 larg...

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Bibliographic Details
Published in:American journal of physics 2011-10, Vol.79 (10), p.1030-1035
Main Author: Lerner, L.
Format: Article
Language:English
Subjects:
Approximation
Magnetic fields
Permeability
Physics
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Summary: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 μ r 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.
ISSN:0002-9505
1943-2909
DOI:10.1119/1.3602096