### 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 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.

Original language | English |
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Pages (from-to) | 1030-1035 |

Number of pages | 6 |

Journal | American Journal of Physics |

Volume | 79 |

Issue number | 10 |

DOIs | |

Publication status | Published - 26 Sep 2011 |

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## Cite this

*American Journal of Physics*,

*79*(10), 1030-1035. https://doi.org/10.1119/1.3602096