四个平行共轴等大载流方线圈磁场的均匀性分析

昝会萍, 张引科

doi:10.16854 / j.cnki.1000-0712.200373

大学物理 >

2021 , Vol. 40 >Issue 6: 14

DOI: https://doi.org/10.16854 / j.cnki.1000-0712.200373

教学讨论

四个平行共轴等大载流方线圈磁场的均匀性分析

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西安建筑科技大学理学院，陕西西安 710055

昝会萍( 1963—) ，女，陕西泾阳人，西安建筑科技大学理学院副教授，硕士，主要从事光电信息处理方向研究和大学物理教学工作.

收稿日期: 2020-08-18

修回日期: 2020-12-27

网络出版日期: 2021-06-18

基金资助

陕西省教育厅专项科研基金项目( 2013JK0639) 资助

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Uniformity of magnetic field created by four parallel，coaxial and current-carrying square coils of equal size

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Science College，Xi’an University of Architecture & Technology，Xi’an，Shaanxi 710055，China

Received date: 2020-08-18

Revised date: 2020-12-27

Online published: 2021-06-18

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摘要

匀强磁场广泛应用于科学研究和工程技术. 以毕奥-萨伐尔定律和磁场叠加原理为基础，建立了 4 个平行共轴等大载流方线圈磁场磁感应强度的表达式;

用泰勒级数展开方法，发现了线圈系统磁场均匀性最好的条件; 借助于数值计算，讨论了 3 种具体情况下线圈系统磁场的均匀性. 结果表明: 在最佳状态下，线圈系统能够在较大空间区域产生相对偏差小于0.01%、方向偏差小于 0.01 度的均匀性极高的磁场，并且磁场的均匀性和空间范围都明显优于方形亥姆霍兹线圈的磁场.

关键词： 磁场均匀性; 方形载流线圈; 亥姆霍兹线圈; 毕奥-萨伐尔定律

本文引用格式

昝会萍, 张引科 . 四个平行共轴等大载流方线圈磁场的均匀性分析[J]. 大学物理, 2021 , 40(6) : 14 . DOI: 10.16854 / j.cnki.1000-0712.200373

Abstract

Uniform magnetic field has many applications in scientific research and

engineering technology. Based on Biot-Savart law and the superposition principle of magnetic

field，the mathematical expressions of magnet- ic induction intensity created by four

parallel，coaxial and current-carrying square coils of equal size ( FPCSCS) are derived. By

using Taylor series expansion method，the conditions，under which the FPCSCS generates a mag-

netic field of the best uniformity，have been found. The uniformity of magnetic fields

produced by the FPCSCS in three cases is discussed. The results show that，in the optimum

situation，the FPCSCS can generate a very homoge- nous magnetic field with magnitude relative

deviation of less than 0.01% and direction deviation of less than 0.01 degree. Compared

with the homogenous magnetic fields of square Helmholtz coil，the magnetic field of FPCSCS has

obvious advantages，which are greater magnitude and better uniformity.

Key words： magnetic field homogeneity; square current-carrying coil; Helmholtz coil; Biot-Savart law

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