【电磁】基于 Biot-Savart 定律模拟沿螺旋（螺线管或环形）电流回路的磁场附matlab代码

1 内容介绍

在我国现行通用的各电动力学教程中,二阶反对称电磁张量Fuv都是根据电磁场(?)与电磁势(?),φ的关系以及四维电磁势Aμ((?),i/Cφ)与电磁张量Fuv的定义关系导出的.本文不从抽象的数学关系出发,而从基本的电磁实验规律—Coulomb定律和Biot-Savart定律出发,根据机矢量和轴矢量的物理性质,直接从电场与磁场这两个具体物理量的分量组成导出电磁场张量这个完美的整体结构.​

2 部分代码

Initialize

clear all;

close all;

set(groot,'defaultLineLineWidth',1)

set(groot,'defaultAxesLineWidth',1)

set(groot,'defaultAxesFontWeight','bold')

Set some default numerical values for current. SI units are used throughout.

I = 1;                  % current in amps

mu0=4*pi*10^(-7);       % permeability of the vacuum

Loopradius = 1;         % helix radius (m)

Try this: Change the pitch Loopstep of the helix to see the impact on the central field strength.

Loopstep=Loopradius/2;  % variable pitch of helix (m)

Loopstep=Loopradius/5;  % variable pitch of helix (m)

% Loopstep=Loopradius/10; % variable pitch of helix (m)

Loopstep=0.05;          % a fixed pitch

% Loopstep=0;

Try this: Change the sampling distance Zstep to create a smoother plot of the variation along the sampling line.

Zstep = 0.05*Loopradius;% steplength along z axis for field points

Set transverse coordinates of line parallel to the -axis along which we find the field.

Try this: Change the transverse coordinates of the sampling line to profile the magnetic field along your choice of line parallel to the solenoid axis.

x0=Loopradius/2;y0=0;z0=0;

x0=0;y0=0;z0=0;

Try this:  Replace the solenoidal field with  a toroidal winding. 

The value torus=1 switches torus on. The value torus=0 switches torus off. For the toriodal current, the field outside the coil should approach zero and the field in the coil approach the ideal value as the number of windings becomes large.

torus=1;

Create figures for plots.

3 运行结果

4 参考文献

[1]冯士德, 冯涛. Biot-Savart流体力学理论与索马里低空急流形成机理的研究[J]. 物理学报, 2011, 60(2):8.

[2]钟克武. 直接从Coulomb定律与Biot—Savart定律导出电磁场张量Fμv[J]. 九江学院学报(社会科学版), 1988(5):25-30.

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