如何使用Contourf在Matlab中模拟和绘制电场? [英] How to simulate and draw electric fields in Matlab with contourf?

问题描述

我想知道如何针对特定点(例如(4,5))以等高线f绘制带有两个电荷Q和-Q以及它们的总E的图形. 我的M文件实际上扫描该区域(从-3x到3x)并计算每个点的E，并将其存储在表格中，但是此后，我不知道如何使用Contourf绘制它..

I'd like to know how to draw a graph with 2 electric charges Q and -Q and their total E, for a specific point (eg (4,5)), with contour f.. My M-file actually scans the area (from -3x to 3x) and calculates E for every spot, stores it in a table, but after this, I don't know how to use contourf to draw it..

syms i
syms j
syms d
d=input('dwse thn timi tou d,ths apostashs')
j=0
i=0
for j=-d:d/1000:d

    j=j+1

for i=-d:d/1000:d

    i=i+1
    z=(i,j)

end, end

推荐答案

基于库仑定律，距离为r的单个离散电荷q产生的电场由下式给出:

Based on Coulomb's law, the electric field created by a single, discrete charge q at a distance r is given by:

E = q/(4 * pi * e0 * r.^ 2);

E=q/(4*pi*e0*r.^2);

如果您有多个费用，则可以使用叠加原理并添加每个费用的贡献.

If you have several charges you can use the superposition principle and add the contribution of each charge.

剩下要做的就是创建一个网格来计算电场.为此，您可以使用Matlab函数meshgrid.

The only thing left to do is to create a grid to compute the electrical field. For this you can use tha Matlab function meshgrid.

在Matlab中一个简单的例子是:

A simple example in Matlab would be:

k=1/4/pi/8.854e-12;
d=2;
q=[-1 1];
x=[-d/2 d/2];
y=[0 0];

dx=0.01;
X=(-d:dx:d);
Y=(-d:dx:d);
[X Y]=meshgrid(X,Y);

E=zeros(size(X));

for i=1:numel(q)
    r=sqrt((X-x(i)).^2+(Y-y(i)).^2);
    E=E+k*q(i)./r.^2;
end

E(isinf(E))=NaN;

figure;
contourf(X,Y,E);
axis image;

希望它对您有帮助.您可以阅读contourf的文档以根据需要调整图.

Hope it helps you. You can read the documentation of contourf to tweak the plot to your needs.

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