How to simulate and draw electric fields in Matlab with contourf?

Question

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 (fr

Answer 1

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);

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

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.

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;

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