Question

I have to plot in the xz plane the magnetic field of a dipole in matlab. The dipole is centered in (0,0) and has a magnetic dipole moment M parallel to the z axis. How can I achieve this?

Answer 1

function h=lforce2d(n,color)
% LFORCE2D: Generates a 2D polar plot of n-lines of force of the Gecentric Axial Magnetic Dipole

n=10;
color=[1 0 0];
rad = pi/180;
theta = (0:5:360)'*rad;
A = 2:n;
r = sin(theta).^2*A;
nC = size(r,2);
u = ones(1,nC);
ct = cos(theta)*u;
st = sin(theta)*u;

x = r.*st;
y = r.*ct;

figure;
R = max(x(:))/8;
axis equal;
h = plot(x,y,'r');
[nR,nC] = size(x);

for iR=2:6:floor(nR/2)
for jC=1:2:nC;
p1 = [x(iR-1,jC) -y(iR-1,jC)];
p2 = [x(iR,jC) -y(iR,jC)];
hv=plotvec(p1,p2,'r');
end
end

for iR=floor(nR/2)+2:6:nR;
for jC=1:2:nC;
p1 = [x(iR-1,jC) y(iR-1,jC)];
p2 = [x(iR,jC) y(iR,jC)];
hv=plotvec(p1,p2,'r');
end
end

hold on;
hc = fcircle(R,[0,0],'r');
hv = plotvec([0 R/2], [0 -R/2],'r');
h=plot([0 0],[R/2, -R/3],'r','LineWidth',3);

title('Magnetic Dipole Field','FontSize',15);
hold off;
grid on;

h=[h;hc];
  

function hh=fcircle(r,o,s)
% FCIRCLE - draws a filled cirlce

axis equal;
if nargin==2
h=patch(r*cos(phi)+o(1),r*sin(phi)+o(2),'');
else
h=patch(r*cos(phi)+o(1),r*sin(phi)+o(2),s);
end
set(h,'edgec',get(h,'facec'));
set(h,'user',{'fcircle',r,o});
if nargout,hh=h;end

function h=plotvec(p1,p2,linespec)
% PLOTVEC - Draws a vector.

if nargin==2,linespec='';end
held=ishold;hold on
x=[p1(1) p2(1)];
y=[p1(2) p2(2)];
dx=diff(x);
dy=diff(y);
hh(1)=plot(x,y,linespec);
ax=axis;
lx=diff(ax(1:2))*15e-3;
ly=diff(ax(3:4))*10e-3;
phi=atan2(dy,dx);
hd=rotate2([-lx 0 -lx;ly 0 -ly],[0;0],phi);
col=get(hh(1),'color');
hh(2)=patch(hd(1,:)+p2(1),hd(2,:)+p2(2),col);
set(hh(2),'edgec',col)
set(hh(1),'user',{'vector',p1,p2,hh(2)})
set(hh(2),'user',{'vector',p1,p2,hh(1)})
if ~held,hold off,end
if nargout,h=hh;end

function n_p=rotate2(points,origo,phi)
%ROTATE2 rotate points in 2 dimensions.

A=[cos(phi) -sin(phi);sin(phi) cos(phi)];
n_p=A*points+origo*ones(1,size(points,2));