Using trigonometric function in Matlab

Hi, I am trying to model a dipole magnetic field using the quiver3 function. However when I use a trigonometric function in one of my arrow direction vectors i get the error:

Error using * Inputs must be 2-D, or at least one input must be scalar. To compute elementwise TIMES, use TIMES (.*) instead.

Here is the code i'm using

if true
[X,Y,Z] = meshgrid(-10:.5:10, -10:.5:10, -10:.5:10); %defines meshgrid coverage
r=(X.^2+Y.^2+Z.^2).^0.5 ;
k=50;
T=Z./r;
U=3*k*Z.*sin(acos(T))*r.^-4;
V=3*k*Z.*sin(acos(T))*r.^-4;
W=2*k*((3*Z.^2 * r.^-2)-1)*r.^-3;
%magnetic field function
figure
quiver3(X,Y,Z,U,V,W,0.5)% no defines arrow length, other define direction
%defines arrow direction (u,v,w) at point (x,y,z)
hold on
%surf(X,Y,Z) %produces surface
axis equal %defines axis parameters
hold off

    % code
  end

Does anyone have any idea how i can rectify this? Thanks in advance, John

Answer 1

[Star Strider]

When in doubt, vectorise everything:

U=3*k*Z.*sin(acos(T))./r.^4;
V=3*k*Z.*sin(acos(T))./r.^4;
W=2*k*((3*Z.^2 ./ r.^2)-1)./r.^3;

This produces your plot, but you may want to tweak the arrow lengths in order to see them.

[John Draper]

Thanks, It still gives me an unusual plot for a magnetic dipole but at least it works!

[Star Strider]

My pleasure!

That’s not my current area of expertise, so I can’t otherwise help to troubleshoot your code.

I’m not certain this will improve things a great deal, but an easier meshgrid call would be:

vec = linspace(-10, 10, 75);
[X,Y,Z] = meshgrid(vec); %defines meshgrid coverage

The third argument to linspace is the number of points, so you can experiment to vary them at will. The difference between linspace and the colon operator is that linspace varies the interval betwen points to create a specified length, and the colon operator varies the length at a constant interval.