MATLAB: Using trigonometric function in Matlab

magnetic fieldquiver3

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

Best Answer

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.

Related Solutions

MATLAB: How to plot only certain values in a surface plot

Two options:

1. Set Z > 4 to NaN:

[X,Y] = meshgrid(-5:.2:5);                                
Z = -0.15*sin(X).*(X) + 0.2*(Y.^2) +3 ;
Z(Z>4) = NaN;
figure
surf(X,Y,Z)

2. Use a zlim cutoff:

[X,Y] = meshgrid(-5:.2:5);                                
Z = -0.15*sin(X).*(X) + 0.2*(Y.^2) +3 ;
figure
surf(X,Y,Z)
zlim([min(zlim) 4])

There may also be other possibiloities.

MATLAB: Component of a vector parallel with a spherical surface

Hi,

I am assuming that you would like to plot in 3D, components of the magnetic field that are parallel to the tangent of a sphere.

As a first step, you have created a plot of the magnetic field. As a second step the gradient plot was done which clearly shows the tangents at various points on the surface of the sphere.

As a third step, you have identified the dot product of the point and its gradient. There are two issues.

1. You have an array of vectors 2. The dot product of the points and its gradient doesn't give the necessary angle between the magnetic field and the gradient.

So since an array of vectors are under consideration, the 'dot' function doesn't work directly for the dot product. But it has to be manually done for vectors.

If you have two vectors say, a = a1x+a2y+a3z and b = b1x+b2y+b3z, then a.b = (a1*b1)+(a2*b2)+(a3*b3). Now extrapolate it considering the coefficients as matrices. So in your code,

A = U.*dx; B = V.*dy; C = W.*dz;

Finally adding them would give the dot product.

k = A+B+C;

Now we have the dot product which gives us the angle information between the magnetic field and the gradient (the surface of the sphere). In order to find the components of the magnetic field along the surface of the sphere, dot product will not be sufficient but the projection of magnetic field vector on the gradient vector has to be found.

So if a and b are the vectors as shown above, then projection of a on be can be written as,

projaonb = dot(a,b)*unitVector(b) = dot(a,b)* b / b.

So implementing it here for this problem.

k1 = k./sqrt(dx.*dx + dy.*dy + dz.*dz); projx = k1.*dx; projy = k1.*dy; projz = k1.*dz;

quiver3(X, Y, Z, projx, projy, projz);

Now you should possibly see the components of magnetic field vector along the tangent vectors.

-Venkatachala Sarma

Best Answer

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MATLAB: How to plot only certain values in a surface plot

MATLAB: Component of a vector parallel with a spherical surface

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