3D vector field on MATLAB - matlab

Question

I want to write a script to generate a 3D vector field of the electric flux density of 8 different point charges in a [-2,2]x[-2,2]x[-2,2] box in 3D space.
I have a function definition in a separate .m file as follows:
function[Dx,Dy,Dz]= question3function(Q,Loc,XX,YY,ZZ)
Q=1e-6;
Loc=[];
XX=(2,-2);
YY=[2,-2];
ZZ=[2,-2];
% Position vector from the point charge
Rx=(XX)-Loc([]);
Ry=(YY)-Loc([]);
Rz=(ZZ)-Loc([]);
% Distance between position in interest and the point charge
R=sqrt(Rx.*Rx+Ry.*Ry+Rz.*Rz);
% Unit Position vector
Ax=Rx./R;
Ay=Ry./R;
Az=Rz./R;
% Electric flux density XYZ components
K=Q./(4*pi*R.^2);
Dx=K.*Ax;
Dy=K.*Ay;
Dz=K.*Az;
And then in my main script I have the function calls:
%function calls
[Dx1,Dy1,Dz1]=question3function(Q,[1 1 1],XX,YY,ZZ);
[Dx2,Dy2,Dz2]=question3function(Q,[1 1 -1],XX,YY,ZZ);
[Dx3,Dy3,Dz3]=question3function(Q,[1 -1 1],XX,YY,ZZ);
[Dx4,Dy4,Dz4]=question3function(-Q,[1 -1 -1],XX,YY,ZZ);
[Dx5,Dy5,Dz5]=question3function(2*Q,[-1 1 1],XX,YY,ZZ);
[Dx6,Dy6,Dz6]=question3function(-2*Q,[-1 1 -1],XX,YY,ZZ);
[Dx7,Dy7,Dz7]=question3function(-Q,[-1 -1 1],XX,YY,ZZ);
[Dx8,Dy8,Dz8]=question3function(-Q,[-1 -1 1],XX,YY,ZZ);
Dx=Dx1+Dx2+Dx3+Dx4+Dx5+Dx6+Dx7+Dx8;
Dy=Dy1+Dy2+Dy3+Dy4+Dy5+Dy6+Dy7+Dy8;
Dz=Dz1+Dz2+Dz3+Dz4+Dz5+Dz6+Dz7+Dz8;
quiver3(XX,YY,ZZ,Dx,Dy,Dz);
axis square equal;
xlabel('X'); ylabel('Y'); zlabel('Z');
title('Electric Flux Density of the sum of 8 Point Charges');
I receive the following errors when I try to run my function file:
??? Error using ==> minus
Matrix dimensions must agree.
Error in ==> question3function at 11
Rx=(XX)-Loc([]);
Could somebody please help me and explain how I can fix this? I will add I am not very experienced with using MATLAB.

Answer 1

There are a number of meaningless things that you are doing here:
function[Dx,Dy,Dz]= question3function(Q,Loc,XX,YY,ZZ)
Q=1e-6; % this is meaningless
Loc=[]; % this is meaningless
XX=(2,-2); % this is meaningless ()
YY=[2,-2]; % this is meaningless
ZZ=[2,-2]; % this is meaningless
% Position vector from the point charge
Rx=(XX)-Loc([]); % this is meaningless ([])
Ry=(YY)-Loc([]); % this is meaningless ([])
Rz=(ZZ)-Loc([]); % this is meaningless ([])
% Distance between position in interest and the point charge
R=sqrt(Rx.*Rx+Ry.*Ry+Rz.*Rz);
% Unit Position vector
Ax=Rx./R;
Ay=Ry./R;
Az=Rz./R;
% above why do you need all of them to be unit vectors
% you can
% Electric flux density XYZ components
K=Q./(4*pi*R.^2);
Dx=K.*Ax;
Dy=K.*Ay;
Dz=K.*Az;
Moreover, in %function calls how are defining XX, YY and ZZ?

Answer 2

The second half of your function declaration is sound, but you're missing the point of how functions work. The point of function parameters is that the function uses those variables as input. Assigning to input parameters is usually a semantic error: it's generally not what you want to do. Another problem is that in matlab vectors are defined with square brackets, and frankly (2,-2) should give you an error about unbalanced parentheses... Always make sure to check your code before posting a question about it on Stack Overflow: if you change it before posting, you might have inadvertently removed your original problem.
You can use your original function by removing the superfluous variable redefinitions at the beginning, and by fixing the assignment to Rx/Ry/Rz. When you say Loc([]), you are indexing with an empty vector, and the result is an empty variable. This is obviously not what you need. Instead:
function [Dx,Dy,Dz]=question3function(Q,Loc,XX,YY,ZZ)
%Q, Loc, XX, ZZ, YY: input!
% Position vector from the point charge
Rx = XX - Loc(1); %use first component of Loc for every x
Ry = YY - Loc(2); %use second component of Loc for every y
Rz = ZZ - Loc(3); %use third component of Loc for every z
% Distance between position in interest and the point charge
R=sqrt(Rx.^2+Ry.^2+Rz.^2); % .^2 takes less characters
% Unit Position vector
Ax=Rx./R;
Ay=Ry./R;
Az=Rz./R;
% Electric flux density XYZ components
K=Q./(4*pi*R.^2);
Dx=K.*Ax;
Dy=K.*Ay;
Dz=K.*Az;
Then you should define XX, YY, ZZ, Q and Loc in your calling function/script. Also, if you're only interested in the total flux density, you could spare some keyboard-time by defining every charge and their location in arrays, and calling your function in a loop:
%define mesh
N = 5; % number of points for mesh in each dimension
[XX,YY,ZZ] = meshgrid(linspace(-2,2,N));
%define charges and locations in arrays
Q0 = 1e-6;
Qvec = Q0*[1 1 1 -1 2 -2 -1 -1];
Locmat = [1 1 1; 1 1 -1; 1 -1 1; 1 -1 -1;...
-1 1 1; -1 1 -1; -1 -1 1; -1 -1 1]; % last 2 are duplicates!!
%function calls in loop, keep adding up flux components
Dx=zeros(size(XX));
Dy=zeros(size(XX));
Dz=zeros(size(XX));
for k=1:length(Qvec)
Q = Qvec(k);
Loc = Locmat(k,:);
[Dxtmp, Dytmp, Dztmp] = question3function(Q,Loc,XX,YY,ZZ);
Dx = Dx + Dxtmp;
Dy = Dy + Dytmp;
Dz = Dz + Dztmp;
end
%plot, no changes here
quiver3(XX,YY,ZZ,Dx,Dy,Dz);
axis square equal;
xlabel('X'); ylabel('Y'); zlabel('Z');
title('Electric Flux Density of the sum of 8 Point Charges');
Output: