CODEWITHSUNDEEP
matlabplotvector-graphics
Alice1nw0
Alice1nw0

Reputation: 69

Plot vector function in matlab using quiver

I have the function of an electric dipole expressed in cartesian coordinates and I want to create the vector field using Matlab .

The function is

enter image description here and

enter image description here

The code I've come up with is : 

clear;
clc;
p = 1;
e = 8.85*10^(-12);
x  =linspace(-5 , 5, 50);
z = linspace(-5 , 5 ,50);
[X, Z ] = meshgrid(x,z );
R=sqrt(X.^2+Z.^2) ; 
EX =( p .* 3 .* X .* Z )./ (4.*pi.*e ./ R.^5);
EZ = p./( 4 .* pi .* e ) .* ( 3.* Z.^2 ./R.^5 -1./ R.^3);
quiver ( X , Z , EX , EZ ) ;

But it doesn't give me the output I want which looks like this enter image description here

Does anyone have any ideas? I would be grateful!

Upvotes: 2

Views: 2621

Answers (1)

mikkola
mikkola

Reputation: 3476

As my previous attempt was unsuccessful, I'll give it another try. :) I believe you are very close to the solution. There's two things that I noticed.

First, I believe you have a typo in the MATLAB equation for EX. Shouldn't it be EX =( p .* 3 .* X .* Z ./ R.^5 )./ (4.*pi.*e ); to correspond to your written equation?

Second, the figure you show as example seems to show the direction (but not magnitude) of the field, judging from the equal-length vectors. The original vectors vary quite a bit in magnitude, and thus don't really all show up in the plot. This is due to them decreasing as function of 1/r^3 or 1/r^5- so quickly to make seeing any of the smaller ones compared to those closer to the origin impossible.

So I decided to try with the fixed equation for EX, and normalizing the vectors [EX(jj) EZ(jj)] to unit length before plotting them (also changed slightly plotting range):

p = 1;
e = 8.85*10^(-12);
x  =linspace(-0.5 , 0.5, 50);
z = linspace(-0.5 , 0.5, 50);
[X, Z ] = meshgrid(x,z );
R=sqrt(X.^2+Z.^2) ; 
EX =( p .* 3 .* X .* Z ./ R.^5 )./ (4.*pi.*e );
EZ = p./( 4 .* pi .* e ) .* ( 3.* Z.^2 ./R.^5 -1./ R.^3);

%// normalize the vectors so the arrows are visible
V = [EX(:) EZ(:)];
Vn = bsxfun(@rdivide, V, sqrt(sum(V.^2,2)));
Exn = reshape(Vn(:,1), size(EX));
Ezn = reshape(Vn(:,2), size(EZ));

quiver ( X , Z , Exn , Ezn ) ;

This is the end result, slightly zoomed in - better?

field image

By the way, you can control the resolution of the plot by tuning the vectors you construct the grid from. Hopefully you will be able to find a suitable choice!

Upvotes: 1

Related Questions