Ocatve script to Plot the normalised electrostatic field vectors of a system of charges in 3 dimentions

field.m

clear all;
clf;
global Q;
global K;
% --------- User Configuration --------- %
%% Charges are defined as structures 'Q' containing two fields 'q' and 'x'
%% specifying the charge and position position is given as a three dimensional
%% row vector Multiple charges can be defined by creation an array of these
%% structures.
%% Define Charges
%%   The default setup is an electric dipole.

%% The separation between charges
sep = 0.1;

Q(1).q = 1;
Q(1).x = [sep,0,0];

Q(2).q = -1;
Q(2).x = [-sep,0,0];

% % Uncomment the below lines for additional test charges
% Q(3).q = 3;
% Q(3).x = [-sep,-sep,0];
%
% Q(4).q = -1;
% Q(4).x = [-sep,sep,0];
%
% Q(5).q = 5;
% Q(5).x = [0.5,-0.6,0];

% Coulombs constant, It really does not matter what you set here, as long
% as it is non zero
K = 1;
% This defines the plot limits. Specifically the box if a square box with
% x,y limits between -plot_len to plot_len.
plot_len = 1;
% The density of the grid of points where the field vectors should be plotted
density = 0.25;
% The size of the smallest charge
marker_size = 20;
% --------- End Configuration --------- %
%% Everything below this line is not meant to be normally edited by
%% the user unless you know what you are doing.
global number = uint8(length(Q));   % Number of charges

% calculate field at point r
function E = e_field(r)
	global Q;
	global K;
	global number;
	E = [0,0,0];
	for i = 1:number;
		E += K*Q(i).q*(r - Q(i).x)/norm(r - Q(i).x)^3;
	endfor
endfunction

% normalise a vector.
function ret = normalise(v)
	ret = v/norm(v);
endfunction

% number of elements in a given dimension of the plot window
box_length   = uint16(length(tmp = -plot_len:density:plot_len));
% Define the meshgrid
[xx, yy, zz] = meshgrid(tmp);
% Allot space for field vector data
E            = zeros([size(xx),3]);

% calculate E
for n = 1:box_length
	for m = 1:box_length
		for p = 1:box_length
			tmp = e_field([xx(1,m,1),yy(n,1,1),zz(1,1,p)]);
			tmp = normalise(tmp);
			E(n,m,p,1) = tmp(1);
			E(n,m,p,2) = tmp(2);
			E(n,m,p,3) = tmp(3);
		endfor
	endfor
endfor

% Start plot
hold("on");
h = quiver3(xx,yy,zz,E(:,:,:,1),E(:,:,:,2),E(:,:,:,3),0.5,"k","filled","linewidth", 1);
set (h, "maxheadsize", 0.25);

% smallest charge.
smallest_Q = abs(Q(1).q);
for i = 1:number;
	if(smallest_Q > abs(Q(i).q))
		smallest_Q = abs(Q(i).q);
	endif
endfor
% Plot markers for the charges
for i = 1:number;
	if(Q(i).q > 0)
		plot(Q(i).x(1),Q(i).x(2),".r","markersize",abs(Q(i).q)/smallest_Q*marker_size);
	else
		plot(Q(i).x(1),Q(i).x(2),".b","markersize", abs(Q(i).q)/smallest_Q*marker_size);
	endif
endfor
% define limits and axis.
plot_len += 0.1;
axis("off","equal",[-plot_len,plot_len,-plot_len,plot_len]);
grid("off");
xlabel("x");
ylabel("y");
zlabel("z");

Introduction

This GNU octave¹ script plots the electrostatic field vectors²
of a system of charges that you define.

Usage

Usage is exactly as with my other script Just edit the section titled
User Configuration:

% --------- User Configuration --------- %
%% Charges are defined as structures 'Q' containing two fields 'q' and 'x'
%% specifying the charge and position position is given as a two dimensional
%% row vector. Multiple charges can be defined by creation an array of these
%% structures.
%% Define Charges
%%   The default setup is an electric dipole.

%% The separation between charges
sep = 0.1;

Q(1).q = 1;
Q(1).x = [sep,0];

% .....

The comments are pretty verbose. But you need to know some basics of
octave. At least enough to define variables and vectors.

Footnotes

1. This script is not compatible with Matlab as it is. ↩

2. This one is for three dimensions ↩