% Example 5.4a (Physics 330)

clear;close

x=-5.25:.5:5.25;y=x; % define the x and y grids (avoid (0,0))
[X,Y]=meshgrid(x,y);

% Electric field of a long charged wire

Ex=X./(X.^2+Y.^2);
Ey=Y./(X.^2+Y.^2);

% make the field arrow plot

quiver(X,Y,Ex,Ey)
title('E of a long charged wire')

axis equal  % make the x and y axes be equally scaled

% Magnetic field of a long current-carrying wire

Bx=-Y./(  X.^2+Y.^2);
By=X./(X.^2+Y.^2);

% make the field arrow plot

figure
quiver(X,Y,Bx,By)
axis equal
title('B of a long current-carrying wire')

%*********************************************************
% The big magnitude difference across the region makes most arrows too small
% to see.  This can be fixed by plotting unit vectors instead (losing all
% magnitude information
%*********************************************************

B=sqrt(Bx.^2+By.^2);
Ux=Bx./B;
Uy=By./B;

figure
quiver(X,Y,Ux,Uy);
axis equal
title('B(wire): unit vectors')

%*********************************************************
% Or, you can still see qualitative size information
% without such a big variation in arrow size by
% having the arrow length be logarithmic.  If s is
% the desired ratio between the longest arrow and
% the shortest one, this code will make the  appropriate
% field plot.
%*********************************************************

Bmin=min(min(B));
Bmax=max(max(B));
s=2;  % choose an arrow length ratio
k=(Bmax/Bmin)^(1/(s-1));

logsize=log(k*B/Bmin);
Lx=Ux.*logsize;
Ly=Uy.*logsize;

figure
quiver(X,Y,Lx,Ly);
axis equal
title('B(wire): logarithmic arrows')