Plot quiver polar coordinates - matlab

Question

I want to plot the field distribution inside a circular structure with radius a.
What I expect to see are circular arrows that from the centre 0 go toward a in the radial direction like this
but I'm obtaining something far from this result. I wrote this
x_np = besselzero(n, p, 1); %toolbox from mathworks.com for the roots
R = 0.1:1:a; PHI = 0:pi/180:2*pi;
for r = 1:size(R,2)
for phi = 1:size(PHI,2)
u_R(r,phi) = -1/2*((besselj(n-1,x_np*R(1,r)/a)-besselj(n+1,x_np*R(1,r)/a))/a)*cos(n*PHI(1,phi));
u_PHI(r,phi) = n*(besselj(n,x_np*R(1,r)/a)/(x_np*R(1,r)))*sin(PHI(1,phi));
end
end
[X,Y] = meshgrid(R);
quiver(X,Y,u_R,u_PHI)
where u_R is supposed to be the radial component and u_PHI the angular component. Supposing the formulas that I'm writing are correct, do you think there is a problem with for cycles? Plus, since R and PHI are not with the same dimension (in this case R is 1x20 and PHI 1X361) I also get the error
The size of X must match the size of U or the number of columns of U.
that I hope to solve it if I figure out which is the problem with the cycles.
This is the plot that I get

Answer 1

The problem has to do with a difference in co-ordinate systems.
quiver expects inputs in a Cartesian co-ordinate system.
The rest of your code seems to be expressed in a polar co-ordinate system.
Here's a snippet that should do what you want. The initial parameters section is filled in with random values because I don't have besselzero or the other details of your problem.
% Define initial parameters
x_np = 3;
a = 1;
n = 1;
% Set up domain (Cartesian)
x = -a:0.1:a;
y = -a:0.1:a;
[X, Y] = meshgrid(x, y);
% Allocate output
U = zeros(size(X));
V = zeros(size(X));
% Loop over each point in domain
for ii = 1:length(x)
for jj = 1:length(y)
% Compute polar representation
r = norm([X(ii,jj), Y(ii,jj)]);
phi = atan2(Y(ii,jj), X(ii,jj));
% Compute polar unit vectors
rhat = [cos(phi); sin(phi)];
phihat = [-sin(phi); cos(phi)];
% Compute output (in polar co-ordinates)
u_R = -1/2*((besselj(n-1, x_np*r/a)-besselj(n+1, x_np*r/a))/a)*cos(n*phi);
u_PHI = n*(besselj(n, x_np*r/a)/(x_np*r))*sin(phi);
% Transform output to Cartesian co-ordinates
U(ii,jj) = u_R*rhat(1) + u_PHI*phihat(1);
V(ii,jj) = u_R*rhat(2) + u_PHI*phihat(2);
end
end
% Generate quiver plot
quiver(X, Y, U, V);