F=zeros(length(z),1); for i=1:length(z) Phi=@(theta,R,r)(z(i)+lc-lm).*r.R.(R-r.sin(theta))./... ((R.^2+r.^2-2R.*r.*sin(theta)).sqrt(R.^2+r.^2+(z(i)+lc-lm).^2-2R.*r.*sin(theta)))+... (z(i)-lc+lm).*r.R.(R-r.sin(theta))./... ((R.^2+r.^2-2R.*r.*sin(theta)).sqrt(R.^2+r.^2+(z(i)-lc+lm).^2-2R.*r.*sin(theta)))+... (z(i)+lc+lm).*r.R.(R-r.sin(theta))./... ((R.^2+r.^2-2R.*r.*sin(theta)).sqrt(R.^2+r.^2+(z(i)+lc+lm).^2-2R.*r.*sin(theta)))+... (z(i)-lc-lm).*r.R.(R-r.sin(theta))./... ((R.^2+r.^2-2R.r.sin(theta)).sqrt(R.^2+r.^2+(z(i)-lc-lm).^2-2R.r.sin(theta))); F(i)=BrNI/(4lc(Rc-rc))integral3(Phi,0,2pi,rc,Rc,rm,Rm); end

Sure! Here's your code with comments added:

F = zeros(length(z), 1); % Initialize the F vector with zeros

for i = 1:length(z)
    % Define the Phi function using anonymous function
    Phi = @(theta, R, r) (z(i) + lc - lm) .* r.R .(R - r.sin(theta)) ./ ...
        ((R.^2 + r.^2 - 2*R.*r.*sin(theta)).sqrt(R.^2 + r.^2 + (z(i) + lc - lm).^2 - 2*R.*r.*sin(theta))) + ...
        (z(i) - lc + lm) .* r.R .(R - r.sin(theta)) ./ ...
        ((R.^2 + r.^2 - 2*R.*r.*sin(theta)).sqrt(R.^2 + r.^2 + (z(i) - lc + lm).^2 - 2*R.*r.*sin(theta))) + ...
        (z(i) + lc + lm) .* r.R .(R - r.sin(theta)) ./ ...
        ((R.^2 + r.^2 - 2*R.*r.*sin(theta)).sqrt(R.^2 + r.^2 + (z(i) + lc + lm).^2 - 2*R.*r.*sin(theta))) + ...
        (z(i) - lc - lm) .* r.R .(R - r.sin(theta)) ./ ...
        ((R.^2 + r.^2 - 2*R.*r.sin(theta)).sqrt(R.^2 + r.^2 + (z(i) - lc - lm).^2 - 2*R.*r.sin(theta)));
    
    % Calculate the value of F(i) using the integral3 function
    F(i) = BrNI / (4 * lc * (Rc - rc)) * integral3(Phi, 0, 2*pi, rc, Rc, rm, Rm);
end

This code calculates the values of the vector `F` using a loop. The `Phi` function is defined as an anonymous function that takes `theta`, `R`, and `r` as input parameters. It performs a series of calculations and returns a value. The integral of `Phi` is then calculated using the `integral3` function. The result is stored in the corresponding element of the `F` vector.

Please note that I have made some assumptions about the variables and functions used in your code since I don't have the complete context. Feel free to modify or clarify anything as needed.