Multiple Summation of Series using For Loops (Magnetic Flux through Coil Simulation)

Hello all,

I am trying to sum the following series for various positions, y being the position of the magnet in the function.

The 'r' and 'z' values are known dimensions of a coil, indicating the thickness and height of the coil respectively. I have included the values in the table below. The plot that I get from this code is incorrect and I can't figure out why. Is my methodology for executing the series summation for each value of position (y) correct? Any help would be greatly appreciated.

clearvars
clc
close all

position = -0.09:0.001:0.09;
L = length(position);
Flux = zeros(1,L);
s = 0;
r = [0.00875 0.0125]; %inner and outer radius of coil (thickness)
z = [-0.015 0.015]; % z(2)-z(1) = height of coil (30 mm), centred at 0 
Ac = (r(2) - r(1))*(z(2)-z(1)); %cross-sectional area of coil

Nc = 1500; % constants from table 1
Br = 1.31;
Vm = 5e-6;
Ff = 0.33;

for y = 1:L
    for ii=1:2
        for jj=1:2
          
            x1 = (-1)^(ii+jj);         
            Zij = sqrt(r(ii)^2 + (z(jj) - position(y))^2);            
            x2 = log(r(ii)+Zij);
            x3 = r(ii)/Zij;                  
            
            s = s + x1*(x2 - x3);
            
        end
    end

    s = s * 3*Nc*Br*Vm*Ff/(2*Ac); 

    Flux(y) = s/2.1079; %maximum flux should be 2.1079
    
    s = 0; 
end

y_h = position/0.03;

figure
plot(y_h,Flux)
xlabel('y / h')
ylabel('Flux / Maximum Flux')

The correct plot should look like the one below.

Answer 1

[Daniel M]

Hi Samuel, I don't see anything wrong with the code. The only thing I would change is to do the following outside the loops:

Flux = Flux./max(Flux);

This will normalize it to [-1,1] properly, since the actual max doesn't seem to be 2.1079.

As for the inflection point on your plot on both sides of the center (y/h =0), it is supposed to be there. It just isn't very clear in their plot. I'm sure if you found the 2nd derivative of the equation with respect to z, you would see clear inflection points analytically.