Multiple Summation of Series using For Loops

Hello all,

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

The 'r' and 'z' values are known dimensions of a coil, indicating the thickness and height of the coil respectively. 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.

position = -0.1:0.001:0.1;
L = length(position);
Coupl = zeros(1,L);

s = 0;
r = [0.01746 0.0247]; 
z = [-0.0063 0.0063];
Ac = (r(2) - r(1))*(z(2)-z(1));
Nc = 1500;
Br = 1.31;
Vm = 3.218e-6;
Ff = 0.33;

for y = 1:L
    for i=1:2
        for j=1:2         
        s = s + Nc*Br*Vm*Ff/(2*Ac)*((-1)^(i+j)*(log(r(i)+sqrt(r(i)^2+(z(j)-position(y))^2)) - r(i)/sqrt(r(i)^2+(z(j)-position(y))^2)));   
        end
    end
Coupl(y) = s;
end

figure
plot(position,Coupl)
xlabel('Position')
ylabel('Coupling Term')

The correct plot should look similar to the one below:

Answer 1

[Daniel M]

Very close. You need to reset the value of s for each y.

I also cleaned it up a bit. This now produces the specified figure.

clearvars
close all
clc

position = -0.1:0.001:0.1;
L = length(position);
Coupl = zeros(1,L);
s = 0;
r = [0.01746 0.0247];
z = [-0.0063 0.0063];
Ac = (r(2) - r(1))*(z(2)-z(1));

Nc = 1500;
Br = 1.31;
Vm = 3.218e-6;
Ff = 0.33;

for y = 1:L
    for ii=1:2
        for jj=1:2
            % simplify the formula a bit
            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
    % multiply by a constant once (outside of loop)
    s = s * Nc*Br*Vm*Ff/(2*Ac); 
    Coupl(y) = s;
    s = 0; % reset value of s
end

figure
plot(position,Coupl)
xlabel('Position')
ylabel('Coupling Term')

[RPS19]

That's perfect, thank you so much Daniel!

[Daniel M]

No problem. What's the name of this equation anyways, I'm interested.

[RPS19]

I'm not sure that it has a particular name, though I may be wrong. I came across the derivation for it in a few papers recently.

[Daniel M]

I do stuff with magnet design so I was just curious.

[RPS19]

Hi Daniel, Could you possibly take a look at an updated version of this question if you have a chance, I realise I should have just amended this question my apologies for that..

https://www.mathworks.com/matlabcentral/answers/489118-multiple-summation-of-series-using-for-loops-magnetic-flux-through-coil-simulation?s_tid=prof_contriblnk