How can I use custom equation in cftool?

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Jenni
Jenni 2024-3-15
评论： Jenni 2024-3-17
Hey!
I am trying to plot the magnitude of the magnetic field along the axis of symmetry of the magnet as a function of the distance from the surface of the magnet. But I have a problem to find a way to use custom equation in cftool space. My equation would be:
,
where
μ_0 = 1.25663706212 × 10−6 H/m (Permeability in vacuum)
M = slope
z = data point
R = 0.4 * 10^-2 m (radius)
L = 0.5*10^-2 m. (height)
So this equation I would like to fit to my data points. How could I replace the circled equation with my own one?
Here is my data:
data = [0.1218 0.0643 0.0389 0.0268 0.0186 0.0139 0.0107 0.0085 0.007 0.0057 0.0045 0.0035];
number of data points = 1:1:12;
Thank you for your help! :)

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VBBV
VBBV 2024-3-15
In the custom equation, function box , replace the x with z and define the equation as in your case in the box below
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Sam Chak
Sam Chak 2024-3-15
Ran in:
Hi @Jenni
Could you please verify if there is only a single free parameter (slope) M in your proposed model? Additionally, it would be helpful if you could check whether I entered the Magnetic Field equation correctly.
%% data
zdat = (1:12)';
Bdat = [0.1218 0.0643 0.0389 0.0268 0.0186 0.0139 0.0107 0.0085 0.007 0.0057 0.0045 0.0035]';
%% fixed parameters
mu0 = 1.25663706212e-6; % H/m (Permeability in vacuum)
R = 0.4e-2; % m (radius)
L = 0.5e-2; % m (height)
%% proposed model by the OP
z = linspace(1, 12, 1301);
B = @(M, z) (mu0*M/2)*(z./sqrt(z.^2 + R^2) - (z - L)./sqrt((z - L).^2 + R^2));
%% plot and compare
plot(zdat, Bdat, 'o'), hold on
plot(z, B(2.4e12, z)), grid on
legend('data points', 'fitted curve', 'fontsize', 20)
title('Magnetic Field'), xlabel z, ylabel B(z)
Jenni
Jenni 2024-3-17
Thank you @VBBV and @Sam Chak for your comments! With your help I solved the problem!

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