How can I use custom equation in cftool?

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! :)

Answer 1

[VBBV]

In the custom equation, function box , replace the x with z and define the equation as in your case in the box below

[VBBV]

A better option is to use polyfit and polyval functions

https://www.mathworks.com/help/matlab/ref/polyfit.html

[Sam Chak]

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]

Thank you @VBBV and @Sam Chak for your comments! With your help I solved the problem!