To confirm the analytical and numerical modeling of the magnetic force, we measured the repelling force between two cylinder magnets as a function of gap between them. We used a very simple setup with a weighting scale as shown schematically in the following figure.
We measured the cases of 17 different distances with each 3 times. The data after processing are listed in the table below.
d [cm] |
Mean [N] |
Standard deviation [N] |
0.000 |
2.95 |
0.105 |
0.145 |
3.37 |
0.0389 |
0.289 |
3.25 |
0.0143 |
0.444 |
3.05 |
0.0340 |
0.578 |
2.73 |
0.0534 |
0.732 |
2.42 |
0.0864 |
0.868 |
1.97 |
0.0901 |
1.01 |
1.69 |
0.00559 |
1.16 |
1.35 |
0.00441 |
1.30 |
1.11 |
0.00950 |
1.45 |
0.887 |
0.0121 |
1.59 |
0.779 |
0.00383 |
1.74 |
0.642 |
0.00368 |
1.88 |
0.516 |
0.0135 |
2.02 |
0.438 |
0.00902 |
2.17 |
0.374 |
0.00218 |
2.31 |
0.301 |
0.00730 |
The data and the corresponding numerical fit are shown by the figure below. Here we fit them by the analytical expression in the current loop approximation [cf. Basical principle page].
We choose R1 and R2 to be coincide with the radius of the two magnets. Therefore, the only free parameter is the numerical factor in front of this expression, namely, 
which is related to the magnetization of two magnets. As we can see from the figure, the current-loop approximation gives pretty good quantification. Therefore, the conclusions that we drew based upon the current-loop approximation, such as the stiffness of the suspension, to great extents are valid.
