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. 

{{attachment:forec_mea_config.JPG}}

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]. 

{{attachment:fig_2_current_loops_force.JPG}}

We choose ''R'',,1,, and ''R'',,2,, 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, {{attachment:factor.JPG}} 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. 

{{attachment:mag_force_mea.JPG}}