M is the pole strength (proportional to the magnetic moment) - it is not the field at some distance from the magnet.

 

Think of the electrostatic analogue, the force between two charges.

 

[math]F = \frac {kQ_1Q_2}{r^2} [/math]

 

[math]E_{Q_1}® = \frac {kQ_1}{r^2} [/math]

 

[math]\implies F(on~Q_2) = Q_2 \cdot E_{Q_1}|_{r=r_{Q_2} [/math]

I have done some calculations using the empirical result from the website. I generally got this type of equation:

 

F = ax^2 + bx + c where F=Force between identical magnets & x=separation distance between identical magnets.

 

It can be inferred that for small separation distances F=bx + c and large separation distances F=ax^2.

 

Is this above reasoning logical. It is based on empirical evidence.

 

Should it be F=ax^4 + bx^3 + cx^2 + dx + e ?