Magnetic field variation with distance

[dfx]

First of all I have put in ALOT of research into this and I do realize there is no standard formula for the variation of B with the distance because the configuration/polarities and so on tend to get complicated.

However, part of my investigation involves measuring the variation of the magnetic field with the distance. The values I have got so far tend to indicate no standard relationship and I get really ugly functions like:

$$f(x) = 53.491265*0.48728247^x and f(x) = 85.849644*0.28785481^x$$

showing the magnetic field as function of distance, x for 2 separate magnets.

The initial values, 53... and 85... are $$B_0$$ which is the magnetic field at the surface (distance 0).

The graph digitally plotted seems to intersect through only 2 out of 5 points (it JUST shaves the error bars of some other points).

I am tempted to say the relationship holds for my magnets. While I do realize in physics what you observe is true, are such almost random relationship possible? Would my data be viable? Can you advise any other way of establishing the relationship?

PLEASE HELP! Advice/feedback much appreciated. :)

 

[haruspex]

Basing a formula purely on data is hard to justify. You can have little confidence what happens beyond the range you tested. In this case, you can calculate from theory what the asymptotic behaviour must be and check that your formula behaves the same way. (It doesn't.)