This Instructabler describes how to make a scientific investigation to determine how magnetic field varies with distance. Two methods are presented , and reasonable conclusions made.
Note that the magnet used in this Instructable is a thin disk type, not a bar magnet.
Tools and equipment:
One rare earth neodymium magnet, 16mm diameter x 3mm.
Precise scale measuring to 0.1 gram
Balance beam apparatus to allow measuring magnetic attraction
Tape measure (non magnetic)
Many phenomena of nature, like light, obey the inverse square law. That means as you get farther away from the source of light, the intensity decreases as the square of the distance. The inverse square law applies to light, gravity, and electrostatic charge. And the equation is simple and beautiful: basically it is I = 1/d2 , where d is distance (or I = 1/r2 in the photo, where r is distance) and I is intensity.
It is often assumed that the strength of a magnetic field also obeys the inverse square law. Researching the Internet produces many complex equations, most indicating that magnet field varies inversely with the third power of distance, in other words an inverse cube law.
Since it all seemed vague, or at best theoretical, I decided to test for myself.